NetworkX.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In questa lezione iniziamo a manipolare alcuni grafi attraverso il package __NetworkX__ (https://networkx.github.io/)<br>\n",
    "Il package NetworkX è parte della distribuzione Anaconda, quindi può essere importato attraverso la parola riservata __import__, che abbiamo introdotto nel precedente Jupyter notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La parola riservata __as__ viene utilizzata per rinominare il package. In questo caso risparmio solo caratteri, in altri casi posso utilizzare l'alias per evitare _name conflict_."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creare un grafo\n",
    "Iniziamo creando un grafo vuoto. In particolare creeremo un grafo non orientato.\n",
    "\n",
    "I grafi non orientati vengono modellati dalla classe __Graph__. Questa classe utilizza una struttura di tipo dictionary di dictionary di dictionary per memorizzare i nodi, gli archi e gli attributi relativi.\n",
    "<img src=\"figures/Graph_internal.JPG\">\n",
    "Il dictionary più esterno utilizza come chiave i nodi. Più precisamente l'insieme dei nodi può essere rappresentato da una qualsiasi struttura dict-like (stesso comportamento di un dictionary). Per questo motivo i nodi possono essere  qualsiasi oggetto _hashable_.<br>\n",
    "\n",
    "Per __creare un grafo__ invoco il costruttore..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato = nx.Graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una grafo può essere generato in modi diversi: dall'aggiunta/rimozione di ogni singolo nodo/arco alla lettura da file, passando per la generazione di grafi casuali. NetworkX supporta tutti questi processi di creazione/evoluzione.\n",
    "\n",
    "In questa prima parte utilizzare i metodi per la creazione step-by-step.\n",
    "### Nodi\n",
    "Aggiungiamo un singolo nodo..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_node('A')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oppure possiamo inserire più nodi nello stesso momento passando un qualsiasi oggetto iterabile, anche un grafo stesso ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_nodes_from(['B','C'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esempio con un 'line' graph ...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "line_graph = nx.path_graph(4)\n",
    "grafo_non_orientato.add_nodes_from(line_graph.nodes()) #nodi 'semplici'\n",
    "grafo_non_orientato.add_node(line_graph) #nodo complesso e' un grafo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nella seconda istruzione viene creato un iteratore sull'insieme dei nodi del grafo *line_graph*, mentre nella terza istruzione viene inserito il grafo come nodo. In sintesi si possono creare grafi di grafi, etc...\n",
    "\n",
    "Il metodo __nodes()__ mi restituisce una NodeView, passabile come argomento del costruttore **list()**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView(('B', 'C', 0, 1, 2, 3, <networkx.classes.graph.Graph object at 0x000001BDD7272DD8>, 'A'))"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grafo_non_orientato.nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['B', 'C', 0, 1, 2, 3, <networkx.classes.graph.Graph at 0x1bdd7272dd8>, 'A']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(grafo_non_orientato.nodes())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Attributi del nodo\n",
    "Ad un nodo posso associare uno o più oggetti che lo caratterizzano = __attributi__. Gli attributi vengono memorizzati in una struttura dict-like.\n",
    "\n",
    "Posso assegnare un attributo ad un nodo al momento della creazione ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_node('D',name='James',drink='beer')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oppure posso modificare o inserire un nuovo attributo ad un nodo già inserito, utilizzando l'attributo __node__ dell'oggetto _Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.node['B']['name'] = 'Marco'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per iterare sui nodi e i relativi attributi utilizzo il metodo **nodes** "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B', {'name': 'Marco'}),\n",
       " ('C', {}),\n",
       " (0, {}),\n",
       " (1, {}),\n",
       " (2, {}),\n",
       " (3, {}),\n",
       " (<networkx.classes.graph.Graph at 0x1bdd7272dd8>, {}),\n",
       " ('A', {}),\n",
       " ('D', {'name': 'James', 'drink': 'beer'})]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(grafo_non_orientato.nodes(data=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'name': 'Marco'},\n",
       " {},\n",
       " {},\n",
       " {},\n",
       " {},\n",
       " {},\n",
       " {},\n",
       " {},\n",
       " {'name': 'James', 'drink': 'beer'}]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[e[1] for e in list(grafo_non_orientato.nodes(data=True))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beer\n",
      "{'name': 'James', 'drink': 'beer'}\n"
     ]
    }
   ],
   "source": [
    "print(grafo_non_orientato.node['D']['drink'])\n",
    "print(grafo_non_orientato.node['D'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.node['D']['place'] = 'Milano'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'name': 'James', 'drink': 'beer', 'place': 'Milano'}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grafo_non_orientato.node['D']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Archi\n",
    "Come per i nodi, posso inserire gli archi uno alla volta, specificandone gli estremi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_edge('A','B')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oppure passando una lista di coppie (__tuple__ in Python) o triplette. Le triplette vengono utilizzate per specificare gli attributi associati all'arco"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_edges_from([('B','C'),('C','D'),(line_graph,'D')])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il metodo __edges()__ restituisce una lista di tuple rappresentati gli archi nel grafo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B', 'A'),\n",
       " ('B', 'C'),\n",
       " ('C', 'D'),\n",
       " (<networkx.classes.graph.Graph at 0x1bdd7272dd8>, 'D')]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(grafo_non_orientato.edges())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Attributi\n",
    "Anche agli archi posso associare degli attributi memorizzati come dictionary.\n",
    "\n",
    "Posso assegnare un attributo al momento della sua creazione ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_edge(0,1,peso=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "oppure si può modificare il dictionary __edges__ associato all'oggetto _Graph_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.edges['A','B']['peso'] = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "oppure in modo più conciso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato['C']['B']['peso'] = 40"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__N.B.__ Se gli estremi dell'arco che inserisco non sono presenti nella rete, NetworkX automaticamente aggiunge gli estremi all'insieme dei nodi.\n",
    "\n",
    "Per visualizzare gli archi e i relativi attributi utilizzo il metodo _edges()_ con il parametro __data=True__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B', 'A', {'peso': 3}),\n",
       " ('B', 'C', {'peso': 40}),\n",
       " ('C', 'D', {}),\n",
       " (0, 1, {'peso': 30}),\n",
       " (<networkx.classes.graph.Graph at 0x1bdd7272dd8>, 'D', {})]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(grafo_non_orientato.edges(data=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.edges['A','B']['peso'] = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('B', 'A', {'peso': None}),\n",
       " ('B', 'C', {'peso': 40}),\n",
       " ('C', 'D', {}),\n",
       " (0, 1, {}),\n",
       " (<networkx.classes.graph.Graph at 0x1bdd7272dd8>, 'D', {})]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(grafo_non_orientato.edges(data=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Rimozione archi e nodi\n",
    "Per rimuovere gli archi e i nodi posso applicare i seguenti metodi:\n",
    "* remove_node()\n",
    "* remove_nodes_from()\n",
    "* remove_edge()\n",
    "* remove_edges_from()\n",
    "\n",
    "che rappresentano la controparte dei metodi di inserimento visti in precedenza.\n",
    "\n",
    "Per cancellare tutti gli elementi si invoca il metodo __clear()__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizzare un grafo \n",
    "NetworkX fornisce dei metodi per visualizzare i grafi, tuttavia la visualizzazione è piuttosto semplice e limitata. Per questo motivo solo in questa lezione utilizzeremo i metodi di NetworkX, mentre nelle successive sfrutteremo dei tool specifici per la visualizzazione, quali Gephi\n",
    "\n",
    "### Visualizzazione con matplotlib\n",
    "__Matplotlib__ è la libreria più utilizzata per visualizzare grafici."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il metodo più semplice per la visualizzazione del grafo è __draw()__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(grafo_non_orientato)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__draw(G, pos=None, ax=None, hold=None, **kwds)__\n",
    "\n",
    "Draw the graph as a __simple representation with no node labels or edge labels__ and using the full Matplotlib figure area and no axis labels by default. See draw_networkx() for more full-featured drawing that allows title, axis labels etc.\n",
    "\n",
    "Parameters:\t\n",
    "__G__ (graph) – A networkx graph\n",
    "\n",
    "__pos__ (dictionary, optional) – A dictionary with nodes as keys and positions as values. If not specified a spring layout positioning will be computed. See networkx.layout for functions that compute node positions.\n",
    "\n",
    "ax (Matplotlib Axes object, optional) – Draw the graph in specified Matplotlib axes.\n",
    "\n",
    "hold (bool, optional) – Set the Matplotlib hold state. If True subsequent draw commands will be added to the current axes.\n",
    "\n",
    "kwds (optional keywords) – See networkx.draw_networkx() for a description of optional keywords."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E' possibile passare la posizione dei nodi attraverso il __parametro pos__. Tale opzione permette di utilizzare più algoritmi di visualizzazione. In particolare adotteremo il metodo **spring_layout** ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "posizione = nx.spring_layout(grafo_non_orientato)\n",
    "nx.draw(grafo_non_orientato, pos = posizione)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_non_orientato.add_edge('A','D')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gli altri metodi supportati sono:\n",
    "* circular_layout\n",
    "* fruchterman_reingold_layout\n",
    "* random_layout\n",
    "* shell_layout\n",
    "* spectral_layout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una visualizzazione più piacevole e più informativa si può ottenere utilizzando il metodo **draw_networkx()** (https://networkx.readthedocs.io/en/stable/reference/generated/networkx.drawing.nx_pylab.draw_networkx.html#networkx.drawing.nx_pylab.draw_networkx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posizione_circular = nx.circular_layout(grafo_non_orientato)\n",
    "nx.draw_networkx(grafo_non_orientato, pos= posizione_circular, node_size=20, alpha=0.5, node_color='blue')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Leggere un grafo da file\n",
    "Esistono molti formati per memorizzare un network e gli attributi relativi ai suoi elementi. In particolare ci soffermeremo sulle liste di adiacienza, le liste di archi, GEXF e gpickle.\n",
    "### Lista di adiacenza\n",
    "E' un formato adatto a network senza attributi associati a nodi o archi, dove i nodi sono facilmente rappresentabili come stringhe.\n",
    "\n",
    "Il formato del file di testo prevede che ogni riga corrisponda ad un nodo, indicato dal primo elemento della linea. I suoi vicini costituiscono gli altri elementi della linea, separati da un carattere di separazione.\n",
    "\n",
    "Per la creazione del grafo dato un file testuale che contiene una lista di adiacienza, possiamo utilizzare i metodi visti precedentemente e nella lezione 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "adj_graph = nx.Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1,2,3,4\\n', '2,3,1\\n', '3,6,2,1\\n', '4,5,1\\n', '5,6,4\\n', '6,5']\n",
      "['1', '2', '3', '4']\n",
      "['2', '3', '1']\n",
      "['3', '6', '2', '1']\n",
      "['4', '5', '1']\n",
      "['5', '6', '4']\n",
      "['6', '5']\n",
      "[('1', '2'), ('1', '3'), ('1', '4'), ('2', '3'), ('3', '6'), ('4', '5'), ('6', '5')]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = open('data/grafo_lista_adiacienza.txt')\n",
    "lista_righe = f.readlines()\n",
    "print(lista_righe)\n",
    "for line in lista_righe:\n",
    "    info = line.strip().split(',')\n",
    "    print(info)\n",
    "    for e in info[1:]:\n",
    "        adj_graph.add_edge(info[0],e)\n",
    "print(list(adj_graph.edges()))\n",
    "nx.draw_networkx(adj_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NetworkX fornisce un metodo per la lettura di questo formato:\n",
    "\n",
    "**read_adjlist(path, comments='#', delimiter=None, create_using=None, nodetype=None, encoding='utf-8')**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "adj_graph = nx.read_adjlist('data/grafo_lista_adiacienza.txt',\n",
    "                            delimiter=',',nodetype=int,\n",
    "                            create_using=nx.Graph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView((1, 2, 3, 4, 6, 5))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "adj_graph.nodes()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lista degli archi, o meglio edge list\n",
    "Questo formato prevede che ogni riga corrisponda ad un arco del grafo. Anche in questo caso utilizzo questo formato quando le informazioni circa il grafo sono facilmente rappresentabili attraverso stringhe. \n",
    "\n",
    "Non posso memorizzare informazioni riguardanti i nodi.\n",
    "\n",
    "Se non prevedo attributi ogni riga segue il formato:<br>\n",
    "_1 2_<br>\n",
    "altrimenti gli attributi possono essere rappresentati come Python dictionary:\n",
    "\n",
    "_1 2 {'peso':30,'colore':'verde'}_\n",
    "\n",
    "oppure posso inserire solo i valori degli attributi senza specificarne il nome\n",
    "\n",
    "_1 2 30 verde_\n",
    "\n",
    "Per leggere una edge list, NetworkX fornisce il metodo\n",
    "\n",
    "**read_edgelist(path, comments='#', delimiter=None, create_using=None, nodetype=None, data=True, edgetype=None, encoding='utf-8')**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "edgelist_graph = nx.read_edgelist('data/grafo_edge_list.txt',\n",
    "                                  delimiter=' ', \n",
    "                                  create_using=nx.Graph(),\n",
    "                                  nodetype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_networkx(edgelist_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GEXF\n",
    "GEXF (Graph Exchange XML Format) è un formato XML per la descrizione di network statiche e dinamiche e dei relativi attributi. Non ci soffermeremo sulle specifiche e lo schema del formato. \n",
    "\n",
    "Gephi,  software di visualizzazione, utilizza principalemente questo formato. Specificamente, una volta creato il grafo, lo salveremo nel formato GEXF e lo apriremo con Gephi per visualizzarlo (specialmente con reti di medie/grandi dimensioni).\n",
    "\n",
    "Per salvare il grafo nel formato GEXF, NetworkX fornisce il metodo:\n",
    "\n",
    "**write_gexf(G, path, encoding='utf-8', prettyprint=True, version='1.1draft')**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.write_gexf(edgelist_graph,'data/edgeList4Gephi.gexf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### JSON\n",
    "NetworkX permette di salvare il grafo nel formato JSON. Questa funzionalità è molto utile per un utilizzo combinato con d3.js (http://d3js.org/), una libreria  Python per la visualizzazione di grafici.\n",
    "\n",
    "Il metodo **node_link_data** restituisce un dictionary che può essere esportato in JSON utilizzando il package json"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import json\n",
    "from networkx.readwrite import json_graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'directed': False, 'multigraph': False, 'graph': {}, 'nodes': [{'id': 1}, {'id': 2}, {'id': 3}, {'id': 4}, {'id': 6}, {'id': 5}], 'links': [{'source': 1, 'target': 2}, {'source': 1, 'target': 3}, {'source': 1, 'target': 4}, {'source': 2, 'target': 3}, {'source': 3, 'target': 6}, {'source': 4, 'target': 5}, {'source': 6, 'target': 5}]}\n"
     ]
    }
   ],
   "source": [
    "graph_json = json_graph.node_link_data(adj_graph)\n",
    "print(graph_json)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "json.dump(graph_json,open('data/graph_json.json','w'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pickle\n",
    "Il formato pickle è utilizzato da Python per la serializzazione degli oggetti. Per leggere/scrivere un grafo in formato pickle si utilizzano i seguenti metodi ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.write_gpickle(adj_graph,'data/test_graph.pkl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_reload = nx.read_gpickle('../)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network Repository\n",
    "Finora abbiamo creato i nostri piccoli grafi, tuttavia possiamo sfruttare la presenza di molti repository. __Network Repository__ è tra i più completi (http://networkrepository.com/).\n",
    "\n",
    "Le collezioni di dataset sono categorizzate secondo il tipo di dato. Oltre alle reti sociali (online e offline) ci sono reti biologiche, brain network, reti infrastrutturali, reti tecnologiche e grafi risultanti da crawling massivi.\n",
    "\n",
    "### 1. Ricerca di una rete\n",
    "Attraverso la funzione di ricerca possiamo cercare una network inviando una stringa di query. Nel caso delle online social network è sufficiente specificarne il nome: facebook, twitter, orkut, etc ..\n",
    "\n",
    "Iniziamo la nostra analisi da una rete piccola, ma significativa: Zachary's Karate Club. Come parole chiave utilizziamo __karate__.\n",
    "\n",
    "La pagina relativa alla network ci fornisce la sua descrizione, la sua visualizzazione (qualora la rete sia piccola), una serie di proprietà e alcune distribuzioni.\n",
    "<img src=\"figures/netrepo_karate.png\">\n",
    "\n",
    "Procediamo scaricando il file 'karate.zip'. Il grafo è contenuto nel file 'karate.mtx' che possiamo aprire con un qualsiasi editor testuale.\n",
    "\n",
    "Di seguito sono state riportate le prime righe del file.<br>\n",
    "\n",
    "%%MatrixMarket matrix coordinate pattern symmetric<br>\n",
    "34 34 78<br>\n",
    "2 1<br>\n",
    "3 1<br>\n",
    "4 1<br>\n",
    "5 1<br>\n",
    "6 1<br>\n",
    "7 1<br>\n",
    "8 1<br>\n",
    "9 1<br>\n",
    "11 1\n",
    "\n",
    "Le prime due righe contengono metadati, quindi si possono saltare. Le righe rimanenti seguono il formato edge list. In questo caso dobbiamo __caricare il grafo leggendo il file testuale riga per riga__.\n",
    "\n",
    "### 2.Caricamento del grafo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "karate_graph = nx.Graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Scrivere il codice per il caricamento del grafo utilizzando il file 'karate.mtx'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/karate.mtx') as f:\n",
    "    f.readline()\n",
    "    f.readline()\n",
    "    for line in f:\n",
    "        source, destination = line.strip().split(' ')\n",
    "        karate_graph.add_edge(source,destination)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In questo caso apro e chiudo esplicitamente l'oggetto file.\n",
    "\n",
    "Per verificare il corretto caricamento del grafo, contiamo il __numero dei nodi e degli archi__ utilizzando i metodi **order()** e **size()**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Numero di nodi: 34 - numero di archi:78'"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'Numero di nodi: {} - numero di archi:{}'.format(karate_graph.order(),karate_graph.size())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Visualizzare la rete dello Zachary Club"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\matte\\Anaconda3\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "posizione = nx.spring_layout(karate_graph)\n",
    "nx.draw_networkx(karate_graph,pos=posizione,\n",
    "                alpha=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analisi del grado\n",
    "Una volta caricato il grafo in memoria una delle proprietà che solitamente si analizzano è la __distribuzione del grado__, una delle misure di centralità in una network. Dal momento che il karate graph non è orientato, per ora non distinguiamo tra grado in ingresso (in-degree) e grado in uscita (out-degree).\n",
    "\n",
    "In NetworkX il metodo __degree()__ calcola il grado di ogni nodo. Passando la vista al costruttore dict() ottengo un dictionary con chiave id del nodo e valore il grado del corrispettivo nodo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'2': 9,\n",
       " '1': 16,\n",
       " '3': 10,\n",
       " '4': 6,\n",
       " '5': 3,\n",
       " '6': 4,\n",
       " '7': 4,\n",
       " '8': 4,\n",
       " '9': 5,\n",
       " '11': 3,\n",
       " '12': 1,\n",
       " '13': 2,\n",
       " '14': 5,\n",
       " '18': 2,\n",
       " '20': 3,\n",
       " '22': 2,\n",
       " '32': 6,\n",
       " '31': 4,\n",
       " '10': 2,\n",
       " '28': 4,\n",
       " '29': 3,\n",
       " '33': 12,\n",
       " '17': 2,\n",
       " '34': 17,\n",
       " '15': 2,\n",
       " '16': 2,\n",
       " '19': 2,\n",
       " '21': 2,\n",
       " '23': 2,\n",
       " '26': 3,\n",
       " '24': 5,\n",
       " '30': 4,\n",
       " '25': 3,\n",
       " '27': 2}"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict(karate_graph.degree())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per farmi restuire il grado di un singolo nodo ho le seguenti opzioni ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "karate_graph.degree()['34']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "karate_graph.degree('34')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(list(karate_graph.neighbors('34')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il secondo metodo mi permette di ottenere il grado data un lista di nodi. Ciò è molto utile per ottenere il grado di un sottoinsieme di nodi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'34': 17, '22': 2, '1': 16, '10': 2}"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict(karate_graph.degree(['34','22','1','10']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Si scarichi il grafo dei retweet pubblicato all'indirizzo http://networkrepository.com/rt-pol.php. I nodi sono gli utenti di Twitter ed esiste un link tra due utenti solo se uno dei due ha retweetato uno status(tweet) dell'altro.\n",
    "\n",
    "Caricare in memoria la rete scaricata (attenzione ai campi di ogni riga) e rispondere alle seguenti domande:\n",
    "\n",
    "- Quanti nodi ci sono nella rete? \n",
    "- Quanti archi?\n",
    "- Qual è l'id del nodo con grado massimo?\n",
    "\n",
    "Per estrarre il nodo di grado massimo posso ordinare i valori del dictionary del grado e cercare il primo nodo il cui grado corrisponde al grado massimo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numero di nodi: 18470\n",
      "Numero di archi: 48053\n"
     ]
    }
   ],
   "source": [
    "twitter = nx.Graph()\n",
    "with open('data/rt-pol.txt') as f:\n",
    "    for line in f:\n",
    "        source, destination, _ = list(map(int,line.strip().split(',')))\n",
    "        twitter.add_edge(source, destination)\n",
    "print('Numero di nodi: {}'.format(twitter.order()))\n",
    "print('Numero di archi: {}'.format(twitter.size()))\n",
    "user_max_twitter = sorted(dict(twitter.degree()).items(),key= lambda x:x[1], reverse=True)[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vicini di un nodo\n",
    "Per ottenere i vicini di un nodo _n_ posso utilizzare due metodi:\n",
    "1. Accedere al dictionary associato alla chiave _n_ dell'oggetto **Graph.adj**: G.adj()[n]\n",
    "2. Utilizzare una sintassi più concisa: G[n]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11', '17', '7', '1'}\n",
      "{'11', '17', '7', '1'}\n"
     ]
    }
   ],
   "source": [
    "print(set(karate_graph.adj['6'].keys()))\n",
    "print(set(karate_graph['6'].keys()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Estrarre i vicini del nodo con grado massimo nel grafo di  Twitter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
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       " 17112,\n",
       " 17130,\n",
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       " 18288,\n",
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       " 18378,\n",
       " 18393,\n",
       " 18420,\n",
       " 18429,\n",
       " 18437,\n",
       " 18439}"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(twitter[user_max_twitter].keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistiche puntuali\n",
    "Una volta ottenuto il campione (lista dei gradi) posso calcolare alcune statistiche:\n",
    "* il grado medio\n",
    "* il grado massimo\n",
    "* il grado minimo\n",
    "* la mediana del campione\n",
    "* la moda del campione\n",
    "\n",
    "Per calcolare queste statistiche introduciamo due librerie per il calcolo scientifico: __numpy__ e __scipy__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as sp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grado medio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "campione_grado_karate = list(dict(karate_graph.degree()).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.588235294117647"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(campione_grado_karate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "oppure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.588235294117647"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(campione_grado_karate)/karate_graph.order()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grado massimo e minimo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "17\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "print(np.max(campione_grado_karate))\n",
    "print(np.min(campione_grado_karate))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### moda e mediana"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.0\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "print(np.median(campione_grado_karate)) # mediana\n",
    "print(sp.mode(campione_grado_karate).mode[0]) # moda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## La distribuzione del grado - PDF/CDF/CCDF\n",
    "Dato il nostro campione il primo passo nella costruzione della varie funzioni che descrivono la distribuzione è contare quante volte un elemento occorre.\n",
    "\n",
    "In questo caso possiamo utilizzare il metodo __histogram__ di numpy.\n",
    "\n",
    "Vediamo un esempio del suo funzionamento ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = [random.randint(1,10) for i in range(1000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per avere un'idea del contenuto di test utilizzo lo slicing per estrarre una sottolista. __list[start:end]__ indica che voglio la sottolista che inizia all'indice _start_ incluso e termina all'indice _end_ escluso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[6, 3, 3, 6, 7, 4, 8, 2, 10, 3]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'interfaccia del metodo histogram è la seguente:\n",
    "\n",
    "**numpy.histogram(a, bins=10, range=None, normed=False, weights=None, density=None)**\n",
    "\n",
    "L'unico parametro che ci interessa è __bins__, il quale accetta:\n",
    "1. un intero\n",
    "2. una lista di float\n",
    "3. una stringa (non ci interessa)\n",
    "\n",
    "Il parametro è propedeutico alla computazione di intervalli consecutivi:\n",
    "<img src=\"figures/intervalli.jpg\">\n",
    "\n",
    "Nel nostro caso utilizzeremo una lista di numeri.\n",
    "\n",
    "Come primo passo estraiamo max e min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 10)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_t = min(test)\n",
    "max_t = max(test)\n",
    "min_t, max_t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creo una lista con gli estremi degli intervalli. Nel nostro caso ogni intervallo ha lunghezza 1. Utilizzo il metodo __arange__ di numpy la cui semantica è uguale al metodo __range__ visto nelle lezione precedente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(min_t,max_t+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora eseguiamo il conteggio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "counts, bins = np.histogram(test, bins=np.arange(min_t,max_t+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10]\n",
      "[ 99  99  84  99  98 102 102 110 207]\n"
     ]
    }
   ],
   "source": [
    "print(bins)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La lunghezza di count è 9. C'è un errore !! I conteggi dei 9 e dei 10 vengono aggregati.\n",
    "\n",
    "Gli intervalli sono chiusi a sinistra e aperti a destra: [a,b) <=> a<= x < b, ad eccezione dell'ultimo intervallo che è chiuso su entrambi gli estremi. Nel nostro caso l'ultimo intervallo sarà [9,10] => vengono conteggiati sia i 9 che i 10. Per ovviare al problema basta estendere l'intervallo di un'altra unità."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "counts, bins = np.histogram(test, bins=np.arange(min_t,max_t+2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10 11]\n",
      "[ 99  99  84  99  98 102 102 110 108  99]\n"
     ]
    }
   ],
   "source": [
    "print(bins)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora possiamo calcolare la PDF, i.e.\n",
    "\\begin{equation*}\n",
    "P(K = k) = \\frac{count(k)}{N}\n",
    "\\end{equation*}\n",
    "dove $N$ è il numero di elementi del campione."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.099, 0.099, 0.084, 0.099, 0.098, 0.102, 0.102, 0.11 , 0.108,\n",
       "       0.099])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdf = counts / len(test)\n",
    "pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: come possiamo verificare che pdf sia veramente una distribuzione di probabilità?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(([e for e in pdf if not (e >= 0 and e<=1)]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora possiamo applicare lo stesso procedimento al campione con i gradi dei nodi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "min_k = min(campione_grado_karate)\n",
    "max_k = max(campione_grado_karate)\n",
    "count_karate, bins_karate = np.histogram(campione_grado_karate,\n",
    "                                        bins = np.arange(min_k,max_k+2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 1,\n",
       " 2: 11,\n",
       " 3: 6,\n",
       " 4: 6,\n",
       " 5: 3,\n",
       " 6: 2,\n",
       " 7: 0,\n",
       " 8: 0,\n",
       " 9: 1,\n",
       " 10: 1,\n",
       " 11: 0,\n",
       " 12: 1,\n",
       " 13: 0,\n",
       " 14: 0,\n",
       " 15: 0,\n",
       " 16: 1,\n",
       " 17: 1}"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dict(zip(bins_karate,count_karate))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02941176 0.32352941 0.17647059 0.17647059 0.08823529 0.05882353\n",
      " 0.         0.         0.02941176 0.02941176 0.         0.02941176\n",
      " 0.         0.         0.         0.02941176 0.02941176]\n"
     ]
    }
   ],
   "source": [
    "pdf_karate = count_karate / karate_graph.order()\n",
    "print(pdf_karate)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Visualizzazione della PDF\n",
    "Utilizzando matplotlib possiamo visualizzare la PDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF')"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "assi = fig.gca()\n",
    "assi.plot(bins_karate[:-1],pdf_karate, color='orange',marker='o', linestyle='--', ms=16)\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('PDF',size=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calcolo della PDF in We Heart It"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph loading from db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sqlite3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "database = sqlite3.connect('whispider/link_db')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "whi_graph = nx.DiGraph()\n",
    "for e in database.execute('select * from links;'):\n",
    "    whi_graph.add_edge(e[0],e[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(61686, 92472)"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whi_graph.order(), whi_graph.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribuzione del grado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "campione_gradi_whi = list(dict(whi_graph.degree()).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 847)"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_whi = min(campione_gradi_whi)\n",
    "max_whi = max(campione_gradi_whi)\n",
    "min_whi, max_whi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "count_whi, bin_whi = np.histogram(campione_gradi_whi, bins = np.arange(min_whi,max_whi+2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf_whi = count_whi/ whi_graph.order()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(pdf_whi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizzazione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF')"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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z31VV26rqo9Pb9/WRc1n93b9L/uYH+k4BAAAwajNxKXVVrUpyeZKXJtmaZGNVbWit3bDH0De31i5b8YCdsio1AABAl2Zlxvi8JJtba1taazuTXJnkop4zdc+q1AAAAJ2blWK8Lslti463Th/b0zdX1XVV9baqOnVlonXNjDEAAECXZqUYLzV1umdjfGeSM1prX5Xk3Un+YMkTVV1aVZuqatO2bduWOeZyM2MMAADQtZn4jHEmM8SLZ4BPSXLH4gGttbsWHf63JL+y1Ilaa1ckuSJJ1q9fP+zp2Gf9TPLIjr5TAAAAjNqsFOONSc6qqjOT3J7kkiSvXjygqp7cWrtzenhhkhtXNmIHTnpe3wkAAABGbyaKcWttoaouS3J1klVJfr+1dn1VvTbJptbahiQ/XFUXJllIcneS7+ot8HK5a2OysD154ov6TgIAADBa1dqwrybu0vr169umTZv6jrF3H7g4eWBz8vLr+k4CAAAwc6rqmtba+v2Nm5XFt+bXHP/iAgAAYCUoxkNmH2MAAIDOKcaDZ8YYAACgS4rxoJkxBgAA6NpMrEo9t875+eSRB/tOAQAAMGqK8ZCd8JV9JwAAABg9l1IP2ec+mGx9Z98pAAAARk0xHrJP/Jfkoz/VdwoAAIBRU4wHz6rUAAAAXVKMB82q1AAAAF1TjIeumTEGAADokmI8ZGXGGAAAoGu2axqyr/6lZME+xgAAAF1SjIfsmDP7TgAAADB6LqUess+8N/nUm/pOAQAAMGqK8ZBt+f3kun/fdwoAAIBRU4wHz6rUAAAAXVKMB82q1AAAAF1TjIfOPsYAAACdUowHzYwxAABA12zXNGTP+dXkkR19pwAAABg1xXjIjnxS3wkAAABGz6XUQ3bHXySbr+g7BQAAwKgdcDGuqr+tqmuq6oVdBmKRT785+dgv9p0CAABg1A5mxvjZ09vxextQVVuq6paqesljTkZSFt8CAADo2nJ/xviMJC3JUct83jlmuyYAAIAu+YzxoFUUYwAAgG4pxoPmUmoAAICu2a5pyM799eSRL/adAgAAYNQU4yE74oS+EwAAAIyeS6mHbOuG5MZf6zsFAADAqCnGQ3b7O5OPv67vFAAAAKN2KJdSP6uq7l2GMUmS1toHDiHDHLEqNQAAQJcOpRj/wj6eawcwZs/xPue8V1alBgAA6NqhlFJtbSU1M8YAAABdOphi/IG4rndlld9BAAAAdO2Ai3Fr7UUd5mApz/3Pybm/0XcKAACAUfP53iFbtabvBAAAAKNnu6Yhu/WPk+t+tu8UAAAAo6YYD9ln35Pc/Dt9pwAAABi1ZbmUuqqelOR5SdYmOSmTRbruTrItycbW2meW43Xmk/XOAAAAunTIxbiqjk5yWZLvSfL0/Yy9Ocnrk/x2a237ob7m/LEqNQAAQNcO6VLqqnpRkk8m+aVMSnHt53ZWkl9JcktVvfAxp54rZowBAAC6dNAzxlV1UZI3Jzk8j05ptiSfSPKpJPdkUrhPSHJGJqV497iTk1xdVd/WWtvwWILPBzPGAAAAXavWDnxGsqqenORjSR4/feiWJL+e5MrW2r17+Z4Tkrw6yY8leer04buTnNNau/MQcy+L9evXt02bNvUZAQAAgI5U1TWttfX7G3ewl1L/YialuCV5W5Kvbq39zt5KcZK01u5trf1Wkq9K8sfThx+f5D8c5GsDAADAsjvgYlxVxyX5tkxK8d8keXVr7cED/f7p2Fcn2ZjJNcLfXlXHHsTrX1BVN1XV5qp6zT7GfUtVtara728FBu9TVyabfqTvFAAAAKN2MDPGFyY5anr/J1prCwf7Yq21hzO5pDpJjpyec7+qalWSy5O8LMnZSV5VVWcvMe7YJD+c5CMHm22QPv+h5JN/2HcKAACAUTuYYrx7BvbG1tr/OdQXnH7vDdPD8w7w285Lsrm1tqW1tjPJlUkuWmLcLyT51SQPHWq+4bEqNQAAQJcOphifm0lL++AyvO4HM7mc+jkHOH5dktsWHW+dPvYlVfWcJKe21v5sGfINQ1mVGgAAoGsHU4x3F9GPLcPr7j7HKQc4fqmG+KWp1Ko6LMnrkvz4fk9UdWlVbaqqTdu2bTvAl++TGWMAAIAuHUwxPm76da8rUB+Ee/Y45/5sTXLqouNTktyx6PjYJM9K8v6q+lSSFyTZsNQCXK21K1pr61tr69euXXvQwVfUqiOT1cf0nQIAAGDUDqYYHz/9+oVleN0Hpl8PdFXqjUnOqqozq+qIJJck2bD7ydbafa21J7TWzmitnZHkw0kubK3N9ibFz/6PyStv7zsFAADAqB1MMV7dwesf0DmnK2BfluTqJDcmeUtr7fqqem1VHdDK1gAAALCULspuJ1prVyW5ao/HfnYvY1+0Epk698n/mXzm3cnXvKHvJAAAAKN1KMX45Ko67TG+7smP8fvnwz0fTW57m2IMAADQoUMpxr+77CnYu2ZVagAAgC4dSjG2ue5KsY8xAABA5w6mGN8am+r2wD9yAACALh1wMZ5ug8RKOvz45Mgn950CAABg1A5muyZW2rN+Jrnwlr5TAAAAjJpiDAAAwFx7TMW4qtZU1ZOq6qjlCsQiW96QfOCVfacAAAAYtYMuxlV1QlX9x6q6Ocn2JLcnub+qbqmqX66qk5Y95bz6wseTO67qOwUAAMCoHVQxrqqzklyb5KeSPDWTrZt2385I8pNJrq2qZy5vzHlluyYAAICuHXAxrqrVSd6W5PTdD+05ZHo7Jclbq+rwZUk492zXBAAA0KWDmTH+5iTnZNLU7kpyaZJ1SY6Yfv2XSbZNx56d5FuXL+a8qqQpxgAAAF06mGJ88fTrjiQvbK29vrV2Z2ttYfr1vyV5YZIHp+OsGvVYrVmbHHtW3ykAAABG7WCK8bmZzBa/sbV241IDWmsfT/LGTC6pfs5jjzfnnvmjyStu6DsFAADAqB1MMX7i9Otf72fc7udPPvg4AAAAsLIOphgfM/16z37G3Tv9evTBx+EfuOX3knd/fd8pAAAARu2g9zFmBT3wqeRzf9l3CgAAgFFTjIes7GMMAADQtUMpxvYPWlH+cQMAAHRp9SF8z5/Ugc1kVlU9sp8xrbV2KBnmhBljAACArh1qKd1XY2t5dJpTs3ssjlqXnPjcpDWXVQMAAHTkYC+lruy/7NYBjmN/nn5pcsEmpRgAAKBDBzxj3FqzUBcAAACjo+wO2eYrkr84N2m7+k4CAAAwWorxkO34THLPtX2nAAAAGDXFeBY0WzYBAAB0RTEetN2LbinGAAAAXVGMh8xq1AAAAJ1TjIfs6NOTk1/UdwoAAIBRO+DtmujBmf9icgMAAKAzZowBAACYa4rxkN38O8mGs5JHdvadBAAAYLQU4yHbeU/ywOYku/pOAgAAMFqK8aBZlRoAAKBrivEsaPYxBgAA6IpiPGT2MQYAAOicYjxkxzw9WffPkvKvCQAAoCv2MR6y0755cgMAAKAzpiIBAACYa4rxkN3828nbn5QsbO87CQAAwGgpxkO2sD156LNJs48xAABAVxTjQbMqNQAAQNcU45lgH2MAAICuKMaDZsYYAACga4rxkB33zOT0VydlVy0AAICuzEwxrqoLquqmqtpcVa9Z4vkfqKq/r6qPVtUHq+rsPnIuq3UvT77ujcnqo/pOAgAAMFozUYyralWSy5O8LMnZSV61RPH9o9baOa21Zyf51SS/scIxAQAAmEEzUYyTnJdkc2ttS2ttZ5Irk1y0eEBr7QuLDo/OGFas+sTlyVuOSXbe23cSAACA0ZqVD6+uS3LbouOtSZ6/56Cq+sEkP5bkiCTnr0y0Du16eLKX8Qg6PgAAwFDNyozxUsszf1lbbK1d3lp7WpJ/k+RnljxR1aVVtamqNm3btm2ZYy636R+7KcYAAABdmZVivDXJqYuOT0lyxz7GX5nkm5Z6orV2RWttfWtt/dq1a5cxYgfKdk0AAABdm5VivDHJWVV1ZlUdkeSSJBsWD6iqsxYdfmOSm1cwX8fMGAMAAHRlJj5j3FpbqKrLklydZFWS32+tXV9Vr02yqbW2IcllVfWSJA8nuSfJd/aXeJmccE7y9H+ZHPa4vpMAAACMVrU5/vzq+vXr26ZNm/qOAQAAQAeq6prW2vr9jZuJGeO5tfiXFj5vDAAA0IlZ+YzxfLr5t5I3HZZ88fN9JwEAABgtxXgmzO/l7gAAAF1TjAfNPsYAAABdU4yHzOeKAQAAOqcYzwQzxgAAAF1RjIfshGcnz/zxZPVRfScBAAAYLds1Ddnar5ncAAAA6IwZ4yF7ZGfy8BeStqvvJAAAAKOlGA/ZJ9+QvPX4ZMdn+k4CAAAwWorxTLD4FgAAQFcU40GzXRMAAEDXFOOZYMYYAACgK4rxoJkxBgAA6JpiPGQnnpuc83PJ6mP7TgIAADBa9jEeshPPndwAAADojBnjIVvYnjx4e7Jroe8kAAAAo6UYD9mn35L8ySnJjtv7TgIAADBaivEsaFalBgAA6IpiPGRlVWoAAICuKcYzwYwxAABAVxTjQTNjDAAA0DXFeMhOXJ8859eTI07sOwkAAMBo2cd4yE74yskNAACAzpgxHrKd9yX3fTx5ZGffSQAAAEZLMR6y29+Z/PlXJA/e2ncSAACA0VKMZ4F9jAEAADqjGA+aVakBAAC6phjPBDPGAAAAXVGMh6zMGAMAAHRNMR6yk85LzrsiWXNy30kAAABGyz7GQ3bs0yc3AAAAOmPGeMi+eHdy16ZkYUffSQAAAEZLMR6yO9+VXP28ZPun+04CAAAwWorxTLAqNQAAQFcU4yH70qrUijEAAEBXFONBmxbjphgDAAB0RTEeMvsYAwAAdE4xHrKTnp987ZuSo07pOwkAAMBo2cd4yI4+bXIDAACgM2aMh+yhbcln35c8/EDfSQAAAEZLMR6yz30gec/5yfZP9p0EAABgtBTjWWBVagAAgM4oxkNmH2MAAIDOKcaDphgDAAB0TTEeNPsYAwAAdG1minFVXVBVN1XV5qp6zRLP/1hV3VBV11XVe6rq9D5yLqsnvCB54TuTo8/sOwkAAMBozUQxrqpVSS5P8rIkZyd5VVWdvcewa5Osb619VZK3JfnVlU3ZgSOflKx7RXLE8X0nAQAAGK2ZKMZJzkuyubW2pbW2M8mVSS5aPKC19r7W2oPTww8nOWWFMy6/HZ9Jtm5Idt7bdxIAAIDRmpVivC7JbYuOt04f25vvTfIXnSZaCXf9TfKBi5IHtvSdBAAAYLRW9x3gAC21CtWSSzVX1XckWZ/khXt5/tIklybJaaedtlz5OmZVagAAgK7Myozx1iSnLjo+Jckdew6qqpck+XdJLmytfXGpE7XWrmitrW+trV+7dm0nYZePVakBAAC6NivFeGOSs6rqzKo6IsklSTYsHlBVz0nyu5mU4s/1kLE7zYwxAABAV2aiGLfWFpJcluTqJDcmeUtr7fqqem1VXTgd9v8lOSbJW6vqo1W1YS+nmx1lxhgAAKBr1eZ4NnL9+vVt06ZNfcfYuy/eldz7seTEc5PDj+07DQAAwEypqmtaa+v3N25WFt+aT487KXnikmuIAQAAsExm4lLqufXgHckn35g89Pm+kwAAAIyWYjxk9/5d8qHvSB64pe8kAAAAo6UYz4T5/Rw4AABA1xTjQbMqNQAAQNcU41kwxyuHAwAAdE0xHjQzxgAAAF2zXdOQrf2a5IJrkmOf0XcSAACA0VKMh+zw45ITz+07BQAAwKi5lHrIHtya3Pw7yY47+04CAAAwWorxkH3h48nGf5Xcbx9jAACArijGM8Gq1AAAAF1RjAfNqtQAAABdU4xnghljAACArijGg2bGGAAAoGu2axqyJ7wgecUnkqPW9Z0EAABgtBTjIVt9VHLcWX2nAAAAGDWXUg/Z9tuSG39t8hUAAIBOKMZD9sAtybU/mTywue8kAAAAo6UYD5rFtwAAALqmGM+CZrsmAACArijGQ1a7Z4wVYwAAgK4oxoPmUmoAAICu2a5pyE56fvLKO5MjHt93EgAAgNFSjIds1RHJkU/qOwUAAMCouZR6yLbfmlz3/yb339J3EgAAgNFSjIfswduSj712sp8xAAAAnVCMB83iWwAAAF1TjGeBfYwBAAA6oxgPmn2MAQAAuqYYD1m5lBoAAKBrtmtecRMpAAAWXUlEQVQashOfl3zr/cmqNX0nAQAAGC3FeMgOW5UcdkzfKQAAAEbNpdRDtv3W5JofS+67oe8kAAAAo6UYD9mOzyQ3vS554FN9JwEAABgtxXgmWJUaAACgK4rxkFmVGgAAoHOK8UwwYwwAANAVxXjQpjPGTTEGAADoiu2ahuyk9cmrlWIAAIAumTEGAABgrinGQ7b91uQj35/c89G+kwAAAIyWYjxkX7wrueX1yfZP950EAABgtBTjWWDxLQAAgM4oxkNmH2MAAIDOKcYzwYwxAABAV2amGFfVBVV1U1VtrqrXLPH8P6mqv62qhar6lj4yLrtalaw+dvIVAACATszEPsZVtSrJ5UlemmRrko1VtaG1dsOiYbcm+a4kP7HyCTtywjnJt32h7xQAAACjNhPFOMl5STa31rYkSVVdmeSiJF8qxq21T02f29VHQAAAAGbTrFxKvS7JbYuOt04fG7fttyUfvCT5/If7TgIAADBas1KMl1qe+ZBWpKqqS6tqU1Vt2rZt22OM1bGH70tufXPy4Na+kwAAAIzWrBTjrUlOXXR8SpI7DuVErbUrWmvrW2vr165duyzhumdVagAAgK7MSjHemOSsqjqzqo5IckmSDT1nWgH2MQYAAOjaTBTj1tpCksuSXJ3kxiRvaa1dX1WvraoLk6SqnldVW5N8a5Lfrarr+0u8zJoZYwAAgK7MyqrUaa1dleSqPR772UX3N2ZyifV4HHZ4cuRTklVr+k4CAAAwWjNTjOfScc9IXnl73ykAAABGbSYupQYAAICuKMZD9uDW5P2vSD77l30nAQAAGC3FeMgWtid3/Hmy45B2pgIAAOAAKMYzwarUAAAAXVGMB226j7HtmgAAADqjGA9a9R0AAABg9GzXNGi7kiOfnNxxVVKVnHqxPY0BAACWmRnjobprY3L1C5KH708+/abkb/5l8vYnTx4HAABg2SjGQ7SwI3nvNyQP35ssPJCkTb4+fO/k8Uce6jshAADAaCjGQ7T1HUlbWPq5tpDc9vaVzQMAADBiivEQ3X/LZA/jpSxsTx7YsrJ5AAAARkwxHqJjn5asPnrp51YfnRzz1JXNAwAAMGKK8RCdenFSe1kwvFZPngcAAGBZKMZDtGpNcv67ksNPePSx1cdMjs9/ly2bAAAAlpF9jIfqpOclr7wjueqc5Pizk9MvsY8xAABABxTjIVt9ZHLh5r5TAAAAjJpLqQEAAJhrivHQfeCVybX/pu8UAAAAo+VS6qF74JYk1XcKAACA0TJjPHSrjkweebDvFAAAAKOlGA/dqqOSBcUYAACgK4rx0K06MnlkR98pAAAARstnjIfuxOcmD3227xQAAACjpRgP3Vf/Qt8JAAAARs2l1AAAAMw1xXjorv+l5M/P6TsFAADAaCnGQ/fw/cn9N/WdAgAAYLQU46FbdVSy6+Fk10LfSQAAAEZJMR661UdOvtqyCQAAoBOK8dCtOmrydeHBfnMAAACMlGI8dMeelZzyyqT8qwIAAOiCfYyH7skvndwAAADohGI8dAs7kq3vSO6/JTn2acmpFyer1vSdCgAAYDQU4yG7a2PynvOThQeSVLL66GTjDybnvys56XmHfl5lGwAA4EsU46Fa2JG89xumpThJ2qP33/sNycV3HlqZvWvj5PvbQrKwffnKNgAAwIyyotNQbX3HpLwupS0kt7394M+5u2w/fO+0ZE/L9sP3Th5/5KHHFBkAAGAWKcZDdf8tkxndpSxsTx7YcvDn7KJsAwAAzDjFeKiOfdrkMuelrD46OeapB3/OLso2AADAjFOMh+rUi5Pa20fAV02eP1hdlG0AAIAZpxgP1ao1kwWxVh2zxJO7knv//uDPua+yXasPrWwDAADMOMV4yI5/VnLYEkV24f5DWyxrd9k+/IRk9TGZbAF1zOT4/HfZsgkAAJhLivGQbX1HsuuLSz+364uHtljWSc9LXnlHctolyeHHJ0/6p8lzX5eccM5jywoAADCjFOMhu+/jySM7ln7ukR3JF246tPNe++PJltdPtmna+vZk0w8lb3/yZI9jAACAOaMYD9nOu/b9/E2/mXzg4mTLGw78suqFHcktr1/0wKK9jN/zUnsZAwAAc2dvyx4zBI97wr6ff/jeyeXWW9+RfPh7kmOfsfdVp3fbeXey6+Gln1u4L/njJyXHnJnUIfzOpA5Ljjo1ecoFk+Pb/1ey4/bkqHXJKRcmp1/ic8x0b2FH8uk3J3f8+eR43Td67wEAsE/VWus7wwGpqguS/Ockq5K8vrX2y3s8/7gkf5jkuUnuSvLtrbVP7euc69evb5s2beom8HL41B8lH/rupO3sO8nyWfPkZM0TD614L6XtSnbek+zamRx2RHLE45fv3F2ff5azd33+Qz33wvbk/puT7NrjifqHvziax382Qzj/LGfv+vyznL3r88s+zvPLPs7zz3L2rs8/xuy7J8UGPgFWVde01tbvd9wsFOOqWpXkE0lemmRrko1JXtVau2HRmP8nyVe11n6gqi5J8srW2rfv67yDL8aPPJS89fHJLpc3AwAAA7X62OTF75ks9DswB1qMZ+Uzxucl2dxa29Ja25nkyiQX7THmoiR/ML3/tiQvrqpawYzLb9Wa5Cv/bd8pAAAA9u5Qt5MdkFkpxuuS3LboeOv0sSXHtNYWktyX5KQVSdels38yWXVU3ykAAAD27pGHDm072YGYlWK81MzvnteAH8iYVNWlVbWpqjZt27ZtWcJ1atWa5Ouv7jsFAADA3u16KHlgS98pDtmsFOOtSU5ddHxKkjv2NqaqVic5Psnde56otXZFa219a2392rVrO4q7zE7+x8lLPpAc9ri+kwAAAHy5w9Ykxzy17xSHbFaK8cYkZ1XVmVV1RJJLkmzYY8yGJN85vf8tSd7bZmFlsQN18v+VfMs9yfP/e7LulcmxX5HZ+dcHAACM2qo1yakX953ikM3EPsattYWquizJ1Zls1/T7rbXrq+q1STa11jYk+b0k/6OqNmcyU3xJf4k7svrI5GnfNbklj+7XunVD8uBt+fItavZi8dLq6y5Kbn1rsvm/JTvuSA47PDnixORg1y3b6zY5AADAqK0+Njn/XYPdsulAzMR2TV0Z/HZNs2Z3Ub/jzyfH675x+Yr33nzZvmrLeO6uzz/L2bs+/2M59+5f/Dzlgsnx7f/ry39xNK//bPo+/yxn7/r8s5y96/PLPs7zyz7O889y9q7PP8bs9jEeD8UYAABgvMa2jzEAAAB0QjEGAABgrinGAAAAzDXFGAAAgLmmGAMAADDXFGMAAADmmmIMAADAXFOMAQAAmGuKMQAAAHNNMQYAAGCuKcYAAADMNcUYAACAuaYYAwAAMNcUYwAAAOaaYgwAAMBcU4wBAACYa9Va6ztDb6pqW5JP951jH56Q5PN9h4CeeP8zr7z3mWfe/8wz7/9unN5aW7u/QXNdjIeuqja11tb3nQP64P3PvPLeZ555/zPPvP/75VJqAAAA5ppiDAAAwFxTjIftir4DQI+8/5lX3vvMM+9/5pn3f498xhgAAIC5ZsYYAACAuaYYD1BVXVBVN1XV5qp6Td95YLlV1alV9b6qurGqrq+qH5k+fmJV/e+qunn69fHTx6uqfnP6d+K6qjq33z8BPHZVtaqqrq2qP5sen1lVH5m+/99cVUdMH3/c9Hjz9Pkz+swNj1VVnVBVb6uqj0//O/A1fv4zD6rqR6f/3/OxqnpTVa3xs384FOOBqapVSS5P8rIkZyd5VVWd3W8qWHYLSX68tfYVSV6Q5Aen7/PXJHlPa+2sJO+ZHieTvw9nTW+XJvntlY8My+5Hkty46PhXkrxu+v6/J8n3Th//3iT3tNaenuR103Ewy/5zkv/VWntmkq/O5O+Bn/+MWlWtS/LDSda31p6VZFWSS+Jn/2AoxsNzXpLNrbUtrbWdSa5MclHPmWBZtdbubK397fT+/Zn8T9G6TN7rfzAd9gdJvml6/6Ikf9gmPpzkhKp68grHhmVTVack+cYkr58eV5Lzk7xtOmTP9//uvxdvS/Li6XiYOVV1XJJ/kuT3kqS1trO1dm/8/Gc+rE5yZFWtTnJUkjvjZ/9gKMbDsy7JbYuOt04fg1GaXhr0nCQfSfLE1tqdyaQ8Jzl5OszfC8bmPyX5qSS7pscnJbm3tbYwPV78Hv/S+3/6/H3T8TCLnppkW5L/Pv0oweur6uj4+c/ItdZuT/JrSW7NpBDfl+Sa+Nk/GIrx8Cz1myBLhzNKVXVMkj9O8q9ba1/Y19AlHvP3gplUVa9I8rnW2jWLH15iaDuA52DWrE5ybpLfbq09J8n2PHrZ9FK8/xmF6efmL0pyZpKnJDk6k48K7MnP/p4oxsOzNcmpi45PSXJHT1mgM1V1eCal+I2ttbdPH/7s7kvkpl8/N33c3wvG5OuSXFhVn8rk4zLnZzKDfML08rrkH77Hv/T+nz5/fJK7VzIwLKOtSba21j4yPX5bJkXZz3/G7iVJPtla29ZaezjJ25N8bfzsHwzFeHg2JjlrukLdEZl8KH9Dz5lgWU0/I/N7SW5srf3Goqc2JPnO6f3vTPKnix7/v6erk74gyX27L7mDWdNa++nW2imttTMy+Rn/3tbaP0/yviTfMh225/t/99+Lb5mON2vATGqtfSbJbVX1j6YPvTjJDfHzn/G7NckLquqo6f8H7X7v+9k/EOWf7/BU1cszmT1YleT3W2u/2HMkWFZV9Y+T/FWSv8+jn7H8t5l8zvgtSU7L5D8g39pau3v6H5D/muSCJA8m+e7W2qYVDw7LrKpelOQnWmuvqKqnZjKDfGKSa5N8R2vti1W1Jsn/yOSz+HcnuaS1tqWvzPBYVdWzM1l47ogkW5J8dyaTNX7+M2pV9fNJvj2T3TmuTfJ9mXyW2M/+AVCMAQAAmGsupQYAAGCuKcYAAADMNcUYAACAuaYYAwAAMNcUYwAAAOaaYgwAHLKqelFVtent5/rOAwCHYnXfAQBgbKpqbZKLk7woybOTPCHJCZnsw3p3khuTXJPkT+3JCgD9U4wBYJlU1TFJfj7JDyQ5aokhx01vZyR5WZKfqapPJPkPSf6otfbICkUFABZRjAFgGVTV05P8SZKvXPTwdUnek+TmJHclWZPk5CTPzWQ2+UlJnpHkD5P8fZKPrlxiAGA3xRgAHqOqOinJu5OcPn3oY0kua6395T6+57AkFyX5qSQv6DwkALBXijEAPHZ/mEdL8f9J8rLW2v37+obW2q4k76iqP0nyg0l2dBsRANgbq1IDwGNQVV+b5OXTwy8kedX+SvFibeK/ttZuWuLcu1d7fv/0+PFV9dNVtbGqPj997g17fM9pVXVZVb21qm6qqgeqamdVfa6q3l9V/6aqjj+IP98/rqorq+r2qnqoqm6rqj+pqgsO9ByLznViVf37qvpQVW2b5rqzqt5dVT9UVWsO9pwAsBzMGAPAY/OvF93/vdbabV28SFWdm8lnmE/dx5gXJXlvklri6bVJXji9/XhVXdxa++B+XvMXk/z0Huc7ZXq7qKr+a5I/PsD8FyV5Qyarcy/2pOntxUl+oqq+qbV27YGcEwCWi2IMAIeoqiqTQrfb/+zopU5K8qeZFNKrkvx5ks8nWZekLRq3JpMSe32S92WyLdTuRb9OTfJNmSz8tTbJn1XVs1trn1rqBavqJ5P82+lhS/LmJP87k0u+vzrJ9yW5bJphn6rq5ZkU6FXThz6Q5G1JPpvJJej/Isk5SU5L8pdVdV5r7eP7Oy8ALJdqre1/FADwZarq7ExKaDLZo/j41trCMp5/8X+kH8nkMu237mP86UmOa639/T7GvCqTAn9Ykje01r57iTFPy+TP9bgkO5N8U2vtL/YY86RMyvczFz388621n9tj3LFJNmeyGneS/ERr7df3GLM6yW8l+f7pQ5taa8/b258BAJabzxgDwKF7yqL7ty5nKV7Cb+6rFCdJa+3T+yrF0zFvyqMz299eVYcvMeyHMinFSfJLe5bi6Xk+k+TbMyns+/LdebQUv2XPUjw910KSf5Xk76YPra+ql+znvACwbBRjADh0Jy26f+/+BlfVwqIFtfa8vX8/3/5fHlPSf+ivp1+PTPJVSzz/yunXh/f1uq2165K8az+vdfGi+7+yj3M9kuTX9vJ9ANApxRgAhu/21tonD3RwVT2/qv7LdPXqu6arP3+phCf5nUXDT9nje0/O5LO+SXJta+3u/bzce/aRo5LsviT68621v93Pua5edP/5+xkLAMvG4lsAcOjuWnR/z9WWl3Jx/uEvpU9O8rsH8H23H0iYqjoiyeszWczqQB23x/Hiy8M3H8D372vMcUmOmt6/eX8naq1tq6r7khyf5MkH8NoAsCwUYwA4dHcsun9aVa3e1+eMW2sbFh9X1RkH+Do7DnDc5Xm0FH8xkxWsN2ZSrLfn0c8Dn5/J54iTR1eK3u2YRfcfPIDX3L6P5449wHGLPZBJMT52fwMBYLkoxgBw6G5McneSEzOZGT0nSS978E5L9vdOD7cmeWFrbctexu5ri6UHFt0/aq+jHnX0Pp67/wDHLba7mN+/z1EAsIx8xhgADlGb7Hm4+DO2/7yvLJnMAtf0/i/vrRRPnb6P5xbPgj/9AF53X2O+kEdnnc/a34mqam0ms8V75gCATinGAPDY/KdF979vP7OxXXriovu37GfsP93bE621zyX59PTw2VV14n7O9eJ9nKtlcil3kjyhqp69n3N9w6L7f7OfsQCwbBRjAHgMWmt/nclneZPJbOebqur/b+9uQmyKwziOf5+mSNmIslKKhbBBsZDJQimbaVZqilJKKMpLiQgLU3ZiYcUoRN5iY6FGsyGJshEiZaNoFhqL8ZLH4n+mmbkz93Yzg8X5fjZz7u1/nnPvbKbfPP+X2S1u+VvGrgde1GxQRHQx+RFNY92pfs4AdreotZzxYXYyt8ZcH2xRqwPY3+Q+SZL+KoOxJElTt5XRLus64FFEdLZx39pp/AxPx1wfiIg5jQMiYg1woY1a5yibdwEciYgJ4Tci5gPXmLh5V6M+4FN13RMReyap1VE9c0X11tPMbHoMlCRJ083NtyRJmqLMHIyIDcBdYCllE66BiHgB9ANvKJt0BTC3GrOR8etz2zqSqYXHwDNgFbAQeBUR54HXwCzKGuTN1We4CvS0+D7vIuIocBqYCdyPiOvAA2CY0nHeDsyjdJe7W9QaiohtwD1KiD4TEd3ATeAz5czkLYx2sYco/2iQJOmfibL8R5IkTVU1hfoksIP2dnQGeAn0Aley4Y9yRIy8HsjM9W08fzEliC9oMuQbsAv4BVys3tuWmX1N6p0CDjG6qVejs8Bt4GH1+kRmHm9Sqwu4xOjmWpP5AHRn5vMWYyRJmnZOpZYkaZpk5tfM3Efp2O4EblC6xYPAT+AL8B64D5wAVmfmssy83BiK//D5bynTkXspR0kNU45fek2ZqrwyM9uZSj1S7zDQWX2Pj8B3Smf7HrApMydMi25R6y5l7fMx4Anld/KDMs26H9gLLDEUS5L+BzvGkiRJkqRas2MsSZIkSao1g7EkSZIkqdYMxpIkSZKkWjMYS5IkSZJqzWAsSZIkSao1g7EkSZIkqdYMxpIkSZKkWjMYS5IkSZJqzWAsSZIkSao1g7EkSZIkqdYMxpIkSZKkWjMYS5IkSZJq7TdcRDdzunbS7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "assi = fig.gca()\n",
    "assi.plot(bin_whi[:-1],pdf_whi, color='orange',marker='o', linestyle='--', ms=7)\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('PDF',size=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CDF\n",
    "La funzione di ripartizione è definita come:\n",
    "$$ F_X(x) = P(X\\leq x);  -\\infty<x<+\\infty $$\n",
    "nel caso discreto possiamo scrivere l'evento $X\\leq x$ come \n",
    "$$ \\bigcup_{k \\leq x} (X = k) $$\n",
    "Ciò permette di riscrevere la formula della funzione di ripartizione come\n",
    "$$ F_X(x) = P(\\bigcup_{k \\leq x} (X = k)) = \\sum_{k\\leq x}P(X=k)$$\n",
    "Nel caso del grado, e in generale per un campione finito, $P(X=k)$ sappiamo come calcolarlo (abbiamo sprecato un quarto di notebook per farlo). Inoltre, dato che il campione è finito e abbiamo un minimo e massimo, tutti i valori di k minore del minimo e maggiori del massimo hanno probabilità 0. Tutto ciò ci permette di ricavare la formula\n",
    "$$ F_X(x) = \\sum_{min \\leq k\\leq x}P(X=k)$$\n",
    "dove min è il valore minimo del campione.\n",
    "\n",
    "Se vogliamo calcolare la CDF - funzione di ripartizione - possiamo sfruttare il seguente schema:\n",
    "<img src=\"figures/somma_cumulativa.jpg\">\n",
    "In sintesi per ogni valore di k ammissibile posso sfruttare la somma calcolata al passo precedente e aggiungo il valore relativo al k che sto considerando.\n",
    "\n",
    "La funzione cumsum di numpy esegue questo tipo di sommatoria. Quindi posso facilmente ottenere la cdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  4,  7, 12])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,1,2,3,5])\n",
    "np.cumsum(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "cdf_karate = np.cumsum(pdf_karate)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02941176, 0.35294118, 0.52941176, 0.70588235, 0.79411765,\n",
       "       0.85294118, 0.85294118, 0.85294118, 0.88235294, 0.91176471,\n",
       "       0.91176471, 0.94117647, 0.94117647, 0.94117647, 0.94117647,\n",
       "       0.97058824, 1.        ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cdf_karate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualizzazione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CDF $P(X\\\\leq x)$')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_cdf_karate = plt.figure(figsize=(16,9))\n",
    "assi = fig_cdf_karate.gca()\n",
    "assi.plot(bins_karate[:-1], cdf_karate, color = 'red', marker = 'o', linestyle = '--', ms = 16)\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('CDF $P(X\\leq x)$',size=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per calcolare la CDF possiamo utilizzare l'oggetto ECDF del modulo statsmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.distributions.empirical_distribution import ECDF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'oggetto ECDF restituisce una CDF partendo dal campione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CDF')"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf_function = ECDF(campione_grado_karate)\n",
    "x = np.unique(campione_grado_karate)\n",
    "y = cdf_function(x)\n",
    "fig_cdf_function = plt.figure(figsize=(16,9))\n",
    "assi = fig_cdf_function.gca()\n",
    "assi.loglog(x,y,color = 'red', linestyle = '--', marker= 'o',ms = 16)\n",
    "assi.set_xlabel('Grado',size = 30)\n",
    "assi.set_ylabel('CDF',size = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analisi di una online social network\n",
    "### L'era della power-law :-)\n",
    "Ripetiamo la stess analisi su una sottorete estratta da Facebook (http://networkrepository.com/socfb-Stanford3.php)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "FB_non_orientato = nx.Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/socfb-Stanford3.mtx') as f:\n",
    "    f.readline()\n",
    "    f.readline()\n",
    "    for line in f:\n",
    "        a, b = line.strip().split()\n",
    "        FB_non_orientato.add_edge(int(a),int(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nodi: 11586\n",
      "Archi: 568309\n"
     ]
    }
   ],
   "source": [
    "print('Nodi: {}'.format(FB_non_orientato.order()))\n",
    "print('Archi: {}'.format(FB_non_orientato.size()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Degree analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "FB_degree = list(dict(FB_non_orientato.degree()).values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Grado medio: 98.10271016744346\n",
      "Standard deviation: 98.33765103364449\n",
      "Grado mediano: 73.0\n"
     ]
    }
   ],
   "source": [
    "print('Grado medio: {}'.format(np.mean(FB_degree)))\n",
    "print('Standard deviation: {}'.format(np.std(FB_degree)))\n",
    "print('Grado mediano: {}'.format(np.median(FB_degree)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "count_FB, bins_FB = np.histogram(FB_degree,bins=np.arange(np.min(FB_degree),np.max(FB_degree)+2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf_FB = count_FB / (FB_non_orientato.order())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF Facebook')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AAJhVvUzJTq31ySSvTPJLSR5LJxQf6fNokv+U5FXd9wAAAOCE1/MRT7XWg0l+qZTygSSvSfKKJOcnOT3Jk0keTGdU+cu11mdmoFYAAACYNcd8JnI3DH+h+wEAAIAFoacp2QAAALDQzXhgLqUsnunvBAAAgNl2TIG5lDJQSnl7KeWPSym7SikHkjxVSjnQ/f2PSyk/VkoZmKF6AQAAYFb0HJhLKa9L59zljyW5OsnyJK10dsZudX+/OsnHk+wspbz2WIsFAACA2dJTYC6l/FiSP0uyIs8dH/Vskm8mubl7fWbMs4uTfL6U8rYZqBkAAACOu2kH5lLKC5P8bp4bTf5Mkn+c5Hm11tW11pfXWlenc7zUq5P8affVVpKPllKumJHKAQAA4DjqZYT5vUlOTVKT/Fyt9QdrrTfWWkfGNqq1jtRav1JrfXOSf9u9fUqSnzumigEAAGAW9BKYX59OWL6h1vrBqbxQa/1QkuvTGZF+fQ99AgAAwKzqJTCf373+r2m+N9r+vB76ZIz2SM31tz2cX7/+jlx/28Npj9S5LgkAAGDB6e/hnT1JBpM8Os33Rts/0UOfdLVHat5+zU3ZtmtP9g+3s3iglbUrlmXzpvVp9ZW5Lg8AAGDB6GWEeUf3Ot3Nuy7vXrf30CddW3buzrZde7JvuJ2aZN9wO9t27cmWnbvnujQAAIAFpZfA/PF01iK/s5Ry6lRe6LbblM7a54/30Cdd24f2Zv9we9y9/cPt7BjaO0cVAQAALEzTDsy11v8vyeeTvCDJ/yqlLDta+1LKGUk+neSyJJ+rtW7upVA61ixfmsUDrXH3Fg+0snr50jmqCAAAYGE64hrmUsrgUd57d5IPJvmBJLeXUj6Wzi7YdybZl2RJOlOwr0ryjiRnJ/mTJP+2lDJYazV/uEcbVg5m7Yplh61h3rDyaH9dAAAATFeptXmH5VLKSDpTqCf9jknaTXxea629bDY2a9atW1e3bt0612UcUXukZsvO3dkxtDerly/NhpWDNvwCAACYolLKzbXWdZO1myy4TjWFTdZOmptBrb6SjavOzcZV5851KQAAAAvW0QLzp2atCgAAADjBHDEw11rfOpuFAAAAwImkl2OlAAAAYMETmAEAAKCBwAwAAAANjul4p1LK6Uk2JXl9klVJzkyyqNZ62oR2r05yTpJHa61fPpY+AQAAYDb0HJhLKT+S5HeSLB291b02ncn8nUl+Lcm+UsryWuveXvsFAACA2dDTlOxSyjuS/GGSM9IJyo8lufsor1ybZDjJ4iRv6qVPAAAAmE3TDsyllAuT/GY6QXkoyT+ttZ6T5L1Heqc7oryl++vG6ZcJAAAAs6uXEeafSXJqkn1Jrqq1fn6K792UTsh+SQ99AgAAwKzqJTC/Pp11yr9fa719Gu99q3u9uIc+AQAAYFb1Epgv6V6/Ms33nupeT++hTwAAAJhVvQTmU7vX/dN873k9vgcAAACzrpfA/O3u9YJpvvfi7vWhHvoEAACAWdVLYN6WzuZdb5jqC6WU/iQ/nM7a57/roU8AAACYVb0E5s92r68rpWyY4jvvT7Ki+/Of9NAnAAAAzKpeAvPHkuxKZ5T5T0opbz5Sw1LKYCnlfyT5hXRGl2+ptX6ml0IBAABgNvVP94Va63Ap5S1Jrk+yNMkflVLuzZi1yaWUjyRZk+S7un2UJE8meetMFA0AAADHWy8jzKm1/m2SN6YTkks6R02tT2cUOUn+ZZJXJ1nUfT6UZGOt9bZjrBcAAABmRU+BOUlqrV9OsjrJv0/yzXSC8cTPt5L8pySra61bj7laAAAAmCXTnpI9Vq31iSS/kuRXSilnJ7k4yRlJnkryQK31gWMvEQAAAGbfMQXmsWqt385zZzQDAADAvNbzlGwAAABYyHoaYS6lvDydNcq7aq0PTqH9+emcwzxiLTMAAADzwbRHmEspr0lyU5K/TXLBFF9bnuTvkvxdKeUfTbdPAAAAmG29TMn+Z93rLVMdLa613pzk6+mMSv9ID30CAADArOolMH93Ouct//k03/tCOoH5lT30CQAAALOql8D8gu51xzTf+2b3enkPfQIAAMCs6iUwn9a9Pj3N90bbn95DnwAAADCregnMe7rXc6b53mj7p3roEwAAAGZVL4H5vu71NdN8b0P3en8PfQIAAMCs6iUw/2U6m3e9uZTywqm8UEp5UZI3p7NZ2A099AkAAACzqpfAfE2SkST9Sf53KeWom3iVUq5Icl23fe2+DwAAACe0aQfmWus3k/xOOqPML0iyrZTy4VLK95ZSLiqlPL97/d5SykfSOX/5BemE5Y/WWm+ZyT8AAAAAHA/9Pb73s+mE4NcnWZLkX3U/TUr3+udJ3tNjf4zRHqnZsnN3tg/tzZrlS7Nh5WBafWXyFwEAAJiyngJzrfVgKeWfJPn3Sd6bZOlRmu9N8v8m+ZVa60gv/fGc9kjN26+5Kdt27cn+4XYWD7SydsWybN60XmgGAACYQb2OMKcbft9fSvlQkjcleVWSC9MJz3vT2Q37r5N8tta6dwZqJcmWnbuzbdee7BtuJ0n2DbezbdeebNm5OxtXnTvH1QEAACwcPQfmUbXWJ5L8fvfDcbZ9aG/2d8PyqP3D7ewY2iswAwAAzKBedslmDq1ZvjSLB1rj7i0eaGX18qPNigcAAGC6BOZ5ZsPKwaxdsSxLBlopSZZ01zBvWDk416UBAAAsKMc8JZvZ1eor2bxpfbbs3J0dQ3uz2i7ZAAAAx8UxBeZSyvIkb0myPs9t+NU66ktJrbWuOZZ+T3atvpKNq861ZhkAAOA46ikwl1L6kvxykp+b8B2jw5y14V4angEAAMAJqdcR5t9K8pN5LgzvSbIsnTD8RPd7nzemfU3y7STOYQYAAGBemPamX6WU70ryU91fb0qyqtb6/DFN3lFrXZrk7CT/PMk/pBOstyZ5Ua31/GMrGQAAAI6/XnbJ/snudX+SN9VadzY1qrU+Vmv9wyTrkvxhkjck+eOeqkxSSnlDKWVnKeXOUsr7Gp6fUkr5VPf5TaWUS7r3X1dKubmUckv3elWvNQAAAHDy6CUwvzKdKdZ/UGv99mSNa60Hk7wzyT1JNpRS/sV0OyyltJJ8JMkbk6xO8tZSyuoJzTYlebzWenmSDyb5QPf+t9MJ9i9O8uNJNk+3fwAAAE4+vQTm0SnVtxzh+akTb9Rah5N8LJ2p2f+8hz5fkeTOWuu3ut/1ySRXT2hzdZKPd3/+dJKNpZRSa/16rXWoe397klNLKaf0UAMAAAAnkV4C8+LudWjC/ae71zOP8N7t3evEkeGpuCDJrjG/39+919imO6r9RJKzJrT5Z0m+Xmt9tocaAAAAOIn0Epj3dK8TR5If7V6vOMJ7o0H6nB76nHg0VXL48VRHbVNKWZPONO2fbuyglHeVUraWUrY+8sgjPZQIAADAQtJLYB4dKb54wv1b0wmt33uE917bve7toc/7k6wY8/uFOXyE+1CbUkp/kjOSPNb9/cIkf5LkX9Ra72rqoNb6u7XWdbXWdeec00umBwAAYCHpJTB/NZ1g/LIJ9/+se11dSvnFsQ9KKT+d5M3pjPh+rYc+v5bkilLKpaWUgSRvSXLdhDbXpbOpV5L8UJIbaq21lLIsyeeS/GKt9Ss99A0AAMBJqJfA/Bfd68ZueB31iSS7uz//cinlnlLKDaWUe5P85ph2H5luh901ye9J8oUktyX5n7XW7aWU95dSvr/b7JokZ5VS7kzy3iSjR0+9J8nlSf5DKWVb9zM43RoAAAA4uZRaJy4FnuSFznTnv05nDfPP11qvH/Ps9Uk+k2R0F+rRLx9dX/xrtdafP6aKZ8G6devq1q1b57oMAAAAjoNSys211nWTteuf7hd3R3u/6wjPvlhKeVmS/5BkY5KzkzybzpTq36i1fnq6/QEAAMBcmHZgnkyt9bYkb0uSUkpfrXVkpvsAAACA462XNcxTJiwDAAAwXx3XwAwAAADz1VGnZJdSfq374zW11u2zUA8AAACcECZbw/xv0tnpekuSxsBcSrm2++Ov11q3zVxpAAAAMHdmYkr2O5L8eJKLZuC7AAAA4IRgDTMAAAA0EJgBAACggcAMAAAADQRmAAAAaCAwAwAAQAOBGQAAABpMNTDXGWoDAAAA80L/FNv9aSnlaM/LFNqMqrXWqfYLAAAAc2I6wfVIabhOoQ0AAADMK1MJzJOFYCEZAACABeeogbnWalMwAAAATkrWEs9T7ZGaLTt3Z/vQ3qxZvjQbVg6m1WewHwAAYKYIzPNQe6Tm7dfclG279mT/cDuLB1pZu2JZNm9aLzQDAADMEFOu56EtO3dn26492TfcTk2yb7idbbv2ZMvO3XNdGgAAwIIhMM9D24f2Zv9we9y9/cPt7BjaO0cVAQAALDwC8zy0ZvnSLB5ojbu3eKCV1cuXzlFFAAAAC4/APA9tWDmYtSuWZclAKyXJku4a5g0rB+e6NAAAgAXDpl/zUKuvZPOm9dmyc3d2DO3NartkAwAAzDiBeZ5q9ZVsXHVuNq46d65LAQAAWJBMyQYAAIAGAjMAAAA0EJgBAACggcAMAAAADQRmAAAAaHDUwFxK+ftSys2llNfMVkEAAABwIphshHlt93PGkRqUUr5VSrmrlPLaGa0MAAAA5tBMnMN8SZKaZMkMfBfT0B6p2bJzd7YP7c2a5UuzYeVgWn1lrssCAABYEGYiMDMH2iM1b7/mpmzbtSf7h9tZPNDK2hXLsnnTeqEZAABgBtj0a57asnN3tu3ak33D7dQk+4bb2bZrT7bs3D3XpQEAACwIAvM8tX1ob/YPt8fd2z/czo6hvXNUEQAAwMIiMM9Ta5YvzeKB1rh7iwdaWb186RxVBAAAsLAIzPPUhpWDWbtiWZYMtFKSLOmuYd6wcnCuSwMAAFgQbPo1T7X6SjZvWp8tO3dnx9DerLZLNgAAwIyaamC+spSyZwbaJElqrX81xX45ilZfycZV52bjqnPnuhQAAIAFZ6qB+f8+yrM6hTYT2xvZBgAA4IQ21eBqni8AAAAnlckC81/luRFkAAAAOGkcNTDXWjfMUh0AAABwQnGsFAAAADQQmAEAAKCBwAwAAAANej7eqZRyXpKXJzknyVnpbA72WJJHknyt1vrQjFQIAAAAc2BagbmUclqS9yT5iSSXT9L2jiQfTfJbtdane64QAAAA5sCUp2SXUjYkuTvJr6QTlssknyuSfCDJXaWU18xo1QAAAHCcTWmEuZRydZJPJVmUThhOOlOwb09yT5LH0wnfy5Jckk5YHm03mOQLpZQfqbVeN1OFAwAAwPE0aWAupZyf5NokA91bdyX51SSfrLXuOcI7y5K8Lcl7k1zWfffaUsqLa60PzkThAAAAcDxNZUr2f0lyZjojyp9O8pJa628fKSwnSa11T631N5N8R5L/1b19ZpJfPsZ6AQAAYFYcNTCXUpYm+ZF0wvJXk7yt1rpvql/ebfu2JF9LZ4r2j5ZSTu+9XAAAAJgdk40wf3+SJd2ff77WenC6HdRaD6QzNTtJFne/EwAAAE5okwXmdd3rbbXWr/TaSffdHd1fX9Hr9wAAAMBsmSwwvyyd6dg3zkBfN6YzLfulM/BdAAAAcFxNFpgv6F5vnYG+Rr/jwhn4LgAAADiuJgvMS7vXI+6IPQ2PT/hOAAAAOGFNFpjP6F73zkBfT3WvdskGAADghDdZYO4/Dn0ej+8EAACAGTVZYAYAAICT0lRHewdLKRcdY1+Dx/g+AAAAzJqpBubfOa5VAAAAwAlmqoG5HNcqAAAA4AQzWWC+L0mdjUIAAADgRHLUwFxrvWSW6gAAAIATiiOe5rn2SM2WnbuzfWhv1ixfmg0rB9PqM4MeAADgWAnM81h7pObt19yUbbv2ZP9wO4sHWlm7Ylk2b1ovNAMAAByjaZ/DXEo5tZRyXillyfEoiKnbsnN3tu3ak33D7dQk+4bb2bZrT7bs3D3XpQEAAMx7UwrMpZRlpZT/p5RyR5KnkzyQ5MlSyl2llP9aSjnruFZJo+1De7N/uD3u3v7hdnYM7Z2jigAAABaOSQNzKeWKJF9P8u+SXJbOEVOjn0uS/J9Jvl5KedHxK5Mma5YvzeKB1rh7A/19edF5p89RRQAAAAvHUQNzKaU/yaeTXDxq2mtlAAAgAElEQVR6a2KT7ufCJH9USlk04xVyRBtWDuYlF56RscuVD7RH8nt/c0/aI04DAwAAOBaTjTD/syQvTucs5keTvCvJBUkGutefTvJIt+3qJD98fMrkSL7z4jNTynOJeaTGOmYAAIAZMFlgfnP3uj/Ja2qtH621PlhrPdi9/o8kr0myr9vuB49XoYw3ukP27/zVtw4bTbaOGQAA4NhNFphfls7o8idqrbc1Nai1fjPJJ9KZmv3SmS2PIxndIftA+/Cp14sHWlm9fOkcVAUAALBwTBaYz+1e/2aSdqPPB4+tHKaqaYfsJFnUKlm7Ylk2rPRXAQAAcCz6J3n+vHRGmB+fpN2e7vW0Y66IKRndIXvfmNC8qFXyr17zgvzsa1+YVt/E/dkAAACYjimdw8yJZ8PKwaxdsSxLBlopSZYMtPLyS54vLAMAAMyQyUaYOUG1+ko2b1qfLTt3Z8fQ3qxevjQbVg4KywAAADNkqoHZob4noFZfycZV52bjqnMnbwwAAMC0TDUw/+nYs36PopRSDt+JarxaazWyPcPaIzVbdu7O9qG9WWO0GQAA4JhNJ7geLX3VPDcKLaXNstEzmbft2pP9w+0sHmhl7Ypl2bxpvdAMAADQo6ls+lUyeQguU2zHcTB6JvO+4XZqkn3D7WzbtSdbdu6e69IAAADmraMG5lpr33H4tGbrD3eyaDqTef9wOzuG9s5RRQAAAPOfY6UWgNEzmcdaPNDK6uVL56giAACA+U9gXgCazmReu2JZNqwcnOvSAAAA5i27VS8Q7/zuS/K5Wx5MkvzT7zg/V73oXBt+AQAAHAOBeZ5r2iF795PP5qoXOZsZAADgWJiSPc/ZIRsAAOD4EJjnOTtkAwAAHB8C8zxnh2wAAIDjQ2Ce5+yQDQAAcHzY9Guea/WVbN60Plt27s6Oob1ZvXxpNqwctEM2AADAMZo3I8yllDeUUnaWUu4spbyv4fkppZRPdZ/fVEq5pHv/rFLKX5ZSniqlfHi2654Nrb6SjavOzc9svCIbVzlOCgAAYCbMi8BcSmkl+UiSNyZZneStpZTVE5ptSvJ4rfXyJB9M8oHu/WeS/IckPz9L5c6p9kjN9bc9nF+//o5cf9vDaY/UuS4JAABgXpovU7JfkeTOWuu3kqSU8skkVyfZMabN1Un+c/fnTyf5cCml1FqfTnJjKeXyWax3TjSdybx2xbJs3rTeqDMAAMA0zYsR5iQXJNk15vf7u/ca29RaDyZ5IslZs1LdCcKZzAAAADNnvgTmpuHRiXONp9LmyB2U8q5SytZSytZHHnlkWsWdKJzJDAAAMHPmS2C+P8mKMb9fmGToSG1KKf1Jzkjy2FQ7qLX+bq11Xa113TnnnHOM5c4NZzIDAADMnPkSmL+W5IpSyqWllIEkb0ly3YQ21yX58e7PP5TkhlrrSbXjlTOZAQAAZs682PSr1nqwlPKeJF9I0kpyba11eynl/Um21lqvS3JNks2llDvTGVl+y+j7pZR7kixNMlBK+YEkr6+17pjYz3zX6iv52DtfkQ/fcEe23vt41l18Zt5z1RU2/AIAAOhBOckGYadk3bp1devWrXNdxrTZJRsAAGBypZSba63rJms3X6ZkMwV2yQYAAJg5AvMCYpdsAACAmSMwLyCrzj89A/3j/0rtkg0AANAbgXmBaI/UXHvj3TnQHjl0ryS56PlL8uor5ucxWQAAAHNJYF4gtuzcnW/c/0RGxuzhVpPc/e2n847f+2raIzZ3AwAAmA6BeYFoWr+cJM8eHLHxFwAAQA8E5gVizfKlWTzQanxm4y8AAIDpE5gXiA0rB7N2xbKc0n/4X+lAf19edN7pc1AVAADA/CUwLxCtvpLNm9bnw299aVYsOzVlzLPhgyP51b+4PcMHR474PgAAAOMJzAtIq6/kdWvOy3/8/jVZ1HouMtck33zoyVz94Rtt/gUAADBFAvMCdNuDT2a4fXgwvvORp2z+BQAAMEUC8wK0ZvnScSPMow62q82/AAAApkhgXoA2rBzMC84+7bD7iwdaWb186RxUBAAAMP8IzAvUmacNjNv4q68ka1csy4aVg3NWEwAAwHwiMC9AW3buzjfufyJjVzEvavXlnd99SVp9h0/VBgAA4HAC8wK0fWhv9g+3x9179uBIPnfLg3bJBgAAmCKBeQFas3xpFg+0Drv/+VsfytuvuUloBgAAmAKBeQHasHIwa1csyyn94/96nz04km279jhaCgAAYAoE5gWo1VeyedP6vPHK8w57tn+47WgpAACAKRCYF6hWX8mbXrI8SyZMzR7o78uLzjt9jqoCAACYPwTmBWzDysG85MIzMnZj7OGDI/nVv7g9wwdH5q4wAACAeUBgXsBafSU/8apL0z8mMdck33zoyVz94Rtt/gUAAHAUAvMCd9uDT2a4fXgwvvORp2z+BQAAcBQC8wK3ZvnSLGqVw+4fbFebfwEAAByFwLzAbVg5mBec87zD7i8eaGX18qVzUBEAAMD8IDAvcK2+kuve86qsOu/0LGqVlCRLBlpZu2JZNqwcnOvyAAAATlj9c10Ax99Af1/+979+dbbs3J0dQ3uzevnSbFg5mFbf4VO1AQAA6BCYTxKtvpKNq87NxlXnznUpAAAA84LAvMC1R2q27Nyd7UN7s8bIMgAAwJQJzAtYe6Tm7dfclG279mT/cDuLu2uXN29aLzQDAABMQmBewLbs3J1tu/Zk33A7SbJvuJ1tu/bkhtseTpJ87pYHkyT/9DvOz1UvOleIBgAAGENgXsC2D+3N/m5YHrVvuJ33f3Z7HnjimYzUzr3rvjGUf3TZWUaeAQAAxnCs1AK2ZvnSLB5ojbt3Sn9fHtz77KGwnCQjNbn53sezZefuWa4QAADgxCUwL2AbVg5m7YplWTLQOnT+8uDpp+Tg2LTc9ezBkewY2jv7RQIAAJygTMlewFp9JZs3rc+Wnbtz6wNPpD1Sc8+jT+fBJ545LDSf0t+X1cuXzlGlAAAAJx6BeYFr9ZVsWDmYa268+9AGYBNXKfeV5DsvPjMbVg7OSY0AAAAnIoH5JDBxt+yaZKBV8rKLzsx5Z5xql2wAAIAGAvNJoGm37OF2zXe94Ky856orsmXn7vzGDXdkZKSmr6/kxReckQ0rBwVoAADgpCYwnwTWLF+aUxf1Zf+BkXH3P3/Lg7np7sfy9fseH/dsyUAra1csc8wUAABwUrNL9klgw8rBXHzWaYfdv/ORp3PzvY8fFqT3Dbezbdcex0wBAAAnNYH5JNDqK3nDlecddv/gSM2zB0ca3kj2D7cdMwUAAJzUTMk+Sbz4gjNySn/fEQPyRIsHWsftmKn2SM2WnbuzfWhv1ixfar00AABwQhKYTxIbVg5m8PRTsuvx/Yc96+9Lxubo0TXME4+Zmomg2x6pefs1N2Xbrj3ZP9zOYuulAQCAE5TAfJJo9ZX8xzetzv/xib/PcLuOe7Z4USurzu+MJpdSct4Zp+afXHlevrTjoXz+1oeSJG+88rx8/G/vPeagO/GIq7HrpTeuOneG/rQAAADHTmA+iVz1onNz2TnPyzcfenLc/Sefbeer9zw+7t5124YyNlZ/ZttQSklGujenEnSbRqSbjrgaXS8tMAMAACcSgfkkMrr5186HnkydpO3E5zVJnXBzNOhuWDl4WDBO0jj1+p2vvCSLB1qHRpiT47teGgAAoFcC80nmxReccVhg7dVAf19eOPi8IwbjpqnXqcnaFcsOaz9xvTQAAMBcE5hPMhtWDmbtimW5+d7Hp7xj9lglz40+H2iP5IPX35H7Htt3WDD+3D882Dj1+psPPZnNm9Zny87d2TG0N6uPcZdsO24DAADHi8B8kmn1lWzetD433PZw3v+/d+SBPfsPrUs+mr6SvHDwebn70X2HgvZITe565KkcnLCJ2GhQnjiSfeqivhxoj+Qjf3ln1ixfmnd/z+U97bJ9w20P53O3PJhaa3Y+/FTue2yfHbcBAIAZJzCfhFp9JVetOjfXfuXuPLz3mcN2zR7fNnn5xc/Ppldfmu1De/OhL90x7vmBds2iVsmBMd/R3yq58MzF46Zen7qoLwP9ffnojXf3HG7bIzU/9tG/y013P9YY8vcNt/P1+x7Ph750e/pbfUacAQCAYyIwn6S27Nydb9z/xLiw3N+XnHfG4jz61LPZf2Aki1oll519Wt75yktz24NPZmSkHr5h16K+XHLWabnn0aez/0Bn5PlAu+bar9yTl1x4Rj70lrX55oNP5kB7JB+98e5jOk5qy87d+fv79hx1RHz/gZH81pfvysF27TmUm+INAAAkAvNJq+l4p4MjyctWnJG/+dZjGW4fyIF2zR27n8q/+sTNqTWHRomXDLTGjRJ/7J2vyIdvuCO/9eW7Do007xtu5+/v25Nz/+HBvOkly3PLA09MepzUZGF1+9DeKa27HlvDdEJ5e6Q2bmBmijcAAJycBOaT1JrlSw8bLe4ryZ/d+nAOjhnCHTuaOzqC/FOvviyLWn150XmnJyX57S/flfse23fYWuZnD47kT7cN5Ys7Hs5Fz19y1OOkphJW1yxfmlP6+xpDc0lnKviBhvXUE894HhvMV3X/DLc9+GQOtkcad/aezig4AACwcAjMJ6nR3bJHA+pAf2dDroOT7AD2zIGRLGr15d3fc3nefs1N+fp9j2f/gZG0+o78zr7hdu599OlcctZpube7Qdepi/py0fOX5JYHnkiSjNR6xLA6es7zLQ88kUvPWpKdDz817pzokuTC5y/O1WuX59ob7znqGc9jg/m+4XZGB45rnXrgBgAATg4C80lqdLfs0eOd7nrkqXxm29Ck75WS3P7wk/nSjocPheUkaXcHfcceOzXWMwdG8oYrz8uVF5yRWx94In9+60O597F9+dCX7sjigVbOOm2gccr2rQ88kWtuvHvc5mHLl52ah/Y+m3Y33Nckjz41nJdcsGzSM5637Nw9LpiP/feBiWE56Zw1fdcjT+X62x62nhkAAE4yAvNJrNVXsnHVudm46txcf9vD+eKOh8eNziaHB+CRmnz2Hx7MF3c83Dg1uq8vWXfxmfn7+/aMC6CnLupLe6Rm+9DetEdq7p1wdnN75NkMTJhu3d8quXP3U+MC7v4DI9n95LMZGTl8JHgqZzw3rd2eaHTX777SOWv6M91p5ZOtZ7ZhGAAALCwCM0nGT9HeN9zOKf19GVx6Sv79P1mV67YN5XO3PjSu/bMHRxpHk9sjydDj+w+N/o4qKfnIlrvSHqlp9ZXDnj97cCRLT+1Pe2Qko5n5QLvmz7c/dNjIb9NRVqMjwaNTuI80hbpp7fZYixf15adefVnue2xfPn/rQ4cC/GTrmW0YBgAAC4/ATJLDp2iPjs62R2r+7f/8RuM7TVOvT+nvy+6nhg87+mnfgecC6sSwPGrvMwcPu9c0TXr0KKvRUerpjARP/IeBsWuYR0Puz772hfnIX96Z4Qkj6EdbzzxxqrcNwwAAYP4TmDlk7BTtpBNsv//DNx5xNHaiJd21yPc/vn/Ga1vUKuPOVv7YO1+Rv77jkXz2G0PTGgme+A8Dozt9f/PBJ8dN4W4aiZ64gdhYTVO9bRgGAADzm8DMEW3ZuTt3PfLUlNqWJGcuXpT9w+3GkedjUZL89D++LKf0t8aF2g0rB/PZbwwdtpZ633A7n/3G0GFriSeuMX7391x+aBT6davPG/cdE3cRb9pAbKzpBmwAAODEJzBzRNuH9jZOiW5SkzzwxDPHpY5SkpesWJbXrT7vUOi95YEn8oVbH8q3vv30Ye37SvL5Wx/K8MGRcSPS7/i9r05pjfFoH6+49PlZd/GZafX15coLjr6J13QD9kQ2DAMAgBOPwMwRrVm+NIsX9R06Omqu1NqZMn3Vi84dd4Zyk9JtP3GK9q9ff3tuvvfxcfe/evdjee+ntuX7vuP8jNSaP7vlwTz0xDO569tP58lnDo4L3O+56vJJd8eeTsCe+L4NwwAA4MQjMHNEG1YO5qUXnXnovOX+vmSgv5Va63EN0X1l/PnIoztgf+hLtx81LCfNG5HtG27nmhvvPmzq9sGRms98Yyif+caRz5/eN9zO1+55LB/60u352de+sHE0uinsHi1gT2TDMAAAODEJzBxR087Zr77inHx55+68/7Pbc/+eZ466Xrnp+KjJjO6Afc+jT2f/gc7RVcMHOztg9084Smo6jiXgH2jX/OaWO/PFHQ/nDVeelxdfcMah0eNewu7E6de3PPCEDcMAAOAEJDBzVBN3zk6Svr6SR/cdGBeWSzojwc8eHMlAq2Tp4kW57JzT8rW7Hz9qqC7d7xsZeW4H7Gt+/OV5829+JbfvfjLtMTm317A8Ew6OJN986Ml886Ens2TMlOnp7o49cUT61EV9Oeu0Uw77xwAbhgEAwNwTmGl0tE2omkJiTfLGK8/LpWeflj+/9aHc+9i+fPXuxxu/+5T+vkPrg19y4Rn5iVddOu5Ypy07d+fex/aNC8tjTZyyPdv2Dbdz872P5+f+57Zc9Pwl09ode+KI9P4DI7l/z/hjuJZMc8MwAADg+BCYOcxkm1A1HaF0Sn/foXfvfWzfUdcZv3TFsvT1lay7+My856orMtDfN+5Yp+1De4/6/lyG5VHPHhzJn24byuJFfRno78uSgda4/1avvuKcXH/bw4f9g0PTPzaMtahV8pOvurRxvTQAADC7BGYOM9m63LFHKO0bbqevJAfaU1tn3FeSr+/ak+GDI9m2a0+23vt4Nm9af6jf7UN7c7A9klO607unqlWSuZixPbo2+qdefVkWtfoOrfMee4TVqYv6cvFZp+UNV553aOr5kf5B4GC7ZlGrb9Kw7BgqAAA4/gRmDjPZutyxm4F99htD+fytDx0Kt0cKy6NrnA+0Rw478umG2x7O7/3NPeMC5lSVdKZAX/T8JblvkpHt4+WZAyNZ1OrLz2y8Ikly/W0PHzbtenT980CrZPFAK0uOEJqnsnbZMVQAADA7pp5MOGmMTrkea2KQG90M7LJznpfhhpHgRa3SCbOL+vKi807Pv3ntC/PGK89LnZCn9w+387lbHjwUMGs6AbPWmv4p/N/53S84K7/x1pfmT979yixqTS0sDrRKzn7ewKFp5Kf09437fbo6o+ojh3YEP9q06+F2zd79B/OOV16cq19y/qF+S6a+dnnsDICa8TMAAACAmWOEmcOMnXI9dgSzKcg1rWfu70vesOa8XD54eq684Lnpwtff9nC+uOPhwzbISnJYwBxu15z9vIE8/ezBIx4JtWSglZ941aXZuOrcXH/bw4cF976S9PeVDI8Z9R4NpR975yvy13c8Mu64rNFp1EcapS5pPuf5QLvmf/z1tw4dO3WwPXJox/Am9f9v787j5CrrfI9/flXVa9LZkw4kJBBIQsISQC4gsr0CyCKKOF5BHRfAcVxARJwZ0XFG5w7jzOgMsijeOyK4AooKiIMKCUG4rIGELSELScjeHdJJp9NLqqvqN3+cU53q6lPV1Z2u7nTyfb9e/UrVqafOeap5OMm3ng247/kNtHSkSKadmMH4EZXcdNlxnDe3vtde4r6uzC0iIiIiIv2jwCw9RO2/XGiObDZcL1m/oyvYpjKw4I1GtrcmuWb+UV3vKxTE33P8IT2CNMCu9k5mTBzJ7Po6/vvVzeTn5unjartC/Oubd9GRVyDjcPFxh3DEhBGkM048FusW4PO3yyo0zDyr2BTp3GHXhYJ1ru2tnd3q+XZrkpsfW8l5c3sPvFFfUmgbKhERERGRgafALJGiAmWhcj+9+lRueWwldzzxZtcc5vyFwnLL5gfxdMaZPq62x77LybSzvqmNoyfXEdVZe+Gxk7vCeFSIrK2M8955h5bc65r9zOfMnkRjy3O8+NaOPi08ltXftcdWNLRwy2MruWb+TJ5cta3ggl59GQEgIiIiIiL9p8As+yweMxLxGKm8Bb+ihgnnB/F0xvnkXc+zbntr5L7L2aHHUWH42Cmju54PZIjMBvsbfrmUB5Zu7vP7+8sdvr9oNT9+Zh2daactmSYRM2or43z89Ol8Yf4sKhOxHl88HD25Dgy+9/hqrZgtIiIiIjKAFJhlQPR3mHB2AatC85RrKuO857hDaGzZUzQM92UYeSniMeO98w6NHCpeTqkMNLencp47uzpS3L7wTX7y9Dq+/cETWNHQ0hWMz5k9SStmi4iIiIiUiQKzDIj+9vAWW1E6u0DX/Dn1zJ9T32sYLnUYeX8/U3VFLFjMqzNNR2rwN33e1ZHmc794kXQmWNn7pGljuOqMI4rumS0iIiIiIv2nwCwDor89vFE901WJGBcdO5n3zju02zkGMgyXIuoznX7kBO5YtJrn127nraY2tjTv6ff56yrjzJkyisXrdpApMX9nh63vSWV4bm0Tk+qqe10xO51xFq1o7DYnGuhxTD3SIiIiIiLdKTDLgOlPD2+hnun/+NAJ+0WAy/1M6Yx3G/68r/VLZpy4GVPG1LBhR3uf359xaNjV0eMLh8pEsPc1QDKV4X23P8Wqxt2kM97VM21mGsYtIiIiItILBWYZUgM997icsvOts+E0VWq3cAF7Uhle3tjMVe86nP96cm3/VuR2Z97U0Ty3tqmrl7ozneGup9dx9uxJvO+2J3mjYXe3az6zpol4bG9vtYZxi4iIiIhEU2CWITfQc48HWnZI851PrY2cb50bPvuqLZlmQ1MbE0dWsnFnR5/f/+L6nYyuSRCPGZlwlfKMw9INO7l1wUpWNu6OfF9+fUsZxp39EqPYayIiIiIiBxIFZpEicodhR62WXVMR4+ozjuChpZtpaNlDMpWhuiLG+BFVNLR0dO1LXUjM4A+vN/SrdxmCXu7trZ09jrcl0/zXk2tLnhtdmYh1rWieP/Q8d8g2oFW5RUREROSgocAsUkT+MOwsg66weP35s7n+/NndhpWfOXMin7zr+a5gWZmIkUxlyM+v7vQ7LPemL+etr6vqthhY/srbL761gxt+uZRp42qH1arc6g0XERERkX2hwCxSRKFtr04/cjxXnXFE0VW8c+dmv7ltNw8u3dzjPIO/OVVPVYkYX79kbtfniPrMe1IZHli6mbhBfqd5WzLN717evN+F0WI95ftTPUVERERk/xUb6gqI7M+y217lqq2Mc9UZR3DunPqiwSs7N/vac2fy3nmH9jhPVSJGVWLo/xc8fFwNGNy6YBWPvr6VZDpNIh79uQqNMH/kta187M7nSGecdMZZsLyBWxesYsHyhj4dG0i5PeVO995wEREREZFSqIdZpIhC215lhy/vy3nmTR3dbXunvsx9Hkjrmtq57t6ltCXTGP3r9d6TyvD82iYu+u4TNLV2srM9SSoDFXFjxoQRjBtRxcsb937OaeNqaUumaQznfZej9zeqpzx/cTMRERERkWIUmEWKGKhtrwqdB+h27NVNzdzy2KoB/xyJGBSa0pw713lfYnoq46xsbO12rDPtrGjYjbG769ztnRlWNHRfvbstmWbJ+h3c8thKEvFY13xjoN9zkLOjA3Lnn9dUxrsWNxMRERER6Y257w+zKPcvJ598si9evHioqyEHoQXLG7j2niWRK3IfDCriRirtkT3w2WNXnXEEy7e09BqgNYdZRERERAoxsxfd/eTeyqmHWWQ/kj90uzIRozOd6bY9VFUixoXH1NOwaw/Prm0ausqWQXYoelsyzQvrmjCMzszeY8+tbeKl9Tt7HcadXR37lCPGcfL0scRjMY6dolWyRURERKRvFJhF9iP5Q7ePnlzHXU+v69FL+p+Xn8iiFY28sqm55N7omEEiZiQHcX50/vX7sq5XMFK8+xsyOdtwZbe7Wri8gfOPmdxVplDP8jXzj+oKywOx3ZS2rBIRERE58GlIdgQNyZb9STaY5c+hzg2GpYTmo+tHcsMFs1m2eRed6Qw/emodbZ3Df+j36OoE3/nQPM6eNYknV23jdy9v5pHXtnabm10RNz579pFcd94sgH0eql1suDf0f951/jUUyEVERETKo9Qh2QrMERSYZbjIhqrXNjXzh9e28lZTW8HwfP15M7sC44LlDXz6p4tJF1gIrFT9XVV7oMUIeufT7gV7sSvixsnTx3LStLH84M9rum1jFY8Znz17BtefP7vry4hFKxp5dVMzmYwTixnHTRndFVqj5prXVsa55fITIkcE9HXedFQg78v8bREREREpTnOYRQ4C2b2ez51TzzXzZ7JoRWNkD2ttZZxjp4zuev765l37HJYTMbjwmMmYwbaWJBPrKlmyoZmtze0FV+QulwyQ6WW8d2faeWZNE8+s6TnvO51xvvf4m7z41g4+efrh/PPvl9Owq6Pb8PXanPAbtWVVWzLNw69s7tbjn937eeHyBmIx6+otPnPmRJ5ctS2y9zidcW55bCUvrGvqNqe71PnbIiIiIjJwFJhFDhDZ8HzO7Ek0tvQcLpy7d/Qxh46ipiJGe2f/k20qA39c1tC1qvUJh41h4Q3n8OSqbTy0dBO/e2VLn+YsDzUHnlnTxPPrmiK/TGhLplm8rombH13B+qY24gapvM/3+IptPXr425JprrtvKemMk0xlqK6IhYu5ede+1NPHj+DCYyczp76OmxesYmVDS4/fXf787aUbdrJoRaP2lBYREREpIw3JjqAh2TLcFZr3nPv6x+58jiXrdxQNzZVx49NnzWDjjvYevdb5aivj3PbhEzl3Tj3pjHP2vy9k486OAf1c0t07Z4zjHdPHsr6pjZgZ7zn+EOYfXd9tWHkpvdq5NHdaREREDgaaw7wPFJjlYJA//3nd9tZu4bk2byGr3Dm1ibh1DRfOMuBL58/i2nNnAvDosq189mcvDvrw7IOZAbPqRzKrfiTPrGliV3snybQTN0jEYqQ9QyoTDKefPKqGv3jHVI6fOjpyIbmoOdiF5nb3FsYVwkVERGR/o8C8DxSY5WCTG57TGY/ctzi317ozneGHT63tsehVtoc5W/6cbz/Ohh3tPa5XWxknmcqQKk0IIlQAABYASURBVDJmOx5jn+dZS+8q4saMCSP40vmzeeS1LZEjCU6ePoZ3HjmBx5Y19PhipSIGFfE4nZkMqbR3G2KeDdOfvOv5rtEMiRjU11Vz4vQxvN2SpH50NZdE9IwXWnAtK51xFi5v4PevbgEo2rse1Y5zX4PCK5vn1ye70l2hehWjLw5ERET2HwdcYDazC4FbgDjwQ3f/17zXq4CfAO8AtgOXu/u68LUbgauBNPAFd/9jsWspMIsU11tPZNajy7ZyzS+W9FiA7JbLTwDgq795lW2tyR7nr4wbJ00by7Nrey7QpSA9fFQlYtRVJdjV0dnr/t9Tx9Rw2UlTeHRZA2u27e5WvioRY8KICuZNG8OaxlZGVSfYuLODzc3dh/yPqkpw9qyJrNq2m3Vv76Yj5RgwsirOX552OPE4PLBkMw27OuhMO5Vxo64qgcWM5vZOOtNOImYcMrqav3/PHIDIBeCy4jEYW1vJTe8/jvPm7g3rUUE+nXEuvf0pVm/b3eOLhWMOGQUGy7e0MGdyHRl3Hnlta7f3Fzp3dju1Vzc1k0ylWfzWDprbOjly0ghiZpFfSpQiN9z3VqdSvuAodN7s5x6qLxBK+RJjoMpkJVMZbl+4isVv7eDk6WO5Zv5MKhOxstR9oPX1C6eBOP/+/qXScKzzvjoYP/OBZDD++w2XNnJABWYziwMrgfOBjcALwIfdfVlOmc8Bx7v7Z8zsCuAyd7/czOYC9wCnAIcCjwGz3L3gBrQKzCK9622edLZMsWCdTGV4321PsqJhd9f2VDGD02aM58p3Hc519y7t1otdUxFj+rjabuVz7S/bXMnBpzpujKmtYHtrkvxlASoMMHocL1VlzJg6torNzUk69mGOQ2XMOGxcNWYx2vakcHNwg5w/jRg1FbC5uZP2Ivu0V8Vh6tgaNjR1kIwYKVIZNw4b2/1anoGmtsJfnlTEYPzISszoVp/aSgN61rnYa6WUya+PEUxXGD+yEmNgy+Res3F3sseifpNH7S1bymd2NzbsaO/2u8z+/mK2b7+XQmUyZGhqTfW4ZiIeo6Mz03Xvrcj77KVeK6rd5baJcraF/pZp7ehke16brojBhLoqRlTGylqfg/Ez78+/l+HymQfj3oEbO8MpYZmM79c7exxogfmdwDfc/YLw+Y0A7v6tnDJ/DMs8Y2YJYCswEfhKbtnccoWup8AsMnBKWYAsqkcOiAzbd195CrcuWMkdT3TfS7kibvz1WTPYsKOdB5du7lGPmDGsVu0WERERORDkT9vbXxxo+zBPATbkPN8InFqojLunzKwZGB8efzbvvVPKV1URyZW7V3Sh188/ZjLnHzO5x2s/vfrUyLB9/fmzeWn9zh5h+vrzZ7NoRSOPLmvo0TP9V2fOoCIe4+hweOlNv1/O5uaOyHnUMYOKeAx3LzqUeEJtBUfV10UOHRcRERERaE+mWbZ5134XmEs1XAJzVP99/r9iC5Up5b2Y2aeBTwNMmzatr/UTkTIoFLbjMSsYps+ZPYkTDhvTI0xfd96sbj3b582dzMLlDfyfh5fR0LKHPakMVYkYk0ZV8Q+XzO2aG/rapmZ+tXhDjy2yqhIxvvUXxzN/Tj1/enUL1963pMeK4KcePpad7Z2sLDCEXERERORAl4gbcw8dNdTV6DcNyY6gIdkiw1sp86v7UjaZynRbsClqPk4yleHWBStZsLyR0TUVXPmuIzhvbhD0c4ecX3TsZG5+bBVvbG3p9XPEY8ZRE0fwxXNn8eNn1vH8uiYNKxcREZFhZc7kOh7+wpmaw1xOYQBeCZwLbCJY9Osj7v56TpnPA8flLPr1AXf/kJkdA/yCvYt+LQBmatEvEemLvoTw3uQH8OqKGJWJGJ1ppy2Z7tbTnbsa8cfufK5re6aYwchwVegp46q5f/Emmlp7LiYEUBWPkcG7rjVtXC1HTx5FJpPm6TU7aGpNRvaAVyeMWCzGns40xRa5NmBMTYKYGdvbOvv1O9kXiZgV3aJMREREBp8BsyfX8dA1Z/RrN4ByO6ACM4CZXQx8l2BbqR+5+01m9k/AYnd/yMyqgZ8CJwJNwBXuviZ879eAq4AU8EV3f6TYtRSYRaTc8gP4mTMn8uSqbb2uOl4otOfupd2ZzrChqR2z7lsP9fa+dMYxM9z37sWdrVf2vOu3t9HYsodJo6qYNr6Wili8a89uCHrTH35lM1ubO3DA3WnuSBEzY/6cicybMpY3tu7qulY6E5yzYVdQ3syoH1XF1HE1bNze3u345NHVXHxsMNc9d4uj7Od7ZeNO3mzczerGVsbUBr38Z82ayB2LVvPC2u2kHWJmTBhZSSxmGDBlXA2bmjoAZ0p4za3N7ezsSGHAkZNGEDdjW0uSSWG9osrvaO+ktSMFsWCrqiMnjSAGrGzYTeueNLVVccaOqKK+rpK0O282tOI4o2oq2BVea8bEWra3drKrrZMZee+vqYxhsRixsE5R5z4k7/fjHtRxw9ttrGho6ToPZrR1pKIWNiWGdV3L3KmrSbC7PQ0GMyeNJENQ94xncDPaw+uPqa0MVql3Z2d7J20FrkXMGFkZp64mQWtHhlHVcSaMrGJ14252J1NQoD5RdS72Wqllsv+9Zkys5e3dSTY1tZetTLY+I6oTzK6vY8q4al5at5ONTW39+szZ3/3omgqaw/Y3UL+XQmViWLdrtuX89yf8b9+6D/+dcttdS1uqW5sod1vob5ncNp2tsw1CfQ7Gz7y//16Gy2cejHvHiOoER08exXvn9W1Lw8F2wAXmwaTALCIiIiIicuAqNTDvf33jIiIiIiIiIvsBBWYRERERERGRCArMIiIiIiIiIhEUmEVEREREREQiKDCLiIiIiIiIRFBgFhEREREREYmgwCwiIiIiIiISQYFZREREREREJIICs4iIiIiIiEgEBWYRERERERGRCArMIiIiIiIiIhEUmEVEREREREQiKDCLiIiIiIiIRFBgFhEREREREYmgwCwiIiIiIiISQYFZREREREREJIICs4iIiIiIiEgEc/ehrsN+x8y2AW8NdT2KmAC8PdSVkGFBbUVKoXYipVJbkVKprUgp1E6kVOVoK9PdfWJvhRSYhyEzW+zuJw91PWT/p7YipVA7kVKprUip1FakFGonUqqhbCsaki0iIiIiIiISQYFZREREREREJIIC8/D0/4a6AjJsqK1IKdROpFRqK1IqtRUphdqJlGrI2ormMIuIiIiIiIhEUA+ziIiIiIiISAQF5mHGzC40sxVmttrMvjLU9ZGhY2aHmdnjZrbczF43s+vC4+PM7FEzWxX+OTY8bmZ2a9h2XjGzk4b2E8hgM7O4mS0xs4fD50eY2XNhW7nPzCrD41Xh89Xh64cPZb1l8JjZGDO738zeCO8t79Q9RaKY2fXh3z2vmdk9Zlate4oAmNmPzKzRzF7LOdbn+4iZfSIsv8rMPjEUn0XKp0A7+Xb4988rZvZbMxuT89qNYTtZYWYX5BwvezZSYB5GzCwOfA+4CJgLfNjM5g5trWQIpYAb3H0OcBrw+bA9fAVY4O4zgQXhcwjazczw59PAHYNfZRli1wHLc57/G3Bz2FZ2AFeHx68Gdrj7UcDNYTk5ONwC/MHdjwbmEbQX3VOkGzObAnwBONndjwXiwBXoniKBu4EL84716T5iZuOAfwROBU4B/jEbsuWAcTc928mjwLHufjywErgRIPz37RXAMeF7vh92AgxKNlJgHl5OAVa7+xp3TwL3ApcOcZ1kiLj7Fnd/KXzcQvAP2ykEbeLHYbEfA+8PH18K/MQDzwJjzOyQQa62DBEzmwq8B/hh+NyA+cD9YZH8tpJtQ/cD54bl5QBmZqOAs4A7Adw96e470T1FoiWAGjNLALXAFnRPEcDd/ww05R3u633kAuBRd29y9x0EQSo/XMkwFtVO3P1P7p4Knz4LTA0fXwrc6+573H0tsJogFw1KNlJgHl6mABtynm8Mj8lBLhzediLwHFDv7lsgCNXApLCY2s/B7bvA3wKZ8Pl4YGfOX0y57aGrrYSvN4fl5cA2A9gG3BUO3f+hmY1A9xTJ4+6bgO8A6wmCcjPwIrqnSGF9vY/o/iJXAY+Ej4e0nSgwDy9R38ZqmfODnJmNBH4NfNHddxUrGnFM7ecgYGaXAI3u/mLu4YiiXsJrcuBKACcBd7j7iUAre4dNRlE7OUiFQ2MvBY4ADgVGEAyJzKd7ivSmUNtQmzmImdnXCKYe/jx7KKLYoLUTBebhZSNwWM7zqcDmIaqL7AfMrIIgLP/c3X8THm7IDosM/2wMj6v9HLzeBbzPzNYRDFeaT9DjPCYcTgnd20NXWwlfH03P4XVy4NkIbHT358Ln9xMEaN1TJN95wFp33+buncBvgNPRPUUK6+t9RPeXg1S4wNslwEd97/7HQ9pOFJiHlxeAmeEqlJUEk98fGuI6yRAJ53/dCSx39//MeekhILua5CeAB3OOfzxckfI0oDk7PEoObO5+o7tPdffDCe4bC939o8DjwAfDYvltJduGPhiW1zf7Bzh33wpsMLPZ4aFzgWXoniI9rQdOM7Pa8O+ibFvRPUUK6et95I/Au81sbDii4d3hMTmAmdmFwN8B73P3tpyXHgKuCFfcP4JgkbjnGaRsZLpfDS9mdjFBz1Ac+JG73zTEVZIhYmZnAE8Cr7J3XupXCeYx/xKYRvCPmv/t7k3hP2puJ1g0ow240t0XD3rFZUiZ2TnAl939EjObQdDjPA5YAvylu+8xs2rgpwTz4puAK9x9zVDVWQaPmZ1AsDBcJbAGuJLgy3XdU6QbM/smcDnBsMklwKcI5g7qnnKQM7N7gHOACUADwWrXD9DH+4iZXUXw7xqAm9z9rsH8HFJeBdrJjUAVsD0s9qy7fyYs/zWCec0pgmmIj4THy56NFJhFREREREREImhItoiIiIiIiEgEBWYRERERERGRCArMIiIiIiIiIhEUmEVEREREREQiKDCLiIiIiIiIRFBgFhERkbIws3PMzMOfbwx1fURERPoqMdQVEBEROZiY2UTgAwT7T55AsAflGII9SJuA5cCLwIPa11hERGRoKTCLiIgMAjMbCXwT+AxQG1FkVPhzOHAR8PdmthL4Z+AX7p4epKqKiIhISIFZRESkzMzsKOAB4Jicw68AC4BVwHagGpgEvIOg93kyMAv4CfAqsHTwaiwiIiKgwCwiIlJWZjYeeAyYHh56DbjG3Z8o8p4YcCnwt8BpZa+kiIiIRFJgFhERKa+fsDcs/3/gIndvKfYGd88AvzWzB4DPA+3lraKIiIhE0SrZIiIiZWJmpwMXh093AR/uLSzn8sDt7r4i4tzZ1acXhc/HmtmNZvaCmb0dvnZ33nummdk1ZvYrM1thZrvNLGlmjWa2yMz+zsxG9+HznWFm95rZJjPrMLMNZvaAmV1Y6jlyzjXOzL5uZs+Y2bawXlvM7DEzu9bMqvt6ThERkX2lHmYREZHy+WLO4zvdfUM5LmJmJxHMkT6sSJlzgIWARbw8ETg7/LnBzD7g7k/1cs2bgBvzzjc1/LnUzG4Hfl1i/S8F7iZYLTzX5PDnXODLZvZ+d19SyjlFREQGggKziIhIGZiZEQS9rJ+V6VLjgQcJgup/A78H3gamAJ5Trpog3L4OPE6wfVV2sbHDgPcTLDg2EXjYzE5w93VRFzSzvwG+Gj514D7gUYKh4/OATwHXhHUoyswuJgjW8fDQn4H7gQaCoewfA44DpgFPmNkp7v5Gb+cVEREZCObuvZcSERGRPjGzuQThFII9lke7e2oAz5/7F3iaYLj3r4qUnw6McvdXi5T5MEGwjwF3u/uVEWWOJPhcVUASeL+7P5JXZjJBKD865/A33f0beeXqgNUEq4MDfNnd/yOvTAL4PvBX4aHF7v6/Cn0GERGRgaQ5zCIiIuVxaM7j9QMZliPcWiwsA7j7W8XCcljmHvb2hF9uZhURxa4lCMsA/5IflsPzbAUuJwjyxVzJ3rD8y/ywHJ4rBXwWeDk8dLKZndfLeUVERAaEArOIiEh5jM95vLO3wmaWylnIK/9nUS9vv22fatrd0+GfNcDxEa9fFv7ZWey67v4K8KdervWBnMf/VuRcaeA7Bd4nIiJSNgrMIiIiw9smd19bamEzO9XMbgtX094erkbdFc6BH+QUn5r33kkEc4kBlrh7Uy+XW1CkHgZkh1a/7e4v9XKuP+Y8PrWXsiIiIgNCi36JiIiUx/acx/mrP0f5AN2/yJ4E/N8S3replMqYWSXwQ4JFtEo1Ku957jDz1SW8v1iZUUBt+HhVbydy921m1gyMBg4p4doiIiL7TIFZRESkPDbnPJ5mZoli85jd/aHc52Z2eInXaS+x3PfYG5b3EKyo/QJB4G5l73zj+QTzlGHvytVZI3Met5VwzdYir9WVWC7XboLAXNdbQRERkYGgwCwiIlIey4EmYBxBT+pxwJDsIRyG76vDpxuBs919TYGyxbaC2p3zuLZgqb1GFHmtpcRyubKBvaVoKRERkQGiOcwiIiJl4MG+jblzeD86VHUh6DW28PG/FgrLoelFXsvtNT+qhOsWK7OLvb3UM3s7kZlNJOhdzq+HiIhI2Sgwi4iIlM93cx5/qpfe23Kqz3n8Zi9lLyj0grs3Am+FT08ws3G9nOvcIudygiHhABPM7IRezvXunMfP91JWRERkQCgwi4iIlIm7P00wVxiC3tF7zGxkkbeUS+584yMLFTKzS4neSirXb8M/K4HPFznXsXQPuVF+nfP4b4qcKw7cUOB9IiIiZaPALCIiUl4fZ2+v7JnA02Z2Vgnve9cA1uGFnMdfNrOx+QXM7FTgRyWc63aCRcMAvmZmPUKxmdUD99Jz0bB8dwON4eOPmNkXIs4VD695YnjoBXcvuF2ViIjIQNKiXyIiImXk7tvN7DzgQWAuweJfT5jZy8BCYCXB4mAGjA/LXED3+b8lbR1VxDPAi8A7gMOBN8zsB8AKoIZgjvPlYR1+AXykyOd508y+Dvw7UAU8Ymb3AY8CHQQ91J8CJhD0Rl9W5FwtZnYl8BBBuL7FzC4D7ge2Eez5/DH29nq3EHwBISIiMigsmEIkIiIi5RQOxf4n4K8pbYVpgGXAt4Cfe95f2GaWff6Eu59TwvWPIgjohxUosgf4HJAB7gqPXenudxc4378AX2HvYmL5bgN+AzwePv+mu3+jwLkuBX7M3kW9oqwHLnP3l4qUERERGVAaki0iIjII3H23u3+JoIf3s8CvCHqXtwMpoBlYCzwCfBM4xd2Pcfef5Yflfl5/NcGw5m8RbHnVQbBN1AqCIc8nuXspQ7Kz5/sqcFb4ObYASYKe8IeAi929x/DqIud6kGBu9T8AzxH8TjoJhmsvBK4DjlZYFhGRwaYeZhEREREREZEI6mEWERERERERiaDALCIiIiIiIhJBgVlEREREREQkggKziIiIiIiISAQFZhEREREREZEICswiIiIiIiIiERSYRURERERERCIoMIuIiIiIiIhEUGAWERERERERiaDALCIiIiIiIhJBgVlEREREREQkggKziIiIiIiISIT/AQAmNArrysU4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_pdf_fb = plt.figure(figsize=(16,9))\n",
    "assi = fig_pdf_fb.gca()\n",
    "assi.plot(bins_FB[:-1], pdf_FB, marker = 'o', linestyle='None', ms = 5)\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('PDF Facebook', size = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'PDF Facebook')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_pdf_fb = plt.figure(figsize=(16,9))\n",
    "assi = fig_pdf_fb.gca()\n",
    "assi.loglog(bins_FB[:-1], pdf_FB, marker = 'o', linestyle='None', ms = 5)\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('PDF Facebook', size = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CDF in linear e logscale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CDF Facebook')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf_FB = ECDF(FB_degree)\n",
    "x_fb = np.unique(FB_degree)\n",
    "y_fb = cdf_FB(x_fb)\n",
    "fig_cdf_fb = plt.figure(figsize=(16,9))\n",
    "assi = fig_cdf_fb.gca()\n",
    "assi.plot(x_fb,y_fb,marker='o',ms=6, linestyle='None')\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('CDF Facebook', size = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CDF Facebook')"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf_FB = ECDF(FB_degree)\n",
    "x_fb = np.unique(FB_degree)\n",
    "y_fb = cdf_FB(x_fb)\n",
    "fig_cdf_fb = plt.figure(figsize=(16,9))\n",
    "assi = fig_cdf_fb.gca()\n",
    "assi.loglog(x_fb,y_fb,marker='o',ms=8, linestyle='--')\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('CDF Facebook', size = 30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'CCDF Facebook')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VnNFpABhahOeYEJ4BAKgc5RqqGZ0GgMIhPA+Smc2WNLulpeXslStXFrscAABQQOUSqk3SWVPHa+7MCYRoAIgJ4TkmjDwDAFCdyiFQM8UbAAaP8BwTwjMAAOhra0da19y3Urc8vEbtXT3FLmcnhGkAyB/hOSaEZwAAkEspBmqCNACEQ3iOCeEZAABE0Ruof/zQc+pIF//nLTYdA4D+EZ5jQngGAACDVUoj02w6BgA7IzzHhPAMAADiVgqbkRGiASCD8BwTwjMAABgKxRydHjW8TqcfyZRuANWJ8BwTwjMAACiGYq2Zrk/U6IwpbDQGoHoQnmNCeAYAAMVWjCDNtG4A1YLwHBPCMwAAKDVDGaYJ0QAqHeF5kMxstqTZLS0tZ69cubLY5QAAAAxoa0daV9y7QjctWVPQ5zClG0AlIjzHhJFnAABQLoZq0zFGowFUEsJzTAjPAACgXBV6RJoQDaASEJ5jQngGAADlrjdE37xkjQrxkx8hGkA5IzzHhPAMAAAqxdaOtOYtflbzH16jTdvTsd+fEA2gHBGeY0J4BgAAlah3ffTNS1arszveexOiAZQTwnNMCM8AAKDSFWptNCEaQDkgPMeE8AwAAKoFIRpANSI8x4TwDAAAqk2hpnQTogGUIsJzTAjPAACgmhViNJoQDaCUEJ5jQngGAAAoTIiuT9To7s8fpeamkbHdEwDyFTY81wxFMQAAAChvqWRCXz35ED156fE6a2pzLPdsT/fo6O8t0prXtsRyPwAoJEaec2DkGQAA4K3iHomuT9TojCnjdd6MFqZyAxhSTNseJDObLWl2S0vL2StXrix2OQAAACUp7hDNemgAQ43wHBNGngEAAHKLO0SPGp7QgrnTNaahPpb7AcBAWPMMAACAIRP3muhN29Oa9K2Fuux3T2lrR3rwBQLAIDHynAMjzwAAAPmLcySaqdwAComRZwAAABRN35Ho0yfvN6h7uaQblzynKd9ZqPWb2+MpEADyRHgGAABAwaSSCX39lMP0wAXTlRjkT55M5QZQTIRnAAAAFFxz00g9fNGxGj1i8NOuGYUGUAyEZwAAAAyJMQ31WnLhsTp3+v4aVju4ezEKDWCosWFYDmwYBgAAUBjrN7fruCsXadP2wYXf+kSN7v78UWpuGhlTZQCqCRuGAQAAoKSNaajXQxcdO+ijrdrTPTr6e4v0tdufYBQaQMEw8pwDI88AAACFF9fRVoxCA8gXI88AAAAoG71HWz365WM1anj0TcUYhQZQKIRnAAAAlIy4pnLPX7qWHbkBxIrwDAAAgJIS1yg0O3IDiBPhGQAAACUprlHoG5c8p9nXPEiABjAohGcAAACUrN5R6CcvPV6nT94v8n1Wv7ZNp934CAEaQGSEZwAAAJS8VDKhr59ymB64YLrqExbpHn95vo110AAiIzwDAACgbDQ3jdTyrx4XeRR60/a0Jn97oda8tiXmygBUOsIzAAAAykrfUejaCIPQ3S4d/b1FBGgAeSE8AwAAoCw1N43U0ouj78h9DAEaQB4IzwMws9lmdkNbW1uxSwEAAMAABrMjtyszAv21259gIzEAOZm7F7uGktba2urLli0rdhkAAADIYf3mdk27/H61p3vy7jtqeEIL5k7XmIb6AlQGoJSZ2XJ3b83VjpFnAAAAVIQxDfVa/KVjIu3GvWl7WtMuv5+duAEMiPAMAACAipEJ0DMirYNuT/do2uX3EaAB9IvwDAAAgIrSuw46ynFW7WnXpG8tZB00gLcgPAMAAKDi9D3OKsJpVpq/dK1OuvpBAjSAHQjPAAAAqFjNTSN1/wXTI/Vd8/o2nXbjIwRoAJIIzwAAAKhwzU0j9cAF01UbYQj6L8+3acp3FrIOGgDhGQAAAJWvuWmkll58bKSNxDZtT2vytxdqzWtbClAZgHJBeAYAAEBV6N1I7PB9G/Pu2+3S0d9bpKdebCtAZQDKAeEZAAAAVSOVTOjWT75P+zeNiNT/xKuXsBM3UKUIzwAAAKgqqWRCd372qEhHWUmZnbhZBw1UH8IzAAAAqk7fo6xqI/xEvGl7Wkddfh8BGqgihGcAAABUreamkVp60bGqT+S/FXdH2gnQQBUhPAMAAKCqjWmo1+IvzYi0E3dH2tmJG6gShGcAAABUvd6duKOsg+7diZsADVQ2wjMAAACgN9dB33X+1Ej9j/3vRUzhBioY4RkAAADoY+LejZmNxPJcBt3t0nFXLuIYK6BCEZ4BAACAXTQ3jdTSi49VMs+NxDZtT+u0Gx8hQAMViPAMAAAA9GNMQ70e/NKMvAP0X55v4xxooAIRngEAAIAB9AbofHfi3rQ9zRRuoMIQngEAAIAsou7EvWl7Wqf+aCkBGqgQhGcAAAAgh96duE+fPC6vfn97YbOOZAo3UBEIzwAAAEBIF846KO8p3G3b0zrq8vsI0ECZIzwDAAAAIaWSCS2YO131ifx+jO5IuyZ9a6Eu+91TTOMGyhThGQAAAMjDmIZ6Lf7SMarPcxduSbpxyXOafc2DBGigDBGeAQAAgDxlAnT+x1hJ0urXtum7dz9dgKoAFBLhGQAAAIig9xir2vzzs+YvXaenXmyLvygABUN4BgAAACIa01CvhV+cHqnviVcvIUADZYTwDAAAAAxCc9NIPXDB9Egj0CdevURrXtsSf1EAYldV4dnM9jezm8zs18WuBQAAAJWjuWmkll58bKQ10Mf+9yKOsQLKwJCHZzMbE7HfzWa23sye2OX9WWa2wsxWmdlF2e7h7qvd/awozwcAAACy6V0Dne850N0uzoEGykDe4dnMvhX1YWa2l6T7Ina/RdKsXe5XK+laSSdImijpVDObaGaHmdnvdnlFCu0AAABAWGMa6vXQRcfqrKnNefXrSLuOu3IRR1gBJSzKyPNFZnZ+vp3MbE9lgvPBEZ4pd18sacMub0+StCoYUe6UdJukU9z9cXc/eZfX+jxqPcfMlpnZsldffTVKuQAAAKhSqWRCXz35ED1wQX4biW3anuYIK6CERZ22fYWZnRq2cTDqe78iBucs9pH0fJ+vXwjeG6iOPczsekmHm9nFA7Vz9xvcvdXdW/fcc8/4qgUAAEDVaG4aqbvOn5pXH46wAkpXlPD8t6DfLWZ2fK7GQXC+T5lp1S7pBxGeOeDt+3nPB2rs7q+7+7nufoC7fzvGOgAAAIC3mLh3Y94BmiOsgNIUJTzPkvScpDpJvzazSQM17Cc4X+vun4tS6ABekLRvn6/HSnoxxvsDAAAAgzJx70adPnlcXn1OvHoJG4gBJSbv8OzuL0s6XtJ6SSlJvzezA3dtFwTnhXozOF/n7nmvlc7hMUnvMLPxZjZM0kck3RHzMwAAAIBBuXDWQXnvwn3WTx4rUDUAooi05tndVymzw/UbkvaQtMDMdqw1DjYHWyjpEGWC8w/d/bODKdTMfiFpqaQDzewFMzvL3dOSzpN0j6SnJf3K3Z8czHP6PG+2md3Q1saUGQAAAAxOKpnQgrnT8zoH+vF/bNaa17YUsCoA+TD3AZcI5+5sdoykuyQNk/SMpKmSEspM1e4Nzte7+2cGX2pxtLa2+rJly4pdBgAAACrA+s3tmvztheoO+SN4rUlLLz5WYxrqC1sYUMXMbLm7t+ZqF3W3bUmSu98v6ePKhOSDJN2tnYPzvHIOzgAAAECcxjTUa+EXwx9h1e3i/GegRAwqPEuSu/9amanTJqlVmeAsST9y908P9v4AAABAJcn3CCvOfwZKw6DDsyS5+/WSLlEmQLukG9z93DjuDQAAAFSaiXs36qOT9s3dMMD5z0DxDbjln5ldF+F+bZJqJXmW/s5UbgAAAFS7r5w0Uf/z53+oI90Tqv2JVy/RXedP1cS9GwtcGYD+DLhhmJn1KDOKHDt3ry3EfeNkZrMlzW5paTl75cqVxS4HAAAAFWjNa1t09PcW5dXngQumq7lpZIEqAqpPXBuGWQFeZcHd73T3cxob+c0eAAAACqO5aaROnzwurz7HX7WYDcSAIsh2UvvBQ1YFAAAAUKUunHWQ7vjrP7Rpe7hA3JF2fffup/X1Uw4rcGUA+howPLv7iqEsBAAAAKhGqWRCC+ZOz+v85/lL1+nMKeOZvg0MoVh22wYAAAAQXb7nP0vSMd9bpDWvbSlQRQB2RXgGAAAASkC+5z+7pKMJ0MCQiSU8m1mDmR1rZqeZ2aeC6wwza4jj/sVgZrPN7Ia2Ns7TAwAAwNDI9/xniQ3EgKEyqPAcBOQFkjZIWiDpJ5J+EFzvlbTBzO42s2MGXekQY7dtAAAAFMNXTpqoxuHZ9vXdWe8GYgAKK3J4NrOrlAnIxwb36e9YqhpJMyX90cyuHHS1AAAAQIVLJRO6d+501eZxyOv8pev01IvMmAQKKVJ4NrPLJZ2vN0Py85J+LOliSZ8NrjdLWtenzflm9t0YagYAAAAqWpQNxE68egnrn4ECyjs8m9k7JX1BmT0K2iR9XFKzu5/l7t9192uD6yfdvVnSaZI2KhOgv2BmHEgHAAAA5NDcNFKnTx6XV59ZrH8GCibKyPM5Qb8uSTPd/WfuPuCJdO7+c0nHBe1rJJ0bpVAAAACg2lw466C81j+3s/4ZKJgo4XmGMqPOt7r7sjAd3H25pJ8qM/pcdpuHAQAAAMXQu/45mQi/AHr+0nVM3wYKIEp43ie4Ls6zX2/7fbK2KhEcVQUAAIBSMKahXg9+aUZeG4gdf+Uipm8DMYsSnnvnjXTl2a+3ffh5J0XEUVUAAAAoFfluINbRLaZvAzGLEp5fCa7/lGe/d+3SHwAAAEBIzU0jddf5U0O3n790ndZvbi9gRUB1iRKelyqzdvlMM2sK0yFod5Yya6WXRngmAAAAUPUm7t2oZCL8j/BHXX4fARqISZTw/LPgurukP5pZS7bGZra/pAWS9gjeujXCMwEAAABIOnPK+NBtO9KumVc8wPpnIAZ5h2d3v0vSPcqMPh8m6XEzu83MzjSzqWZ2eHA9w8x+LukJZaZsu6R73P0Pcf4LAAAAANXkvBktat5jeOj2be3duuz3TxawIqA6WJYjmgfuZLabpD9Kek/wVrab9O4L+Kgy50K/kfcDi6i1tdWXLQt1IhcAAAAwJLZ2pHXM9+7X+jc6Q/e56/ypmrg3m+ECuzKz5e7emqtdlGnbCgLwFEmXStqgTEAe6PW6pEskTS234AwAAACUolQyod999qi8+px49RLOfwYGIdLI8043MKuXNF3SJElvl7SbpDckvaTMaPMidy/bXQoYeQYAAECp+trtT2j+0rWh2ycTpj9/9TilkmVxeiwwJMKOPA86PFcqM5staXZLS8vZK1euLHY5AAAAwFts7UhryncWatP28BuCnT55P339lMMKWBVQXgo6bbsauPud7n5OYyPrQgAAAFCaUsmEFsydrlrL3bbX/KXrmL4NRBB7eDaz8Fv/AQAAABiUMQ31WvjF6Xn1mfX9Bzm+CsjToMKzmdWa2UfN7Ndm9ryZdUraYmadZrYueP8jZlYbU70AAAAAdtHcNFJ3nT81dPv2rh7NW/xsASsCKk/k8Gxm75X0jKSfSvqQpL0lJZTZYTshaZ/g/Z9JetrMJg26WgAAAAD9mrh3oz46ad/Q7W9ZsrqA1QCVJ1J4NrPpku6XtL/ePJKqU9IKScuDa2efz1okPWBm02KoGQAAAEA/vnLSRDUOD7eT9uaOHtY+A3nIOzyb2W6SfiWpXplgvFDSTEm7ufvB7v4edz9Y0sjg/XuDrvWSfmlmI2OpHAAAAMBOUsmE7p0bfv3z8VcuYu0zEFKUkedzJe0pySVd5u4z3X2hu+/0X527dwfvHy/pG8HbY4L+AAAAAApgTEO9Tp88LlTbjm7pu3c/XeCKgMoQJTyfHFz/5O5fC9PB3S+R9IgyI9WzIzwTAAAAQEgXzjoodNv5S9dp/eb2AlYDVIYo4fkgZUadb8uz3y/69AcAAABQIKlkQq3jRodufxzTt4GcooTnUcH1xTz7vRxcGyM8EwAAAEAervvYEaHbbtqeZvo2kEOU8LwxuI7Ns9/ewXVThGcOOTObbWY3tLW1FbsUAAAAIG9jGurzOvt5/tJ17L4NZBElPD+jzNrlU/Ps91Flpns/E+GZQ87d73T3cxobGSgHAABAeZq4d6PeOTb8z7NM3wYGFiV08jiRAAAgAElEQVQ8/y64tprZt8J0MLNvSHpP8OUdEZ4JAAAAIIIbT28N3bazW7rs908WsBqgfEUJzz+U9Erwzxea2UIzO97MhvVtZGZ1Znacmd0r6cvB2+slzYteLgAAAIB85HN0lST94tEX9NSLLF0EdpV3eHb3rZL+XVJn8NbRku6S9IaZrTKz/zWzVZK2SPqDpBnKTPPukPRvQX8AAAAAQ+TCWQfJ8mh/4tVLOL4K2EWUkWe5+2JlQvOzygRjk1QnabykQ4NrXZ/PVkqa5u5LBl8yAAAAgHykkgmdNXV8Xn3O+sljBaoGKE+RwrMkufufJB2szCj0LyU9p8zocu8o83PB+x+WNNHd+a8PAAAAKJK5MyeocXgidPvH/7GZ6dtAH+bu8d7QrMbde2K9aRG1trb6smXLil0GAAAAMGjrN7dr8rcXqjuPCPDABdPV3DSycEUBRWZmy9095856kUeeB1JJwRkAAACoJGMa6rXwi9Pz6nPsfy9i/TOgAoRnAAAAAKWruWmk7jp/auj23c75z4AUQ3g2sxFm9gEz+4aZ3WRmvwyu3wjeHxFHoQAAAADiMXHvRn100r6h22/antY1960sYEVA6Qu/Y8AuzGy4pP+SNEfSblmavmFm10u61N23R30eAAAAgPh85aSJ+vmjz4duf/OS1brohIMLWBFQ2iKNPJvZWEl/lnSBpAa9eSRVf68GSf9H0nIz2yeGmgEAAAAMUiqZ0OmTx4Vu39ktpm6jquUdns1smKQFkg5UJhxvlXSzpNMkvU/SYcH1NEk3SdoStDtI0oKgf8kzs9lmdkNbG9vzAwAAoDJdOOsgNdSHn4x6yR2PF7AaoLRFGXn+rDJB2CU9JOlAd/+ku//c3R919yeD68/d/eyg7ZKg70GSzoul8gJz9zvd/ZzGxsZilwIAAAAURCqZ0B+/MF3JhIVq/+vlL3L2M6pWlPD878H1BUknuPuL2RoHn58oqXdBxakRngkAAACgAMY01OvBL80I3X72NUuYvo2qFCU8T1Bm1Pkmd98SpkPQ7iZlpm9PiPBMAAAAAAUypqFen5w6PlTbbpeuuHdFgSsCSk+U8Nw7p+OZPPvl2x4AAADAEJk7M/wY101L1jD6jKoTJTyvC675Lgbubb8uaysAAAAAQy6VTOjwfUeFbs+5z6g2UcLzHcqMPs/Os98HlJnufXuEZwIAAAAosHkff3fotjc9uLqAlQClJ0p4vlrSK5JOMrNPhOlgZv8h6SRJLwf9AQAAAJSYMQ31+p9zJ4dq29UjrXkt1BZIQEXIOzy7+yvKjCK/KOlGM7vRzCb219bMDjazHymzWdgLkj7g7usHUzAAAACAwnl38+5KJsLFhOOvWszaZ1SNAU9EN7O7cvR9SdI+ks6QdIaZrZe0StI2SSMktUgas0v7b5iZu/tJg6oaAAAAQMGcOWW8frjo2ZztOtKuK+5doa+efMgQVAUUl7l7/x+Y9SizRjnUfQZo2+/77l4btsBia21t9WXLlhW7DAAAAGDIbO1I69BL7gkdBp689HilkgOOywElzcyWu3trrna55mNYyNdAbft7HwAAAEAJSyUTOivkuc8S5z6jOmQLz8ML9BpRgH8PAAAAADHK99zn9ZvbC1gNUHwDhmd37yjUayj/BQEAAADkL5VM6PTJ40K3P+7KRWwehooW5agqAAAAAFXgwlkHhV53uWl7Wtfct7Kg9QDFRHgGAAAA0K981z7fvGR1AasBimvQ4dnM9jSzD5vZJWZ2lZldF0dhAAAAAIpv7swJoUefO7vF1G1UrMjh2cx2N7ObJT0v6ReSvibps5Lm9NP2GjPbbGZPRq4UAAAAwJDLd/T5u3c/XcBqgOKJFJ7NbLykv0j6D0nDlPsoqnmSRko6yMymRXkmAAAAgOKYO3OCRg0Pd47z/KXr2HkbFSnv8GxmCUm/k7SvMmH5/0o6RdLcgfq4+xOSngq+nJV/mQAAAACKJZVMaMHc6aHbn/PTZQWsBiiOKCPPn5B0sCSX9Dl3/3d3v1PSmhz9HlAmbL83wjOHnJnNNrMb2trail0KAAAAUHRjGur1yZDTt//6fBtrn1FxooTnfw2ui9z9mjz69a53Dn/aehG5+53ufk5jY2OxSwEAAABKQj6bh3FsFSpNlPD8LmVGnX+bZ7/Xg+seEZ4JAAAAoMjy2TyMY6tQaaKE592D64tD8CwAAAAAJWTuzHATSTm2CpUmSqDdHFwb8uy3X3B9PWsrAAAAACUrlUzo9MnjQrVl6jYqSZTwvCa4vifPfr27bD+VtRUAAACAknbhrINCtbvl4TWFLQQYQlHC8x+V2TX7I2YWav2ymR0j6Whl1koviPBMAAAAACUilQx35nN7V0+BKwGGTpTwPE9Sl6RGSb8ys5HZGpvZVEm3BV9ukXRThGcCAAAAKCH1deGixFMvcvQrKkPe4dnd10j6ljKjz0dLesbMLlGfadxm1mpmnzCz25U533lPZUadL3T3TYMvGwAAAEAxnXFkuF23T7x6idZvbi9wNUDhRdoB290vVWYE2iTtLelrki5WJiBL0p+UGWE+uc8zLnf36wdVLQAAAICScN6MltBtz/rJYwWsBBgakY+PcvdPSTpV0gplQvRAr1WS/s3dLx50tQAAAABKQiqZ0KjhdaHaPv6PzYw+o+wN6uxld/+lux8s6X2S/o+kayXdKul6SV+VNE3SQe7+P4MtFAAAAEBpOf3IcEdWSYw+o/yF2yYvB3d/VNKjcdwLAAAAQHmYM+0A3bB4dahdtR//x2Zt7UiH3qkbKDWDGnkGAAAAUL1SyYTu/txRodtfce+KAlYDFBbhGQAAAEBkzU0j9dFJ+4Zqe9OSNVrz2pYCVwQURt7h2czGmtmTweuEkH1OMLOnzOxxMxuTf5kAAAAAStVXTpoYuu3R31vE5mEoS1FGnj8m6WBJYyTdG7LPvZL2kDQx6A8AAACgQqSSCb1zbGPo9mwehnIUJTwfq8x5zr9z93SYDkG7O5U5umpmhGcCAAAAKGE3nt4aum3v5mFAOYkSng8Jrvn+umh5cD00wjMBAAAAlLAxDfU6fXL4o6vYPAzlJkp4bgqu6/Ps92pw3TPCMwEAAACUuAtnHaTRI+pCtb1pyRpGn1FWooTnjuA6PM9+ve1zHwIHAAAAoOykkgnd8/lpodt/9+6nC1gNEK8o4bl3xPmwPPv1tn81aysAAAAAZWtMQ33ozcPmL13H6DPKRpTw/IgyG399xMyGhelgZklJpyqz0Rhb6wEAAAAVLJ/Nw1j7jHIRJTz/NrjuI+kHIfv8IGgvSb+J8EwAAAAAZSKfzcNuWrKGc59RFqKE599Iejz457PM7B4z6/dXS2b2HjNbIOlMZUadn5Z0W6RKAQAAAJSNC2cdFLrtcVcuYvo2Sl7e4dndXdKHJW0O3nq/pD+Z2Utmdp+Z3RFcX1JmivexykzzbpP0L0F/AAAAABUslUzo8H1HhWq7aXta19y3ssAVAYMTZeRZ7r5C0lRJK5UJxiZpL0nTJZ0UXPfq89kzkqYG/QAAAABUgXkff3fotjcvWV3ASoDBixSeJcndn5R0qKRPSrpP0na9GZZN0jZJCyWdIemd7v7UoKsFAAAAUDbGNNSHbtvZLaZuo6RFDs+S5O5pd7/Z3d8vaTdJYyS1BNcGd5/p7j9xd/4rAAAAAKpQ67jRoduy8zZK2aDCc1/u3uPur7n76uDaE9e9AQAAAJSn6z52hCxkW3beRimLLTyXCzP7oJn9yMxuN7Pjil0PAAAAUMnGNNTr/gumh27PztsoVWUVns3sZjNbb2ZP7PL+LDNbYWarzOyibPdw9//n7mdL+oSkfy9guQAAAAAkNTeN1Cenjg/Vlp23UapssCdHmVmTpPdIGiupQVJtrj7ufnnEZ02TtEXSfHc/NHivVtLfJc2U9IKkxySdGtTx7V1ucaa7rw/6/bekn7n7n7M9s7W11ZctWxalXAAAAACBrR1pHXLJPaHaJhOmFZedWOCKgAwzW+7urbnaJQbxgHcqE06Pl0IvY+gVKTy7+2Iza97l7UmSVrn76qCu2ySd4u7flnTyrvcwM5P0HUl/GCg4m9k5ks6RpP322y9KqQAAAAD6SCUTqk/UqD2de2ukjrRr/eb2vHbrBgot0rRtMztJ0iOSZgX3sCwv9fN1nPaR9Hyfr18I3hvIZyW9X9K/mtm5/TVw9xvcvdXdW/fcc8/4KgUAAACq2BlTwk3dlqSZVzzA2meUlLzDs5ntKennkuoldSgzivzB4GOXdKmkf5X0RUkL+rw/X9IJkuKef9FfIB9wLrq7X+3u73b3c939+phrAQAAADCA82a0aNTwcJNf29q79d27ny5wRUB4UUaeP63Mmc4u6YPufpG739Hn87+4+2/c/Up3nyVpqqQXJX1c0iHuHm6hQ3gvSNq3z9djg+cBAAAAKCGpZEIL5k5XMhFuQur8pesYfUbJiBKee493WuzuC7K2lOTuS4M+nZK+Y2ZHRHhmNo9JeoeZjTezYZI+IumOHH0AAAAAFMGYhno9+KUZoduz8zZKRZTwPEGZUeeBRpDrdn3D3Z+W9DNlNiibE+GZkiQz+4WkpZIONLMXzOwsd09LOi+o52lJv3L3J6M+o8+zZpvZDW1tbYO9FQAAAIA+xjTUq74uXBS5YfFqRp9REqKE58bgum6X9zuDa2qAfg8G16MjPFOS5O6nuvvb3b3O3ce6+03B+3e5+wR3P8Ddvxn1/rs86053P6exsTF3YwAAAAB5OePIcJuH9bh0yrVLCNAouijhuT247vrduzm47qv+9bbfO8IzAQAAAFSQ82a0hF77vGr9Vl1x74oCVwRkFyU8944473qG06rg+r4B+h0a4VkAAAAAKlAqmdA9n58Wuv1NS9Zo/eb23A2BAokSnv83uB6yy/sPKXNs1PFmttNnZraPpHOVWSvNin8AAAAAam4aqWQifCT51M+WF7AaILso4fkBZULyrlvk/USZcFwrabGZXWpmp5vZpZL+ojfXSv86Yq1Dig3DAAAAgMI7c0q4tc+StHztpgJWAmQXJTzfLqlHmeOhJvW+6e5PSLpGmWA9StJ/SvpxcN0jaPaMpKsGU/BQYcMwAAAAoPDOm9Gi0SPecmDPgNg4DMWSd3h29/WSDpN0hKTndvl4rqRvKrPztu3yukvSMe6+bTAFAwAAAKgcvWufR49IhGr/3bufLnBFQP/M3eO/qdlukqZK2kvSNknL3H117A8aAq2trb5s2bJilwEAAABUtK0daR36X/coTDx54ILpam4aWfiiUBXMbLm7t+ZqF2Xadk7u/oa7/8Hdb3H3X5VrcAYAAAAwNFLJhM4Kuf75/VcsYudtDLmChGcAAAAAyNfcmRNCtUv3SMdftYj1zxhSWcOzmb0zeO02VAUBAAAAqE6pZEL1deHG9zZuS+uKe1cUuCLgTbm+M/+qzDFTxwzUwMymBa/dY62syDiqCgAAABh6ZxwZ/uiqm5asYfo2hkwc07YfkHS/MhuEVQyOqgIAAACG3nkzWlSfCB9TjruS6dsYGqx5BgAAAFAyUsmE7v78UaHbb9rO9G0MDcIzAAAAgJLS3DRSD1wwPXT7m5esYfQZBUd4BgAAAFBymptG6pNTw61/dknX3LeysAWh6hGeAQAAAJSkuTMnyEK2vWHxakafUVCEZwAAAAAlKZVM6KyQo889Ls1b/GyBK0I1IzwPgKOqAAAAgOLLZ/R5/sNrClkKqhzheQAcVQUAAAAUXz6jz5u2M20bhZMI2e58M/tgDG0kyd39rJDPBQAAAFDl5s6coJsfek49nrvt+s3tGtNQX/iiUHXChudjsnzmIdrsivAMAAAAIJRUMqE50w7QDxflXtN8/FWLtOTCY5VKho06QDhhpm1bzC8AAAAAyMt5M1pCtdu4Lc2xVSiIXL+OOWNIqgAAAACALFLJhBI1pnSIuds3L1mti044eAiqQjXJGp7d/SdDVQgAAAAAZPOJI5t145Lncrbr7Ja2dqSZuo1Ysds2AAAAgLIwd+YEjRpeF6rtFfeuKHA1qDaEZwAAAABlIZVMaMHcaaHa3rRkjbZ2cHQV4kN4HoCZzTazG9ra2opdCgAAAIDAmIZ61SfCxRhGnxEnwvMA3P1Odz+nsbGx2KUAAAAA6OOMKeNDtWP0GXEiPAMAAAAoK+fNaAl9Bi6jz4gL4RkAAABAWUklEzprarjR55sZfUZMCM8AAAAAys7cmRNCjT67pHmLny10OagChGcAAAAAZSef0ef5D68pbDGoCoRnAAAAAGUp7Ojzpu1prd/cXvB6UNkIzwAAAADKUj6jz7O+v5i1zxgUwjMAAACAsjV35oRQ7TZs7WLtMwaF8AwAAACgbKWSCY0aXheq7U+Xri1wNahkWcOzmZ0fvMLNhQAAAACAIXb6keNCtdu4ravAlaCS5Rp5vkrSlZIOG6iBmX0teIWbL1EmzGy2md3Q1tZW7FIAAAAAZDFn2gHaPRVu9Jl1z4gqjmnb/yXpEkkHxXCvkuHud7r7OY2NjcUuBQAAAEAWqWRCd39uWqi219y3ssDVoFKx5hkAAABA2RvTUB9q7fMtnPmMiAjPAAAAACpCmLXP7V09Q1AJKhHhGQAAAEBFmDPtgFDtWPeMKAjPAAAAACpCKplQfV3uiMO6Z0RBeAYAAABQMc44Mvcpuz9avJrRZ+SN8AwAAACgYpw3oyVnm26XPnTdQwRo5IXwDAAAAKBipJKJUO2eXb+F6dvIS7jvLOkGM7sqhjaS5O4ebiU/AAAAABRAt0vXL1qtM6eM15iG+mKXgzIQNjzvmeUzD9Gml/VpDwAAAACxq6+rCX0k1azvL9aDX5oResQa1SvMtG2L8QUAAAAABXXGkeNDh48NW7s0b/GzBa0HlSHXr1dyb1UHAAAAACXkvBktuvfpl/Xs+q2hpr3e+sg6fWHmgQWvC+Uta3h297VDVUipMbPZkma3tOTerQ8AAABA6UglE7r9M1N1zX0rdf2i1Tnbb9jaOQRVodyx2/YA3P1Odz+nsbGx2KUAAAAAyFMqmdBFJxysT03PvVexSRxbhZwIzwAAAAAq1nkzWnKuf3aJY6uQ06DDs5nVmtmeZtZkZoRxAAAAACUj7C7a1y9arfWb2wtcDcpZ3mHXzMaa2cVmdreZvS6pU9LLkl6R1GVmr5vZH8zsIjPbJ+6CAQAAACAfo0fUhWo36/uLmb6NAYUOz2Y2wsx+KGmVpMskzZQ0Wm89jmq0pOMkfVPSKjO71sxGxF04AAAAAIRx2uRxodpxbBWyCRWezeztkpZIOkfSMOU+t7n386SkcyU9GNwDAAAAAIbUnGkHaPdUuNHnny6t2gOHkEPO8GxmJulXkv5JbwbmRyV9XtJkSW+XVC9phKS9JR0paa6kx/rc5p8k/TK2qgEAAAAgpFQyobs/Ny3nxmGStHFbF1O30a8wI8+flTRFmU3oXpV0gru/z92vdvc/ufsr7t7p7u3u/rK7P+Lu33f390o6SdJryoTuKWb22YL9mwAAAADAAMY01OvcEMdWSdJRl9/H5mF4izDh+fzg+oakqe5+T9ibu/sfJB0V9DVJn8u7QgAAAACIwXkzWkK127C1i83D8BZZw7OZHS1pf2VGnS9y97wPP3P3v0u6KPhyvJlNz/ceAAAAADBYqWRCo4aHW/u8YWsXZz9jJ7lGnqcF142SfjyI5/w4uIckEZ4BAAAAFMXpR45TMhHu0KEbFq9m9Bk75PquOSK4LnL3jqgPcfd2SQ8oM3X7iOytAQAAAKAw5kw7QOP2CHeSbo+Lo6uwQ67wfKAyU7Yfy9EujN57HBjDvQAAAAAgb6lkQr/99BRNGj86VHuOrkKvXOG5Mbiuj+FZrwTXUTHcCwAAAAAiSSUT+vEnJoU6+3njtq4hqAjlIGx43hTDs9qCa0MM9wIAAACAyHrPfg6Ddc+Qcofn4cE1ju+W7uBaH8O9AAAAAGBQxjSEiyase4YU7pxnAAAAAKhIo0fknrrNumdIhGcAAAAAVezjk8flbMO6Z0hSImS7y8zs84N8VtMg+wMAAABArOZMO0BXL1xV7DJQBsKG50MKWkUJMrPZkma3tLQUuxQAAAAABZJKho1EqHZhpm1bjK+y4e53uvs5jY2NuRsDAAAAKFthggo7biPXr1mOGZIqAAAAAKBIPESbeYuf1RdmHljwWlC6soZnd180VIUAAAAAQDGMHlGXc1OwWx9ZR3iucuy2DQAAAKCqhdlxe8PWziGoBKWM8AwAAACgqs2ZdkCodkd8fYGuuHcF65+rVKjwbGb7Ba+x+T7AzMb29s+/PAAAAAAorFQyofq63NFow7YuzVu0Wh+67iECdBXK+R1iZh+T9Fzw+kyEZ3ymt7+Z/VuE/gAAAABQUB1dPeHapXu09vVtmrf42QJXhFKTNTybmUm6TJnd25dJ+nKEZ3xF0vLgHpdF6A8AAAAABTV6RF3oth3pHv106doCVoNSlGvk+VhJ45TZvf0r7h5mF/eduHuPMgFaklrM7Oh87wEAAAAAhXTa5HFKJsJvCbVxWxdTt6tMru+ODwTXVe7+x6gPcfd7Ja0Kvvxg1PsAAAAAQCHMmXaAxu0xIq8AzdTt6pLrO2OSMqPOf4jhWX9QZur2pBjuBQAAAACxSSUT+u2np2jO9P21e2pYqD5M3a4uucJzc3BdEcOzngmu42O4FwAAAADEKpVM6AszD9SfvzpTT156fM72G7d1DUFVKBW5wvOo4PpqDM/qvceorK0AAAAAoMhSyYQsRDvWPVePXOG5I7iOjOFZqeDaGcO9AAAAAKCgwuyWzJnP1SNXeO4dLR4bw7N67/FaDPcCAAAAgIIKc3wVZz5Xj1zheZUym3wdE8OzZgTXlTHcCwAAAAAK6uMhjq/izOfqkSs8Lwyu08zsoKgPMbODJU1XZubDfVHvAwAAAABDpff4qlw487k65ArPv5XUE7S71sxq832AmSUkXRvco0fSb/K9BwAAAAAMtd7jq+rrcp/9zNTtypf1u8DdV0n6hTJTt4+WdJuZ7Rb25kHb24K+LumXwT0BAAAAoOSlkgmdM23/nO1ufWTdEFSDYsr9KxTpS5JeDP75nyU9YWbnm9keA3Uwsz3M7HOSHpf0oeDtl4N7AQAAAEDZmDPtgJxtNmztZOp2hcsZnt39JWUC8ObgrbGSrpS03sxWmNnvzexnwev3ZvaMpPWSrpC0rzKj1pslfcjdX+znEQAAAABQslLJRKidtzm2qrKFGXmWuz8m6T3KjCRbn1eLpFmSPhK8Zkl6xy5tHpf0Hnd/NO7iAQAAAGAohNl5m2OrKluo8CztWP98hKSPSXpUmc2/bIBXT9DmY5IOd3eOpwIAAABQtsLsvM2xVZUtkU9jd+9RZgOxX5hZo6TJkvaR1Lv++XVl1kcvdfdNcRYKAAAAAMXSu/P2IZfck7Vd77FVqWReUQtlIPLfqLu3Sbo7xloAAAAAoGSlkgntPqJOG7Z1ZW03b/Gz+sLMA4eoKgyV0NO2AQAAAKDanTZ5XM42HFtVmXKOPJtZraQpwZed7v5IPg8ws/dJGhZ8uSSY+g0AAAAAZWfOtAN09cJVWdts3JY5tmre4md169K12ritS6NH1Om0yeM0Z9oBTOkuU2FGnj8t6f7gNSnCMyZJeiDof3aE/gAAAABQEsIcWzVqeJ1OufYhzVu0Whu2dcklbdjWpXmLVnOcVRnLGp7NrE7SfwZf3uvuV+f7gKDPH5XZhftrZsZUcQAAAABlK9uxVclEjfYZNVyr1m9RR3rnSbcd6R6OsypjuYLsSZL2DP75P7M1zOHLwfVtkk4cxH0GxcwONrPrzezXZvapYtUBAAAAoHz1Hlu1a4BOJmo0bo8RWrdh24B9O9I9rIkuU7nC8wnB9Ql3Xxb1IUHfx4MvT4pyDzO72czWm9kTu7w/y8xWmNkqM7soRx1Pu/u5kj4sqTVKHQAAAACqW++xVXOm76/dU8NkJu2eGqY50/fXbz89RW+0Z5+WvWFrJ1O3y1CulervkeSK50iquyUdFtwzilsk/UDS/N43gs3MrpU0U9ILkh4zszsk1Ur69i79z3T39Wb2AUkXBfcCAAAAgLylkgl9YeaB/R5JNTrEcVYfuu4h/fbTU9g8rIzkGnkeG1zjmJTfe4/9onR298WSNuzy9iRJq9x9tbt3SrpN0inu/ri7n7zLa31wnzvc/UhJHxvoWWZ2jpktM7Nlr776apRyAQAAAFSp07Ksie7F2ufykys8NwbX12N4Vm/wbczaKj/7SHq+z9cv/P/27j4+rrLO+/j3l04yJQMNSSgi0AaaQrnrDQuYhZZqyq7UBV5ULN6rwFZ3WaTRLrIuq64Py97iaxfXfeBWQCSgbnW7IshaoLs8yIM0S20XAsoKlEJbTSnlMa0FmpJkMr/7jzOxQ5KZk7Qz58xkPu/Xa16dOec61/klleN8e51zXdltYzKz083sGjPrlHRXvnbufqO7t7l72/Tp0/M1AwAAAIBRhp+JLoRnnytP2D0CuxWE3WIE3mnZP/M/PT9xNsY2z9fY3R9SsGwWAAAAAJTE8DPR7/q/9xZst7NvIKKKUAxhI8+vZf88qgjnGu7jtUKNJmibpBk5n4+UtL2I/QMAAADAhKWSCTWFrActl66+byOTh1WIsPD8tILR3UVFONciBaPCTxehr2GPSjrGzI42szpJ50u6s4j9AwAAAMA+CXv22SV1rtmiJdevJUBXgLDw/ED2z1PM7JR9PYmZnSrp1BF9TrSPmyWtkzTHzLaZ2cXunpZ0qaR7JW2QdKu7P7WvdY4432Izu3HXrl3F6A4AAABAlcm3HnSu/nSGycMqhLnnfURYZna4glmy6yQ9Iand3d+c0AnMDpT0sKQTJPVLanX3irm1uq2tzbu793mJawAAAABVbHd/Wp1dm3XtA5vyT86kYJ3ox68oxg2/mCgze8zd28LaFRx5zobcbxehnO0AABtQSURBVCu4dft3JN1tZkcWOmZEETMUrO98goK7Er5TScEZAAAAAPbH8HrQYZg8rPyF3bYtSV+StDH7/jRJT5rZ1WZ2spmNOt7MarL7/p+kX0qan931rKQvFqNoAAAAAKgkjSGThyUTNTz3XOZCw7O7vy5psYKZrU3SQZL+XMFkXa+b2VNmtjb7ekrS69l9lylYnsqyxy7O9gUAAAAAVSVs8rDBIWfisDI3npFnufsmSSdJuktBGB5+1Us6TtK87Ou47Lbh/coec1K2j4rBhGEAAAAAimV48rApNvb+oYwzcViZG1d4liR33+Hu50haIOlWSb3ZXTbipey+WyUtcPdz3L13ZH/lzt1Xu/uyhoaGuEsBAAAAUOFSyYRWLV+g2pCZt1eu3xphVZiIxEQPcPd1CpaMkpkdJ+kISc3Z3b2Strv7hqJVCAAAAACTQCqZUP9gpmAbJg4rXxMOz7nc/RlJzxSpFgAAAACY1Brra7Wjb7DA/roIq8FEjPu2bQAAAADA/vnw785QnseeZZI+3DbulYERMcIzAAAAAETE8kbn8e1HfAjPAAAAABCRWx7dKs+zzyXd0v18lOVgAgjPebBUFQAAAIBi21ngeedgPxOGlSvCcx4sVQUAAACg2Brra0P2M2FYuSI8AwAAAEBEls5vUTLPWs/JRI2WzpsZcUUYL8IzAAAAAESko71VLc31YwbowaGMrn1gk07+yk909X0btbs/HUOFyIfwDAAAAAARSSUTWrV8gToWzlJTKrhFu8YkMynjwaRhO/oG1blmi5Zcv5YAXUYIzwAAAAAQoVQyocsXzdHjVyzSZe+brdopNfIRU3D3pzPq6e1TZ9fmeIrEKIRnAAAAAIjJynU96k9nxtzXn85o5fqtEVeEfAjPebBUFQAAAIBSY+mqykF4zoOlqgAAAACUGktXVQ7CMwAAAADEpNDSVVNqjKWrykgi7gIAAAAAoFp1tLfqnidfUk9v39uefa4xaWqiRheeMlNX37dRK9f1aGffoBrra7V0fos62luVShLnomQ+clo3vE1bW5t3d3fHXQYAAACASWp3f1qdXZu1cv1W7ewbUGN9nS48ZYaWzmvRx777yKhgnUzUqKW5XquWLyBAF4GZPebubWHt+E0DAAAAQIyGl666fNGct22/+r6N+nVvnwZGzMadu4zVyGNQOjzzDAAAAABlaOW6nlHBeRjLWEWP8AwAAAAAZYhlrMoL4RkAAAAAyhDLWJUXwnMeZrbYzG7ctWtX3KUAAAAAqEKFlrFKJmpYxipihOc83H21uy9raGiIuxQAAAAAVaijvVUtzfWjAvTwbNsd7a0xVVadCM8AAAAAUIZSyYRWLV+gjoWz1JSqk5nUlKpTx8JZLFMVA37bAAAAAFCmUsmEOtpbNTTkWvnfW7Vz94BWruuRFIxME6Cjw28aAAAAAMrU7v60lly/Vptf3a2hjEuSdvQNqnPNFt3z5EuMQEeI27YBAAAAoEx1dm1WT2/fb4PzsP50Rj29fers2hxTZdWH8AwAAAAAZWrluh71pzNj7utPZ7Ry/daIK6pehGcAAAAAKFM7+wZD9g9EVAkIzwAAAABQphrra0P210VUCQjPAAAAAFCmls5vGbXO87BkokZL582MuKLqRXgGAAAAgDLV0d6qlub6UQE6mahRS3O9OtpbY6qs+hCe8zCzxWZ2465du+IuBQAAAECVSiUTWrV8gToWzlJTqk6mIDj/6YKjWaYqYoTnPNx9tbsva2hoiLsUAAAAAFUslUzo8kVz9PgVi3RLx3z1pzM69rADCc4RIzwDAAAAQIVoa2nUEQcfoFU/3x53KVWHf6oAAAAAgAqxZ3BIhx88VV3PvqqjP/+faqyv1dL5Lepob2UkusQYeQYAAACACrC7P60l16/VE88H8zK5pB19g+pcs0VLrl+r3f3peAuc5AjPAAAAAFABOrs2q6e3TwNDmbdt709n1NPbp86uzTFVVh0IzwAAAABQAVau61F/OjPmvv50RivXb424oupCeAYAAACACrCzbzBk/0BElVQnwjMAAAAAVIDG+tqQ/XURVVKdCM8AAAAAUAGWzm9RMjF2hKubUqOl82ZGXFF1ITwDAAAAQAXoaG9VS3P9mAG6pka65D2zYqiqehCeAQAAAKACpJIJrVq+QB0LZ6kpVSczqSlVp/fPPVRvDWa06hcvxF3ipMYq2gAAAABQIVLJhC5fNEeXL5rz223urr+45Rc65MBkjJVNfoTnPMxssaTFs2fPjrsUAAAAAMjLzPT180+Ku4xJj9u283D31e6+rKGhIe5SAAAAACBUeiijm7q26J4nX4q7lEmJkWcAAAAAmCRu/8ULeuWNfs1vbVbDAYWXtsLEEJ4BAAAAYBJITKnR3593gj5w3cO68Kb1evE3e7Szb1CN9bVaOr9FHe2tSiWJgPuK27YBAAAAYJKYNT2lg+tr9dT217Wjb1AuaUffoDrXbNGS69dqd3867hIrFuEZAAAAACaJzq7N6hsYGrW9P51RT2+fOrs2x1DV5EB4BgAAAIBJYuW6HvWnM2Pu609ntHL91ogrmjwIzwAAAAAwSezsGwzZPxBRJZMP4RkAAAAAJonG+sIzbDfW10VUyeRDeAYAAACASWLp/BYlE2PHvGSiRkvnzYy4osmD8AwAAAAAk0RHe6tamutHBWiT1NJcr4721ngKmwQIzwAAAAAwSaSSCa1avkAdC2epKVUnMymVnCKXdMl7Z7HO834wd4+7hrLW1tbm3d3dcZcBAAAAAPtkKOM659qH1Z8e0v1/sVA1NRZ3SWXFzB5z97awdvyzAwAAAABMYlNqTP/0hydo2tRagvN+IDwDAAAAwCT3rsMbfvt+cCij2ik8wTtR/MYAAAAAoApkMq6LVzyqr6x+Ou5SKhLhGQAAAACqQE2NaUZTvX7wyFY99/IbcZdTcQjPAAAAAFAlLnvfMaqvm6Kr7toQdykVh/AMAAAAAFWiKVWny37/GP1046vqevbVuMupKIRnAAAAAKgiHzutRTOb6nXDms1xl1JRmG07DzNbLGnx7Nmz4y4FAAAAAIommZiiG5a+WzOaDoi7lIrCyHMe7r7a3Zc1NDSENwYAAACACjL38Gk6aGqt0kMZvTU4FHc5FYHwDAAAAABVaM/AkM6+5r903YOb4i6lInDbNgAAAABUoQPqpuiYQw/Utx7apH9d36PX9wyqsb5WS+e3qKO9VakkcTEXI88AAAAAUIV296f19ItvaMilXXsG5ZJ29A2qc80WLbl+rXb3p+MusawQngEAAACgCnV2bdb23+wZtb0/nVFPb586u5iNOxfhGQAAAACq0Mp1PepPZ8bc15/OaOX6rRFXVN4IzwAAAABQhXb2DYbsH4iokspAeAYAAACAKtRYXxuyvy6iSioD4RkAAAAAqtDS+S1KJsaOhMlEjZbOmxlxReWN8AwAAAAAVaijvVUtzfVjBuiZTfXqaG+NoaryRXgGAAAAgCqUSia0avkCdSycpaZUncykg6YGazv/YduRrPM8grl73DWUtba2Nu/u7o67DAAAAAAoOXfXBTet16ZX3tSaz/5eVQRoM3vM3dvC2jHyDAAAAACQJJmZPnfmcXrtzQHd8+RLcZdTVib/PyMAAAAAAMbt5JmNuuuy92ru4dPiLqWsMPIMAAAAAHib4eD8Zn865krKB+EZAAAAADDK6ie2a/5VD2jbzr64SykLhGcAAAAAwCjvbmlU/1BGX7//ubhLKQuEZwAAAADAKIcffID+eH6Lfvz4Nj378htxlxM7wjMAAAAAYEzLT5+tVF1C/3jvxrhLiR3hGQAAAAAwpsZUnToWztKDz7yi53dU97PPLFUFAAAAAMjrT99ztM46/p2a0VQfdymxYuQZAAAAAJBXfV1CrdMPlCT1DVTv0lWEZwAAAABAqCtXP6UPfWudMhmPu5RYEJ4BAAAAAKFOmtmoDS++rjuf2B53KbEgPAMAAAAAQp1z/Ds1953T9M/3bdRAOhN3OZEjPAMAAAAAQtXUmD535hw9v2OPbn5ka9zlRI7wDAAAAAAYl4XHTte8WU363s9+XXXPPrNUFQAAAABgXMxMX/vQCZo2tVY1NRZ3OZEiPAMAAAAAxq2lOSVJymRcA0MZTa2dEnNF0ai627bNLGVmj5nZOXHXAgAAAACVaHAooyXXr9U/3rsx7lIiUzHh2cy+a2avmNmTI7afaWYbzWyTmX1+HF39laRbS1MlAAAAAEx+tVNqNOewg/Sv63q0bWdf3OVEomLCs6QVks7M3WBmUyR9U9JZkuZKusDM5prZ8Wb2HyNeh5rZGZKelvRy1MUDAAAAwGTy6TOOlUz6+v3PxV1KJCrmmWd37zKzo0ZsPkXSJnffIklm9kNJ57r7VyWNui3bzH5PUkpB0N5jZne5+6gFysxsmaRlkjRz5sxi/hgAAAAAMCkcfvAB+uP5LfrOw7/SsvZZOvYdB8VdUklV0sjzWI6Q9HzO523ZbWNy9y+5+6cl/UDSTWMF52y7G929zd3bpk+fXtSCAQAAAGCyWH76bKXqEvqXtb+Ou5SSq5iR5zzGmhs9dLExd19R/FIAAAAAoLo0pur0b5ecquMOmxZ3KSVX6eF5m6QZOZ+PlLQ9ploAAAAAoOqccOTB2t2f1jfuf1Y3P7JVO/sG1Vhfq6XzW9TR3qpUstJjZ6DSf4pHJR1jZkdLekHS+ZIujLckAAAAAKgeu/vTOvua/1JP795Zt3f0DapzzRbd8+RLWrV8waQI0BXzzLOZ3SxpnaQ5ZrbNzC5297SkSyXdK2mDpFvd/akinW+xmd24a9euYnQHAAAAAJNSZ9dmvbTrrVHb+9MZ9fT2qbNrcwxVFZ+5hz4iXNXa2tq8u7s77jIAAAAAoCyd/JWfaEffYN79Tak6PX7Foggrmhgze8zd28LaVczIMwAAAACg/OwsEJyD/QMRVVJahGcAAAAAwD5rrK8N2V8XUSWlRXgGAAAAAOyzpfNblEyMHS2TiRotnTcz4opKg/CcBxOGAQAAAEC4jvZWtTTXjwrQyUSNWprr1dHeGlNlxUV4zsPdV7v7soaGhrhLAQAAAICylUomtGr5Al3y3qPVMLVWpmCSsI6FsybNMlVS5a/zDAAAAACIWSqZ0EfnH6XrfrpZVy05XheeOjlu1c7FyDMAAAAAACEIzwAAAAAAhCA8AwAAAAAQgvAMAAAAAEAIwnMeLFUFAAAAAOM3bWqtvnH+iTqttTnuUkrC3D3uGspaW1ubd3d3x10GAAAAAKAEzOwxd28La8fIMwAAAABgv/Wnh7Ruc69efv2tuEspCcIzAAAAAGC//aZvUBfctF4PbHgl7lJKgvAMAAAAAEAIwjMAAAAAACEIzwAAAAAAhCA858FSVQAAAACAYYTnPNx9tbsva2hoiLsUAAAAACh7DQfU6tsfa1P7sYfEXUpJJOIuAAAAAABQ+abWTtEZc98Rdxklw8gzAAAAAGC/vTU4pPufflnbdvbFXUpJEJ4BAAAAAPtt155Bffz73ep69rW4SykJc/e4ayhrZrZL0nP7eHiDpInOODbRYw6RNDn/1xmNffk7KhflUHsUNZTiHMXqc3/62ddjuUZEqxz+O9sX5VB3VDWU6zVif/vgO0T5K4f/zvZVOdTOdwi+Q5STFnefHtrK3XkVeEm6McpjJ3qMpO64f0eV/Nqfv9+4X+VQexQ1lOIcxeoz6uvDvhzHNSK+v+NqrzuqGsr1GrG/ffAdovxf5fDfWSXXzncIvkNU4ovbtsOtjvjY/TkfJq6Sf9/lUHsUNZTiHMXqM+rrw/6eExNXqb/vcqg7qhrK9Rqxv33wHaL8VfLvuxxq5ztE9MeWw997ReO27QpnZt3u3hZ3HQDKE9cIAPlwfQBQCNeI0Rh5rnw3xl0AgLLGNQJAPlwfABTCNWIERp4BAAAAAAjByDMAAAAAACEIzwAAAAAAhCA8AwAAAAAQgvAMAAAAAEAIwvMkY2YpM/uemd1kZn8Udz0AyouZzTKz75jZbXHXAqC8mNkHs98f7jCz98ddD4DyYmb/y8xuMLPbzOyTcdcTB8JzBTCz75rZK2b25IjtZ5rZRjPbZGafz24+T9Jt7n6JpA9EXiyAyE3kGuHuW9z94ngqBRC1CV4fbs9+f/gTSR+JoVwAEZvgNWKDu39C0oclVeX6z4TnyrBC0pm5G8xsiqRvSjpL0lxJF5jZXElHSno+22wowhoBxGeFxn+NAFBdVmji14e/zu4HMPmt0ASuEWb2AUkPS3og2jLLA+G5Arh7l6QdIzafImlTdhRpQNIPJZ0raZuCAC3x9wtUhQleIwBUkYlcHyzwNUl3u/vjUdcKIHoT/Q7h7ne6+2mSqvLxUMJV5TpCe0eYpSA0HyHpx5I+ZGbfkrQ6jsIAlIUxrxFm1mxmN0g6ycy+EE9pAGKW7zvEpySdIen/mNkn4igMQFnI9x3idDO7xsw6Jd0VT2nxSsRdAPaZjbHN3X23pIuiLgZA2cl3jeiVxJdioLrluz5cI+maqIsBUHbyXSMekvRQtKWUF0aeK9c2STNyPh8paXtMtQAoP1wjAOTD9QFAIVwj8iA8V65HJR1jZkebWZ2k8yXdGXNNAMoH1wgA+XB9AFAI14g8CM8VwMxulrRO0hwz22ZmF7t7WtKlku6VtEHSre7+VJx1AogH1wgA+XB9AFAI14iJMXePuwYAAAAAAMoaI88AAAAAAIQgPAMAAAAAEILwDAAAAABACMIzAAAAAAAhCM8AAAAAAIQgPAMAAAAAEILwDAAASsrMTjczz76+HHc9AADsi0TcBQAAUI3MbLqk8ySdLulESYdIOlhSn6QdkjZIekzSHe7eHVOZAAAgi/AMAECEzOxASVdK+oSk+jGaTMu+jpJ0lqS/NrNnJf2tpB+4+1BEpQIAgByEZwAAImJmsyXdLuldOZv/R9IDkp6T1CtpqqRDJb1bwaj0YZKOlfR9Sb+U9IvoKgYAAMMIzwAARMDMmiXdL6klu+lJSZe6+5oCx9RIOlfS5yTNK3mRAAAgL8IzAADR+L72Bue1ks5y9zcKHeDuGUmrzOx2SX8maU9pSwQAAPkw2zYAACVmZqdJOjv78XVJF4QF51weuM7dN47R9/As1g9lPzea2RfM7FEzey27b8WIY2aa2aVm9iMz22hmb5rZgJm9YmYPmdlfmVnDBH6+95jZD83sBTN7y8yeN7PbzezM8faR01eTmV1hZuvM7NVsXS+a2f1m9ikzmzrRPgEAKAZGngEAKL1P57z/jrs/X4qTmNnJCp6pnlGgzemSHpRkY+yeLmlh9vWXZnaeuz8ccs6/k/SFEf0dmX2da2bXSfr3cdZ/rqQVCmYdz3VY9vU+SZ8xsw+6+8/H0ycAAMVCeAYAoITMzBSEvmErS3SqZkl3KAitd0n6T0mvSTpCkue0m6og6D4l6acKlsQanqhshqQPKpisbLqk/zCzE93912Od0Mw+K+mL2Y8u6RZJ9ym4vfx3JH1c0qXZGgoys7MVhOwp2U1dkm6T9LKC290/Kul4STMlrTGzU9z9mbB+AQAoFnP38FYAAGCfmNlcBUFVCtZwbnD3dBH7z/0/8iEFt4T/qED7FknT3P2XBdpcoCDk10ha4e4XjdGmVcHPlZQ0IOmD7n73iDaHKQjox+VsvtLdvzyi3UGSNimYZVySPuPu/zyiTULS9ZIuyW7qdvffzfczAABQbDzzDABAaR2e835rMYPzGK4pFJwlyd17CgXnbJubtXeE/CNmVjtGs08pCM6SdNXI4Jzt5yVJH1EQ6gu5SHuD860jg3O2r7SkT0p6IrupzczOCOkXAICiITwDAFBazTnvfxPW2MzSOZOAjXw9FHL4tftV6dv9LPvnAZJOGGP/kuyfg4XO6+7/I+knIec6L+f91wr0NSTpn/IcBwBASRGeAQCYHF5w91+Nt7GZnWpm12Zn5e7Nzmr926Au6Yac5keOOPZQBc8eS9LP3X1HyOkeKFCHSRq+/fo1d388pK97c96fGtIWAICiYcIwAABKqzfn/chZpMdynt7+j9uHSuocx3EvjKcYM6uT9G0FE3CN17QRn3NvRd80juMLtZkmqT77/rmwjtz9VTPbJalB0jvHcW4AAIqC8AwAQGltz3k/08wShZ57dvc7cz+b2VHjPM+ecbb7pvYG534FM3M/qiB879be55N/X8FzzdLeGbCHHZjzvm8c59xdYN9B42yX600F4fmgsIYAABQL4RkAgNLaIGmHpCYFI6zHS4pljeJsEL84+3GbpIXuviVP20LLS72Z874+b6u9UgX2vTHOdrmGw/sbBVsBAFBEPPMMAEAJebAmZO4zv38UVy0KRpMt+/7v8wXnrJYC+3JH02eP47yF2ryuvaPXx4R1ZGbTFYw6j6wDAICSIjwDAFB6X895//GQUd1SekfO+80hbf8g3w53f0VST/bjiWbWFNLX+wr05QpuG5ekQ8zsxJC+3p/z/pGQtgAAFA3hGQCAEnP3nyl4tlgKRk1vNrMDCxxSKrnPJ7fma2Rm52rs5alyrcr+WSfpzwr09b/19sA7ln/Pef/ZAn1NkfSXeY4DAKCkCM8AAETjY9o7WvteST8zs/ZxHLegiDU8mvP+M2bWOLKBmZ0q6bvj6Os6BROOSdKXzGxUQDazd0j6oUZPODbSCkmvZN9faGaXjdHXlOw5T8puetTd8y6BBQBAsTFhGAAAEXD3XjM7Q9IdkuYqmDhsjZk9IelBSc8qmFjMJDVn2/yB3v688LiWoypgnaTHJL1b0lGSnjGzGyRtlHSAgmeiP5Kt4QeSLizw82w2sysk/YOkpKS7zewWSfdJekvByPXHJR2iYJR6SYG+3jCziyTdqSBof8PMlki6TdKrCtaU/qj2joa/oeAfIwAAiIwFjxoBAIAoZG/X/oqkDo1vpmpJelrSVyX9m4/4P24zG/68xt1PH8f5ZysI6zPyNOmXtFxSRtK/ZLdd5O4r8vR3laTPa+9EZCNdK+nHkn6a/Xylu385T1/nSvqe9k4INpatkpa4++MF2gAAUHTctg0AQITc/U13v1zByO8nJf1Iwahzr6S0pF2SfiXpbklXSjrF3d/l7itHBud9PP8mBbc+f1XBMlpvKVh6aqOC26JPdvfx3LY93N8XJbVnf44XJQ0oGCG/U9LZ7j7qFuwCfd2h4Fnsv5H03wp+J4MKbul+UNKfSzqO4AwAiAMjzwAAAAAAhGDkGQAAAACAEIRnAAAAAABCEJ4BAAAAAAhBeAYAAAAAIAThGQAAAACAEIRnAAAAAABCEJ4BAAAAAAhBeAYAAAAAIAThGQAAAACAEIRnAAAAAABCEJ4BAAAAAAjx/wHFA/eiOlkp6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf_FB = ECDF(FB_degree)\n",
    "x_fb = np.unique(FB_degree)\n",
    "y_fb = cdf_FB(x_fb)\n",
    "fig_cdf_fb = plt.figure(figsize=(16,9))\n",
    "assi = fig_cdf_fb.gca()\n",
    "assi.loglog(x_fb,1-y_fb,marker='o',ms=8, linestyle='--')\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('CCDF Facebook', size = 30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Facebook VS Erdos-Renyi\n",
    "In questa parte confrontiamo la distribuzione del grado di Facebook e la distribuzione di un grafo casuale (Erdos-Renyi) il cui grado medio è lo stesso della rete di Facebook.\n",
    "\n",
    "Come primo passo calcoliamo il grado medio in Facebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "grado_medio_FB = np.mean(FB_degree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dal momento che\n",
    "$$ <k> = p (N-1)$$\n",
    "posso ottenere $p = \\frac{<k>}{N-1}$, dove N è il numero di nodi del grafo.\n",
    "\n",
    "Nel nostro caso ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = grado_medio_FB / (FB_non_orientato.order()-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora possiamo generare grafo casuale Gilbert/ Erdos-Renyi utilizzando il metodo __gnp_random_graph()__."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "random_graph = nx.fast_gnp_random_graph(FB_non_orientato.order(),p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numero nodi: 11586\n",
      "Numero archi: 568282\n"
     ]
    }
   ],
   "source": [
    "print('Numero nodi: {}'.format(random_graph.order()))\n",
    "print('Numero archi: {}'.format(random_graph.size()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora possiamo confrontare la distribuzione del grado di Facebook con la distribuzione del grado del grafo casuale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "rand_degree = list(dict(random_graph.degree()).values())\n",
    "count_rand, bins_rand = np.histogram(rand_degree,bins=np.arange(min(rand_degree),max(rand_degree)+2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf_rand = count_rand / random_graph.order()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((80,), (81,), (80,))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_rand.shape, bins_rand[:,].shape, pdf_rand.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faf4bf5ff28>"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "assi = fig.gca()\n",
    "assi.plot(bins_rand[:-1],pdf_rand, color = 'orange', linestyle='None', marker='o', ms=15, label='Erdos')\n",
    "assi.plot(bins_FB[:-1],pdf_FB, color = 'blue', linestyle='None', marker='o', ms=10, label='Facebook Stanford')\n",
    "assi.set_xlabel('Grado',size=30)\n",
    "assi.set_ylabel('PDF',size=30)\n",
    "assi.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Identificare gli hub\n",
    "Infine vogliamo identificare quali sono i nodi con più alto grado.\n",
    "\n",
    "Il primo passo è definire una soglia per quantificare cosa intendiamo per 'alto grado'. Per questo possiamo utilizzare la CDF. In particolare fissato una $p \\in [0,1]$ vogliamo trovare il valore del grado $k$ tale che $F_X(k)=p$. Questa operazione corrisponde alla definizione di _quantile_.\n",
    "\n",
    "In Python posso calcolare i quantili utilizzando la funzione di Numpy **percentile**. In particolare fissiamo $p=0.95$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "286.0\n"
     ]
    }
   ],
   "source": [
    "percentile_95 = np.percentile(FB_degree,95)\n",
    "print(percentile_95)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ciò indica che il 95% dei nodi ha grado minore di quantile_95.\n",
    "\n",
    "Ora estraggo quali sono i nodi hub utilzzando la list comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "hub_nodi = [k for k,v in dict(FB_non_orientato.degree()).items() if v>= percentile_95]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[193, 2086, 2476, 6095, 7756, 8678, 8771, 8897, 9358, 10069]"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hub_nodi[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Centralità (Zafarani)\n",
    "\n",
    "## Degree Centrality\n",
    "<img src='figures/degree.png'>\n",
    "\n",
    "### Costruzione del grafo diretto dei messaggi tra studenti di UC Irvine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ucirvine_graph = nx.DiGraph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/out.opsahl-ucsocial') as f:\n",
    "    f.readline()\n",
    "    f.readline()\n",
    "    for line in f:\n",
    "        sorgente, destinazione, _ , _ = line.strip().split()\n",
    "        if ucirvine_graph.has_edge(sorgente,destinazione):\n",
    "            ucirvine_graph[sorgente][destinazione]['peso'] += 1\n",
    "        else:\n",
    "            ucirvine_graph.add_edge(sorgente,destinazione,peso=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1899, 20296)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ucirvine_graph.order(), ucirvine_graph.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "degree_ucirvine = list(dict(ucirvine_graph.degree).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In-Degree\n",
    "Il grado in entrata o 'in-degree', $k^{-}(n)$  corrisponde al numero di archi entranti in un nodo $n$. In NetworkX tale proprietà è calcolata dal metodo **in_degree** della classe _DiGraph_. \n",
    "**Parametri**\n",
    "- nbunch: id del nodo, lista di nodi e tutti i nodi (default); di cui voglio calcolare il grado\n",
    "- weight: nome dell'attributo sull'arco utilizzato per calcolare il grado pesato di un nodo $s^-(n)$\n",
    "$$s^-(n)=\\sum_{v\\in \\Gamma^-{n}}w(v,n)$$\n",
    "dove $\\Gamma(n)$ indica l'insieme dei vicini del nodo $n$ e $w(u,n)$ indica il valore dell'attributo associato all'arco $(u,n)$.\n",
    "\n",
    "Il metodo restituisce un iteratore di coppie (id_nodo, in_degree) che posso convertire in un dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137\n",
      "0\n",
      "558\n"
     ]
    }
   ],
   "source": [
    "in_degree_ucirvine = list(dict(ucirvine_graph.in_degree()).values())\n",
    "in_strength_ucirvine = list(dict(ucirvine_graph.in_degree(weight='peso')).values())\n",
    "print(max(in_degree_ucirvine))\n",
    "print(min(in_strength_ucirvine))\n",
    "print(max(in_strength_ucirvine))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Out-Degree\n",
    "Il grado in uscita o 'out-degree', $k^+(n)$, corrisponde al numero di archi in uscita da un nodo $n$. Il metodo corrispondente è **out_degree** ed ha una signature analoga al metodo *in_degree*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "237\n",
      "0\n",
      "1091\n"
     ]
    }
   ],
   "source": [
    "out_degree_ucirvine = list(dict(ucirvine_graph.out_degree()).values())\n",
    "out_strength_ucirvine = list(dict(ucirvine_graph.out_degree(weight='peso')).values())\n",
    "print(max(out_degree_ucirvine))\n",
    "print(min(out_strength_ucirvine))\n",
    "print(max(out_strength_ucirvine))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Esiste una relazione tra in-degree e out-degree\n",
    "\n",
    "**Esercizio guidato**: Ci chiediamo se esiste nella network che stiamo analizzando esista una relazione tra il grado in uscita di un nodo e il rispettivo grado in entrata.\n",
    " \n",
    "Per far ciò dobbiamo creare un dictionary che per ogni nodo contiene i due gradi. Nello specifico associamo un dictionary con le chiavi 'in', 'out' corrispondenti ai valori calcolati"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "in_and_out4nodes = {k: {'in':v } for k,v in dict(ucirvine_graph.in_degree()).items()}\n",
    "for k,v in dict(ucirvine_graph.out_degree()).items():\n",
    "    if k in in_and_out4nodes:\n",
    "        in_and_out4nodes[k]['out'] = v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('1', {'in': 25, 'out': 33}), ('2', {'in': 5, 'out': 0}), ('3', {'in': 41, 'out': 175}), ('4', {'in': 1, 'out': 0}), ('5', {'in': 0, 'out': 1}), ('6', {'in': 49, 'out': 45}), ('7', {'in': 5, 'out': 0}), ('8', {'in': 62, 'out': 28}), ('9', {'in': 53, 'out': 237}), ('10', {'in': 2, 'out': 1})]\n"
     ]
    }
   ],
   "source": [
    "print(list(in_and_out4nodes.items())[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora creiamo un dictionary che per ogni valore del grado in uscita contiene una lista dei gradi in entrata corrispondente al grado in uscita."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "out2ins = {v['out']:[] for v in in_and_out4nodes.values()}\n",
    "for v in in_and_out4nodes.values():\n",
    "    in_d = v['in']\n",
    "    out2ins[v['out']].append(in_d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(33, [25, 48, 51, 37, 34, 39, 25, 24]), (0, [5, 1, 5, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 1, 1, 1, 3, 2, 1, 7, 2, 1, 1, 2, 18, 5, 5, 1, 3, 2, 3, 1, 3, 4, 1, 4, 2, 2, 5, 5, 4, 1, 3, 2, 1, 5, 3, 1, 1, 2, 6, 4, 1, 3, 1, 1, 1, 2, 3, 4, 4, 3, 1, 1, 1, 3, 1, 1, 2, 1, 3, 1, 1, 4, 1, 1, 3, 1, 1, 4, 1, 2, 9, 5, 2, 5, 1, 2, 3, 1, 1, 2, 3, 1, 3, 2, 3, 2, 1, 2, 3, 1, 2, 9, 4, 3, 1, 2, 3, 8, 1, 1, 2, 7, 4, 4, 2, 1, 2, 1, 2, 3, 3, 1, 1, 4, 4, 1, 7, 3, 2, 1, 1, 2, 4, 1, 4, 1, 9, 3, 3, 2, 1, 2, 2, 2, 2, 2, 4, 4, 1, 1, 2, 2, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 1, 1, 2, 21, 1, 1, 1, 3, 1, 1, 4, 2, 1, 3, 1, 1, 1, 1, 2, 12, 3, 3, 26, 1, 2, 2, 8, 1, 7, 2, 6, 6, 2, 1, 1, 2, 2, 15, 4, 2, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 1, 1, 2, 4, 2, 2, 1, 8, 2, 1, 1, 4, 9, 2, 2, 4, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 3, 1, 1, 1, 2, 4, 2, 1, 1, 1, 7, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 4, 2, 2, 1, 1, 1, 2, 10, 2, 1, 1, 1, 1, 4, 2, 1, 5, 1, 1, 1, 2, 1, 1, 1, 7, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 4, 1, 8, 3, 1, 1, 2, 2, 2, 1, 1, 1, 3, 1, 4, 3, 1, 2, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 3, 1, 2, 1, 1, 2, 1, 1, 1, 7, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 2, 4, 1, 1, 2, 1, 2, 2, 2, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 3, 6, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1]), (175, [41])]\n"
     ]
    }
   ],
   "source": [
    "print(list(out2ins.items())[:3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'ultimo passo consiste nel calcolare la media e la mediana delle liste in 'out2ins'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = list(out2ins.keys())\n",
    "y_mean = [np.mean(out2ins[e]) for e in x]\n",
    "y_median = [np.median(out2ins[e]) for e in x]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ora visualizziamo il grafico"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'In Degree')"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AAO5FYgsAJdAR36FdjZHCcVoRHfdOK2UbNGXr5FujKVunlG3Qce90YVsWSdrdFFVHfEc5wkYA8NoCAOBe1CMBQAkYY/Rcd5teefd9zWZ8SdJV26au9Ks64gwqbm5p3O5ZtteoJNWHHZ3qPsB2LFgRry0AAO5FYgsAJdLTGdPbIxMavZGSl51ftTatiN7JPV50fDTk6JF9LepJxLYzTAQQry0AAJajFBkASiTsOjp/skvt+5tVH1797bY+7Kh9f4t6T3Yq7PLWjNXx2gIAYDljrV17VIVKJBJ2aGio3GEAwKoyfk79Q0mdvTim21Oesr5Vxs8p7DoKuUa7m6I61X1APYkYiQfuC68tAEC1M8ZcsdYm1hxHYgsA28Naq+HxSY0mU5pOZ9UYDak91qKOeAt9j9gUXlsAgGq13sSWHlsA2CbGGB1q3alDrTvLHQqqDK8tAECtoy4JAAAAABBoJLYAAAAAgEAjsQUAAAAABBqJLQAAAAAg0EhsAQAAAACBRmILAAAAAAg0ElsAAAAAQKCR2AIAAAAAAo3EFgAAAAAQaCS2AAAAAIBAI7EFAAAAAARaqNwBAAAAAADun7VWw+OTGkmmNJ3OqjEa0sFYszriO2SMKXd424rEFgAAAAACJOPn1D+Y1NmLY7o97Snr55TxrcKuUch1tKsxoue629TTGVPYrY0iXRJbAAAAAAiI6XRWJ3oHdG3ijmYz/rLHPN/K833NeLN65d1v6e2RCZ0/2aXGaPWnfbWRvgMAAABAwGX8nE70Dmj0RuqepPZus5mcRm+kdKJ3QBk/t00Rlg+JLQAAAAAEQP9gUtcm7sjLLiaqUXk66lzSC+5bOupcUlRe4TEvm9O1iZT6h5LlCHdbVf+cNAAAAAAEnLVWZy+OLZupfdSMqS9yRq5yatCcZlSnl9Wr495pXbVtkuZnbs9eHNOxrnhVLyjFjC0AAAAAVLjh8Undnl6cjY3KU1/kjJrNjJrMnBwjNZk5NZsZ9UXOLJu5vT3laXh8shxhbxsSWwAAAACocCPJlLJLemWPOINyVbx31lVOR5zBwnHWtxpNpkoeYzmR2AIAAABAhZtOZ5XxbeG41dxUg+aKjq1XWnFzq3Cc8XOaTmdLHmM5kdgCAAAAQIVrjIYUdhd7ZK/bvZpRXdGxs4pq3O4pHIddp+q3/CGxBQAAAIAKdzDWrJC7mL5dyHXKXyGd8+XoQq6zcBxyjdpjzSWPsZxIbAEAAACgwnXEd2hXY6RwnFZEx73TStkGTdk6+dZoytYpZRt03DuttBbH7m6KqiO+oxxhb5vqno8GAAAAgCpgjNFz3W165d33C1v+XLVt6kq/qiPOoOLmlsbtHl3IdS5LauvDjk51H6jqrX4kElsAAAAACISezpjeHpnQ6I2UvOz8ishpRfRO7vGi46MhR4/sa1FPIradYZYFpcgAAAAAEABh19H5k11q39+s+vDqqVx92FH7/hb1nuxU2K3+tI8ZWwAAAAAIiMZoSG88+5j6h5I6e3FMt6c8ZX2rjJ9T2HUUco12N0V1qvuAehKxmkhqJRJbAAAAAAiUsOvo6cOtOtYV1/D4pEaTKU2ns2qMhtQea1FHvKXqe2rvRmILAAAAAAFkjNGh1p061Lqz3KGUXW3MSwMAAAAAqhaJLQAAAAAg0EhsAQAAAACBRmILAAAAAAg0ElsAAAAAQKCR2AIAAAAAAq1kia0x5neNMbeMMdeWnNtpjPkzY8y3F37fsXDeGGO+ZIz5jjHmqjGmo1RxAQAAAACqSylnbM9L+sm7zv2qpK9Zaz8h6WsLx5L0U5I+sfDrc5J+p4RxAQAAAACqSMkSW2vte5I+uuv0T0v66sKfvyrp7y05/3t23mVJLcaYHypVbAAAAACA6rHdPbZ7rbXfk6SF3/csnN8nKblk3I2FcwAAAAAArKpSFo8yRc7ZogON+ZwxZsgYM/Thhx+WOCwAAAAAQKXb7sT2Zr7EeOH3Wwvnb0iKLRm3X9J3i30Ba+1XrLUJa23igQceKGmwAAAAAIDKF9rm7/eOpF+U9BsLv//hkvP/2BjzB5IOS0rlS5YBAACKsdZqeHxSI8mUptNZNUZDOhhrVkd8h4wpVgyGUuG5AFBuJUtsjTG/L+nTknYbY25I+nXNJ7T9xphnJI1L+rmF4X8i6e9K+o6kGUknSxUXAAAItoyfU/9gUmcvjun2tKesn1PGtwq7RiHX0a7GiJ7rblNPZ0xht1K6rqoTzwWASmGsLdrKGgiJRMIODQ2VOwwAALBNptNZnegd0LWJO5rN+CuOqw87enhfs86f7FJjdLsL1GoDzwWA7WCMuWKtTaw1jltnAADUKGutrlz/SOe+8YG+9LVv69w3PtCV6x+pUm96Z/ycTvQOaPRGatVESpJmMzmN3kjpRO+AMn5umyKsHTwXACoNt80AAKgxQS0f7R9M6trEHXnZxeQoKk9HnEG1mpu6bvfqQq5TaUUkSV42p2sTKfUPJfX04dZyhV2VeC4AVBpKkQEAqCFBLR+11uqJL35dycnZwrlHzZj6ImfkKqcGzWlGdfLl6Lh3WldtW2FcbGe93nvxSRYx2iI8FwC2E6XIAABgmSCXjw6PT+r2tFc4jspTX+SMms2MmsycHCM1mTk1mxn1Rc4oqsWxt6c8DY9Pbmk8QSvj3kqV9lwAgEQpMgAANSPI5aMjyZSySxLsI86gXBVPuF3ldMQZ1Du5xyVJWd9qNJnSodadm44jqGXcW6lSngsAWIrEFgCAGmCt1dmLY8tmaouVj76s3mXlo7OZnM5eHNOxrnhZy0en01ll/MXZ0FZzUw2aKzq2XmnFza3CccbPaTqd3ZIYVirj9nwrz/c1483qlXe/pbdHJiqmjHurVcJzAQB3q85biQAAYJmgl482RkMKu4uJ9XW7VzOqKzp2VlGN2z2F47DrbDrBDHIZ91Yr93MBAMWQ2AIAUAM2Uj6aly8fLaeDsWaFlpT2Xsh1yl/hY4wvRxdynYXjkGvUHmve1PdfqYz7qHNJL7hv6ahzadnNgKVl3NWm3M8FABRDYgsAQA0IevloR3yHdjVGCsdpRXTcO62UbdCUrZNvjaZsnVK2Qce904U+YUna3RRVR3zHhr/3SmXcA9Hn9YXwOX0+9Ka+ED6ngejzetSMFcbky7irbUGpcj4XALASakEAAKgB+fJRbyG5zZePNhVJbiuxfNQYo+e62/TKu+8XEsyrtk1d6Vd1xBlU3NzSuN2zbPEraX7bolPdBzbVH7xaGXde/jr2Rc6oK/1qIYZ8GXc1LZZUzucCAFbCjC0AADWgGspHezpjenjfxxQJLcadVkTv5B7Xv/J/Ru/kHl+WSEVDjh7Z16KeRGxT3zfoZdylUK7nAgBWQmILAEANqIby0bDr6PzJLrXvb1Z9ePWPMPVhR+37W9R7snPT2+4EvYy7FMr1XADASihFBgCgBlRL+WhjNKQ3nn1M/UMLe8lOecr6Vhk/p7DrKOQa7W6K6lT3AfUktmYv2aCXcZdKOZ4LAFhJdb7TAgCAe/R0xvT2yIRGb6QKq/vmy0eLqdTy0bDr6OnDrTrWFdfw+KRGkylNp7NqjIbUHmtRR7xlSxPxfBm358/fELiQ69TL6i06tlLLuEtlu58LYCOstRoen9TIktfnwVizOuI7eH1WERJbAABqRL589ETvgK5NpDSbWXmP1frwfFJbyeWjxhgdat1Z8oWZ8mXcM96spMUy7r7IGbnKqV5pzSoqX07FlnGX2nY9F8D9yPg59Q8uVBRMe8r6OWV8q7BrFHId7WqM6LnuNvV0UlFQDUyQl6BPJBJ2aGio3GEAABAoGT9H+eh9ev3y9WVl3NL86shrlXG/9NRDevpwazlCBmradDq7cBPvzrL/t3erDzt6eF+zzp/sqtq2gaAzxlyx1ibWHEdiCwBAbcqX51E+uraMn9Ox1y4vK+NeTTQ0v2DS688e5uYAsM3u9/9rJOSofX+z3nj2Mf6/VqD1JrbclgAAoEZRPrp+1VbGDVSz/sGkrk3cWZbU5issWs1NXbd7l1VYeNmcrk2k1D+UpMIiwJixBQAAWCfKuIHKZq3VE1/8upKTs4Vzj5qxQk98g+Y0o7pCT/xV21YYF9tZr/defJKKlQrDjC0AAMAWYxVgoLINj0/q9rRXOI7KU1/kjJrNTOFcfquuvsgZdaVfLczc3p7yNDw+SRVLQJHYAgAA3CfKuIHKNJJMKesvliAfcQblqnjrgKucjjiDhS3P5jK+vnzxL3WqW2wFFEAktgAAAACqwnQ6q4y/2GrZam6qYWGG9m71SitubhWOc1b62vs39Y3v/DVbAQUQzxIAAACAqtAYDSnsLs60Xrd7NaO6omNnFdW43bPsnG+lGc9XcnJWr7z7LR177bKm09mSxoytQWILAAAAoCocjDUrtGSG9UKuU/4KKY8vRxdynSt+rdlMTqM3UjrRO6CMv/a2QSgvElsAAAAAVaEjvkO7GiOF47QiOu6dVso2aMrWybdGU7ZOKdug495ppRVRVJ6OOpf0gvuWjjqXFNXi4lNLtwJCZWO7HwAAAABV4/XL1/XKu+9rNuMXzuX3sY2bWxq3ewr72LIVUOVb73Y/zNgCAAAAqBo9nTE9vO9jioQWU520Inon97j+lf8zeif3eGGmNr8VUJOZk2OkJjOnZjOjvsiZZTO3+a2AULlIbAEAAABUjbDr6PzJLrXvb1Z9eOV0Zz1bAeVlfavRZGrLY8XWIbEFAAAAUFUaoyG98exjeumphxTbWa+GiCvnriri+9kKKOPnWB25wpHYAgAAAKg6YdfR04db9d6LT6rvmS797R/dqyU7Ad3XVkBh11FjNFTqkLEJJLYAAAAAqpYxRodad+pU9wFFw27h/P1sBRRyjdpjzSWPFRtHYgsAAACg6m1kK6C83U1RdcR3lCNsrBPz6QAAAACqnjFGz3W3LdsK6KptU1f61aJbAeXVhx2d6j7AVj8VjsQWAAAAQE3o6Yzp7ZEJjd5IycvOr4ic3wqomGjI0SP7WtSTiG1nmNgASpEBAAAA1IT1bgUkzc/Utu9vUe/JToVd0qZKx4wtAAAAgJqR3wqofyipsxfHdHvKU9a3yvg5hV1HIddod1NUp7oPqCcRI6kNCBJbAAAAADUlvxXQsa64hscnNZpMaTqdVWM0pPZYizriLfTUBgyJLQAAAICalN8K6FDrznKHgk1iXh0AAAAAEGgktgAAAACAQCOxBQAAAAAEGoktAAAAACDQSGwBAAAAAIFGYgsAAAAACDQSWwAAAABAoJHYAgAAAAACjcQWAAAAABBoJLYAAAAAgEAjsQUAAAAABFqo3AEAALaGtVbD45MaSaY0nc6qMRrSwVizOuI7ZIwpd3gAAAAlQ2ILAAGX8XPqH0zq7MUx3Z72lPVzyvhWYdco5Dra1RjRc91t6umMKexSqAMAAKoPiS0ABNh0OqsTvQO6NnFHsxl/2WOeb+X5vma8Wb3y7rf09siEzp/sUmOUt34AAFBduHUPAAGV8XM60Tug0Rupe5Lau81mchq9kdKJ3gFl/Nw2RQgAALA9SGwBIKD6B5O6NnFHXnYxUY3K01Hnkl5w39JR55Ki8gqPedmcrk2k1D+ULEe4AAAAJUM9GgAEkLVWZy+OLZupfdSMqS9yRq5yatCcZlSnl9Wr495pXbVtkuZnbs9eHNOxrjgLSgEAgKrBjC0ABNDw+KRuTy/OxkblqS9yRs1mRk1mTo6Rmsycms2M+iJnls3c3p7yNDw+WY6wAQAASqIsia0x5vPGmD83xlwzxvy+MabOGPOgMeabxphvG2P+jTEmUo7YACAIRpIpZZf0yh5xBuWqeO+sq5yOOIOF46xvNZpMlTxGAACA7bLtia0xZp+kfyIpYa19WJIr6ecl/c+Sftta+wlJk5Ke2e7YACAoptNZZXxbOG41N9WguaJj65VW3NwqHGf8nKbT2ZLHCAAAsF3KVYocklRvjAlJapD0PUn/jaQ3Fx7/qqS/V6bYAKDiNUZDCruLPbLX7V7NqK7o2FlFNW73FI7DrsOWPwAAoKpse2JrrZ2Q9JuSxjWf0KYkXZH0fWttfgrhhqR92x0bAATFwVizQu7iW/iFXKf8Fd7SfTm6kOssHIdco/ZYc8ljBAATMR1iAAAgAElEQVQA2C7lKEXeIemnJT0o6YclNUr6qSJDbZFzMsZ8zhgzZIwZ+vDDD0sXKABUsI74Du1qXFyKIK2IjnunlbINmrJ18q3RlK1TyjbouHdaaS2O3d0UVUd8RznCBgAAKIly1KL9bUkfWGs/lCRjzFuSfkxSizEmtDBru1/Sd4v9ZWvtVyR9RZISiUTR5BcAqp0xRs91t+mVd98vbPlz1bapK/2qjjiDiptbGrd7dCHXuSyprQ87OtV9gK1+AABAVSlHYjsu6TFjTIOkWUk/LmlI0tcl/aykP5D0i5L+sAyxAUBg9HTG9PbIhEZvpORl51dETiuid3KPFx0fDTl6ZF+LehKx7QwTAACg5MrRY/tNzS8SNSzpPyzE8BVJvyLpnxpjviNpl6Rz2x0bAARJ2HV0/mSX2vc3qz68+tt5fdhR+/4W9Z7sVNhlC3MAAFBdjLXBreZNJBJ2aGio3GEAQFll/Jz6h5I6e3FMt6c8ZX2rjJ9T2HUUco12N0V1qvuAehIxkloAABAoxpgr1trEWuPY7wEAAi7sOnr6cKuOdcU1PD6p0WRK0+msGqMhtcda1BFvoacWAABUNRJbAKgSxhgdat2pQ607yx0KAADAtqImDQAAAAAQaCS2AAAAAIBAI7EFAAAAAAQaiS0AAAAAINBIbAEAAAAAgcaqyABQg6y1Gh6f1MiSrYEOxprVEd/B1kDi+gAAEDTrSmyNMZ+S9Alrba8x5gFJTdbaD0obGgBgq2X8nPoHkzp7cUy3pz1l/ZwyvlXYNQq5jnY1RvRcd5t6OmMKu7VX1MP1AQAgmIy1dvUBxvy6pISkT1prf8QY88OS/q219vHtCHA1iUTCDg0NlTsMAAiE6XRWJ3oHdG3ijmYz/orj6sOOHt7XrPMnu9QYrZ3CHq4PAACVxxhzxVqbWGvcem43/4yko5KmJcla+11JP7C58AAA2ynj53Sid0CjN1KrJm2SNJvJafRGSid6B5Txc9sUYXlxfQAACLb1JLaenZ/WtZJkjGksbUgAgK3WP5jUtYk78rKLiVhUno46l/SC+5aOOpcUlVd4zMvmdG0ipf6hZDnC3XZcHwAAgm09NVT9xpgvS2oxxjwr6bOSXittWACArWKt1dmLY8tmIh81Y+qLnJGrnBo0pxnV6WX16rh3Wldtm6T5mcmzF8d0rCte1QsmcX0AAAi+NWdsrbW/KelNSf+npE9K+h+stf9bqQMDAGyN4fFJ3Z5enG2MylNf5IyazYyazJwcIzWZOTWbGfVFziybmbw95Wl4fLIcYW8brg8AAMG33iUd/0LSBWvtL0u6ZIyhxxYAAmIkmVJ2SS/oEWdQror3hrrK6YgzWDjO+lajyVTJYywnrg8AAMG3ZmK7UH78pqQvL5zaJ+ntUgYFANg60+msMv7iCvit5qYaNFd0bL3SiptbheOMn9N0OlvyGMuJ6wMAQPCtZ8b2H0l6XNIdSbLWflvSnlIGBQDYOo3RkMLuYg/odbtXM6orOnZWUY3bxbf4sOtU/ZY2XB8AAIJvPYlt2lpbaCgyxoS0sEIyAKDyHYw1K+Quvt1fyHXKX+Ht35ejC7nOwrGV1fhHM7py/SOtte95UG3m+oRco/ZYc8ljBAAAq1tPYnvRGPNrkuqNMT8h6d9K+qPShgUA2Cod8R3a1RgpHKcV0XHvtFK2QVO2Tr41mrJ1StkGHfdOK63FsRnf6vXLf6Xj5wb0xBe/rtcvX6+6vVs3c312N0XVEd9RjrABAMASZq078MYYR9Izkv6OJCPpgqR/bSvg1n0ikbBDQ0PlDgMAKt7rl6/rlXffX7alTVSejjiDiptbGrd7dCHXuSxpK6Y+7Ojhfc06f7KrqkpwN3J96sOOXnrqIT19uLUcIQMAUBOMMVestYk1x62WnxpjXElftdb+g60MbquQ2ALA+mT8nI69dlmjN1LyspubcY2EHLXvb9Ybzz6msLvexfUr2/1en2jIUfv+Fr3+7OGquQYAAFSi9Sa2q/40ttb6kh4wxqx+Cx8AUNHCrqPzJ7vUvr9Z9eG1E7GoPB11LukF9y0ddS4t27vVy+Z0bSKl/qFkKUPeVvdzferD80lt78lOkloAACrEekqRvyypQ9I7kqbz5621/2tpQ1sbM7YAcH8yfk79Q0mdvTim21Oesr6Vd1fP7KNmTH2RM3KVU4PmNKM6+XJ03Dutq7atMC62s17vvfikjDF3f5vAKnZ9Mn5OYddRyDXa3RTVqe4D6knESGoBANgGW1KKvPCFfr3YeWvt/7TB2LYMiS0AbIy1VsPjk/rjq9/T/3H5emEf16g8DUSfV7OZuefvpGyDutKvFvpMGyKu+p7p0qHWndsa+3bIX5/RZErT6awaoyG1x1rUEW+pqkQeAIBKt97Eds2VPyohgQUAbC1jjA617tRIMqWladoRZ1CuiveYusrpiDOod3KPS5KyvtVoMlWViW3++lTjvw0AgGq0ZmJrjPkj3btvbUrSkKQvW2vnShEYAKD0ptPZwmytJLWam2pQ8bf1eqUVN7cKxxk/p+l0tuQxAgAArGU9DUJ/KWlK0msLv+5IuinpRxaOAQAB1RgNKewuztlet3s1o7qiY2cV1bjdUzgOu05VbfkDAACCaz2fSP6WtfaJJcd/ZIx5z1r7hDHmz0sVGACg9A7GmhVyHXn+/P6tF3Kdelm9Rcf6cnQh11k4DrlG7bHmbYkTAABgNeuZsX3AGBPPHyz8effCoVf8rwAAgqAjvkO7Ghd3dEsrouPeaaVsg6ZsnXxrNGXrlLINOu6dLiwcJUm7m6LqiO8oR9gAAADLrGfG9pckfcMYMybJSHpQ0vPGmEZJXy1lcACA0jLG6LnuNr3y7vuazczP2l61bepKv6ojzqDi5pbG7R5dyHUuS2rrw45OdR9ghWAAAFAR1rMq8p8YYz4h6b/UfGL7H5csGPUvShkcAOS3XRlZsu3KwVizOuI7SKq2SE9nTG+PTGj0Rkpedn5F5LQihdWP7xYNOXpkX4t6ErHtDBMAAGBF61kVuUHSP5XUaq191hjzCWPMJ621f1z68ADUqoyfU/9gUmcvjun2tKesn1PGtwq7RiHX0a7GiJ7rblNPZ0xhdz1dFVhJ2HV0/mSXTvQO6NpESrOZ4tv9SPMztY/sa1HvyU6uOwAAqBjG2rt38rlrgDH/RtIVSf/QWvuwMaZe0v9nrT24HQGuJpFI2KGhoXKHAWCLTaezC0nWnUJ5bDH1YUcP72vW+ZNdrM67BTJ+Tv1DCzcTpjxlfauMn1PYdRRyjXY3RXWq+4B6EtxMAAAA28MYc8Vam1hz3DoS2yFrbcIY8++ttX9r4dyotbZ9i2LdMBJboPpk/JyOvXZ5WVnsaiIhR+37m/XGs49tebJVq2XQ+X/36JJ/d3usRR3xlqr+dwMAgMqz3sR2PVMc3sIsrV34wm2S0puMDwCK6h9M6trEnWVJbVSejjiDajU3dd3uXbaQkZfN6dpESv1DST19uHVLYqj1MmhjjA617tSh1p3lDgUAAGBd1jNj+xOSXpL0kKQ/lfS4pBPW2n9X8ujWwIwtUF2stXrii19XcnK2cO5RM6a+yBm5yqlBc5pRnXw5Ou6d1lXbVhgX21mv9158ctMzipRBAwAAVI71ztiuOdVgrf0zSX9f0glJvy8pUQlJLYDqMzw+qdvTi9tjR+WpL3JGzWZGTWZOjpGazJyazYz6ImcUXbKV9u0pT8Pjk5v6/hk/pxO9Axq9kVo1qZWk2UxOozdSOtE7oIy/dsk0AAAASmfVxNYYEzLGfEbSZzU/YytJ3y95VABq0kgypeySJPGIMyhXxZNGVzkdcQYLx1nfajSZ2tT3X6kM+qhzSS+4b+moc2lZMr20DBoAAADls2L9nDHmhyV9XdL3JP17ze9h+5Sk3zLGPGmt/e72hAigVkyns8r4i+0RreamGjRXdGy90oqbW4XjjJ/TdDq74e9trdXZi2PLZmqLlUG/rN5lZdCzmZzOXhzTsa44CysBAACUyWoztl+Q9DvW2k9baz9vrf3vrLXdkv53SWe2JzwAtaQxGlLYXUwOr9u9mlFd0bGzimrc7ikch11nU72u5S6DBgAAwMatltg+Zq39F3eftNZ+SdJjpQsJQK06GGtWaMkqwxdynfJXeJvy5ehCrrNwHHKN2mPNG/7e5S6Dxuqstbpy/SOd+8YH+tLXvq1z3/hAV65/pLUWQAQAALVhtemN2VUem9nqQACgI75DuxojmvHm337Siui4d7pQDlyvtGYVLayKnN/yR5J2N0XVEd+x4e9dzjJorKzWt14CAADrs1pi22yM+ftFzhtJHytRPABqmDFGz3W36ZV33y/0ul61bepKv6ojzqDi5pbG7Z5l+9hK81vvnOo+sKke13wZtLeQ3ObLoJuKJLdbXQaN4lbbesnzrTzf14w3q1fe/ZbeHplg6yUAAGrYap8ALkr6zAqPvVeCWAAEhLVWw+OTGkmmNJ3OqjEa0sFYszriOza9gFJPZ0xvj0xo9EaqsDpxWhG9k3u86PhoyNEj+1rUk4ht6vvmy6A9fz6BupDr1MvqLTr27jJoK6vkRzO6cv2jLbkGWL710tJVqotZuvXSG88+xswtAAA1yAS5PymRSNihoaFyhwHUjO0qC12cqUtpNrNyUlMfnk9qe092bnqmzlqrJ774dSUnF7swlq6KfHcZdH5V5LwIpbFb6vXL15fN3EvzC3odcQbVam7qut1bdOb+pace0tOHW8sRMgAAKAFjzBVrbWLNcSS2ANZjtbLQperDjh7e17zpstCMn1P/0EISPeUp61tl/JzCrqOQa7S7KapT3QfUk9i6BHK1ZGqlMuhituoa1Kq1bjLkt14qdpMhtrNe7734JLPmAABUCRJbAFsm4+d07LXL6yoLlaSwY3Qw3rIlZaH5sufRJWXP7bEWdcRbtjx5ud9/52oiIUft+5spjd2AK9c/0vFzA5rx5m8wROVpIPq8ms296xambIO60q8WbjY0RFz1PdOlQ607tzVmVKdStl0AANZnvYktUwkA1tQ/mNS1iTvLkr3VykIzOavBv5rUL/eP6Dd7Dm4qsTPG6FDrzm1JVMKuo/Mnu9ZVBi2tfg28bE7XJlLqH0pSGnufNrL1Ur4HO7/1EoktNoPVuAEgeNaV2BpjfkzSx5eOt9b+XoliAlBBrLU6e3FsWXlusbLQl9V7T1noO6Pf08T3Z/XVzx4OTEluYzSkN559bFkZdCabUya3vLplPddgNpPT2YtjOtYVZ3bnPrD1EsqJ1bgBIJjWvM1ojOmT9JuSPiWpc+HXmlPBAKrD8Pikbk97heOoPPVFzqjZzKjJzMkxUpOZU7OZUV/kjKJaHGsljSysVpvxN1fau53CrqOnD7fqvRefVN8zXfoHj7Uq7C4mpvdzDW5PeRoenyzHP0PWWl25/pHOfeMDfelr39a5b3ygK9c/UqW3oOS3XsrLb71UDFsvYSstXY17tbUEpOWrcQfp/Q0AqtV6fvonJD1kK/2TEICS2ExZqDRfGhrUktx8GfRIMqWl862VXhob9DLKzWy9FHKN2mPN2xInqs/9tl3QcgAAlWM9n2iuSfrBUgcCoDJtpiw0L1+SG9T7Y0EqjZ1OZ3Xstct65d33lZyc1Yzny/OtrObLKGc8X8nJ+TLKY69drsiy3Y74Du1qXFx5Oq2IjnunlbINmrJ18q3RlK1TyjbouHd62SrVu5ui6ojvKEfYCLiV2i4Gos/rC+Fz+nzoTX0hfE4D0ef1qBkrjAn6+xsAVIv1JLa7JX3LGHPBGPNO/lepAwNQGTZTFrpUOUtyNysopbHVUkZpjNFz3W2qD7uFc1dtm7rSr+rXMs/ot7M/q1/LPKOu9KvLerrrw45OdR+gnxkbspm2iyC/vwFAtVjPp63/sdRBAFhbubad2ExZ6FJBXq02KKWx1VRG2dMZ09sjE8u2XkorsqzMfaloyNEj+1rUk4htZ5ioIqzGDQDBtmZia629uB2BACiu3P2S+bLQGW9W0mJZaH5F4HqlNauofDn3lIXe/e+oxLLX9djMNdiu0tiNrl5dqSs338/WS/Xh+aS292RnRfYMIxiC1HIAALjXiomtMeZvNL+o6T0PSbLW2o+VLCoAkipj24l8Wegr775fiCFfFnrEGVTc3NK43bNsJrCYIK9Wu9FrsJ2lsauVUeY1LXxI74ucUVf61UKs+TLKSpttKrb1Uta3yvg5hV1HIddod1NUp7oPqCdRmQthITjyLQfeQnKbbzloKpLcsho3AFSeFd+FrbU/sJ2BAFhuab/k0tLSYpb2S77x7GNb/gE/XxY6Mv79wn6uq5WFFhP01WorvTS2Wsso81svHeuKa3h8UqNLSvHbYy3qiLdU1EwzgisoLQcAgOLKcnvbGNNijHnTGPMfjTHvG2P+a2PMTmPMnxljvr3wO8taoqat1C951LmkF9y3dNS5tGzxkqX9klstXxZ6MN6y4a8R9NVq89egfX+z6sOrv3XWhx2179/e0thqL6PMb7302U89qBd+/BP67Kce1KHW0vaXo7awGjcABFu56mb+paT/x1r7s8aYiKQGSb8m6WvW2t8wxvyqpF+V9Ctlig8oq0rsl8yXhf5y/4jeGf3esj6F1RYokqpntdpKLo2ljBLYnCC0HAAAVrbtn2SMMR+T9ISkE5JkrfUkecaYn5b06YVhX5X070RiixpVqf2SYdfRb/Yc1MT3ZzVyI6Wsb9dMuFcqyS3XKs+bVamlsZRRAptX6S0HAICVleMW/QFJH0rqNca0S7oi6b+VtNda+z1JstZ+zxhTfDNMoAZUcr9k2HX01c8e1oneAX174kP1OSsn3E/kzuqT+/YsK8kt9yrPWyVfGlspfalBWLkZqHSsxg0AwVWOxDYkqUPSC9babxpj/qXmy47XxRjzOUmfk6R4PF6aCIEyq/R+yXxJ7sA7ZxUeLf7BL2RyerVjQl1HP1P40FcJqzxXK8ooga1RyS0HAICVleMT4w1JN6y131w4flPzie1NY8wPLczW/pCkW8X+srX2K5K+IkmJRKLYdkRA4AWhXzLsOnp855Ss0kUfb1Baj++clpbM1FbKKs/VKihllEEtQ0ftqNSWAwDAyrY9sbXW/mdjTNIY80lr7X+S9OOSvrXw6xcl/cbC73+43bEBlSIw/ZI7HpSJNEre1D0PmUijtOPjheNiqzyvZukqz08fbt2qiKtapZdRVksZOmpHpbUcAABWZqzd/klPY8xBSf9aUkTSX0o6qfmth/olxSWNS/o5a+1Hq32dRCJhh4aGShwtsP2stXrii19XcnK2cG7pIk1390vmV0WWpPjOBl188dP3PZuwoVm0zJz0Wz8izaXufayuWfqlv5DCdUX/PesV21mv9158ktmR+5DxcxVXRrlaGfpS9WFHD+9rpgwdAABIkowxV6y1iTXHlSOx3Soktqhmr1++vqxfUlrcVme1fsmXnnrovmY4Nz2LNnFF6vsZKedL3rQUaZQcVzr+f0n7DkmSrlz/SMfPDWjGWzmhWUlDxFXfM13MmGxA/mZFucsoM35Ox167vK4ydEmKhBy172+mDB0AAKw7seV2OFChtqNfcksWc9p3SPql/yS9/8fS5F/Nlx//6GekcF1hyN2rPBdiXmP/W6n0qzxXs0opoyxWhr7ac7+eMnT6dAEAwFIktkCFKnW/5JYu5hSulx79uRX//t2rPEtac//bpXGWepVnlI61Vmcvji27cbKe5342k9PZi2M61hVflqjSpwsAAIrhpz5QwfLbTrz01EOK7axXQ8RVxHVkJEVcRw0RV/GdDXrpqYf0+rOH76sncTOLOW3k3xF2F5OTqDz1Reb3v20yc3KM1GTm1Gxm1Bc5o6i8wtjtWuUZpTE8Pqnb04vP5/0897enPA2PTxaOp9NZHXvtsl55930lJ2c14/nyfCur+QqDGc9XcnK+wuDYa5e5IQIAQA3h0yJQ4Uqx7USxWbT1WGkWbS13r/J8xBmUq+IJtaucjjiDhZLrbV3lGVvu7jL0+3nul5ahs10UgPWgTQGoXSS2QEBsZb/k3bNo9yM/i3Y/cXTEd2hXY0Qz3vyqyK3mphqK7MkrSfVKK24Wt7He3RRVR3zHhmJF+d1dhn4/z/3SMvRS9OkCqB60KQDgfzZQg1ZazGk98rNo98MYo+e621QfdiVJ1+1ezaiu6NhZRTVu90ia7x0+1X2Au+wBdncZ+nqfe2mxDH2lPt2B6PP6QvicPh96U18In9NA9Hk9asYWv95ChUGQV/8HsDbaFABIJLZATSq2mNN6bXQxp57OmB7e9zFFQo4u5Drlr/D242v+8Y2s8ozKky9Dz1vPc5+XL0Pfyj5dANVlaZvCWu01S9sUMhu8uQugcpHYAjXo7lm0vKg8HXUu6QX3LR11Li1LEPI2uphTfpXn9v3NcsJ1Ou6dVso2aMrWybdGU7ZOKdug495pOeE6te+/v1WeUZnyZeh5aUVWfe6XbveUL0PfSJ9u3kYqDAAEx0ptCiv9LNvMQogAKhs9tkANunsxJ2n92+9sZjGn/CrP/UNJnb0Y1aenvqwnc9/UPntTE2av/l/nsD624wf0UvcB9STog6oG+TL0V959vzCbctW2qSv9qo44g4qbWxq3e+7Zw3hpGfpW9ekCqC5bvZ0YgGAjsQVq0N2LOS0t7cxrWkgc+iJn1JV+tZB0bHYxp3tXeX5E0+msHo6G9PQGV3lGZevpjOntkYllKxqnFSmsfny3u8vQ8xUG3kJym+/TbSqS3K7Upwug+qzWppC30s+yjSyECKCyMR0C1KC7F3Nab2nnVi7mlF/l+bOfelAv/Pgn9NlPPahDrWzHUI2WlqHXh1f/sVMfdu4pQ9+KPl0A1Yc2BWBjrLW6cv0jnfvGB/rS176tc9/4QFeufxT4xRa5jQ3UqKWzaK127dJOFnPCZiwvQx/T7SlPWd8q4+cUdh2FXKPdTVGdKlKGfneFQb5PN19uWK+0ZhWVL2fFPl0A1Yc2BeD+VPu2WCS2QI3Kz6Kd6B3Q9777g6uWdv5nd6/af5jFnLA595ahpzSdzqoxGlL7KmXoW9GnC6D60KYArN90OqsTvQO6NnHnnhXEPd/K833NePPbYr09MqHzJ7sC938kWNEC2FL5WbQ3v7lb9k97i46xxtWhI7+oM4f/C5LabWSt1fD4pEaWJH8HY83qiAe/XDtfhn4/vW2b7dMFUH3uXgjxQq5TL6v4zzLaFFDLlm6LtXQF8WKWbov1xrOPBeqzH4ktUOPCubR+oWlU9lCP/JE/kG+lUG5OWbdejhtS0z98W7+w/0fKHWbNqPYyoY1aWmFwbSKl2czKP5jrw/NJLRUGQHWjTQFYn5W2xTriDKrV3NR1u3dZ1dPSbbGePtxarrDvmwlyk3AikbBDQ0PlDgMIrokrUt/PSDlf8qalSINkrfToz0utPyb96GekcF25o6wZq5UJLVUfdvTwvuZAlgltVsbPbahPF0B1ev3y9WVtCtLiB/bV2hReeuqhQH1gBzbKWqsnvvh1JSdnC+eKbYuVvwG0dIvH2M56vffik2WvFDPGXLHWJtYcR2IL1KjMrPRbn5TmiqwKWdcs/dJfbFtSW81lt+uV8XM69trldZUJSVIk5Kh9f3PgyoS2Sv41s94+XQDV6X7fO6Oh+ZXXX3/2cE2+d6L2XLn+kY6fG9CMN3/zJypPA9Hnl22LlZeyDcu2xWqIuOp7pqvs22KtN7GtrVv9ABa9/8fzM7XF5Hzp/T+SHv25koZA2e2iWikT2iob6dMFUH1oUwBWt5FtsfLrV+S3xQrKz1oSW6BWTX4wX35cjDctTf5VSb99LazOt17WWp29OLbsOhQrE3pZvcvKhGYzOZ29OKZjXXFmKQHUrM1sJwZUu1raFqs6PyUCWNuOB2UjDTJFklsbaZTZ8fENfdn1lBXXyup80vqux/D4pG5Pe4W/E5WnvsiZZWVC+e0r+iJnlpUJ3Z7yNDw+GZi7qQBQChvdTgyodrW0LVZwIgWwZTJ+Tm/+Tbue8qQfKPL4lGf1x3/Trv+/vTuPk6uu8/3/+p5TS29JJwHZku5AImq4QELo7uCARnScjMMmOmbGMNEEJsCgzHLRewH9zeiFIV5/emeuvxlk5MYgGZCJIyAGZ4Jr/IHGbCQhEhEiSToNBIXQobdazvneP6qqU1VdVV1VvVRV1/v5ePAgXVt/u/v06fOp72f54+S73cW+ZrFpxfWQdlvK96Oe0oRERCaSyhREMtXTWCwFtiJ1Jj0F+JvxW/OMRbiV5//zAA8/87uiUoBLSSt+5OkjvHI8MqXTbktNs15y1kl1kyYkIiIik6eexmIpsBWpI9kpwHuZT1fk7txjEYpMAS41rXj3kV58/0QQN9XSbstJs36ld4iAA6meJ1M5TUhEREQmjzGGG5fOzxiLtdcWuP5Lagw63LB0XtVvJqTT1ZBIjSpnRE6uFOAIoeG01mzFpACXmlYc9zJHjFU67Xa8Rw2Vk2b96psRMAZIfG+mcpqQiIiITK7lnW08ursn4033Qtd/4UCig/jyjrbJXOaYKbAVqTHljsjJ1Xm3GIVSgMvt5puuUmm3EzFqqNzvRyTu4zonvrdTOU1IREREJle9jMVSYCtSQ8YyIie7824p8qUAj6Wbb0ol0m4natTQWL4fjgHXdYgmm0hN1TQhERERmXz1MBZLga1IjRjriJzszrulyJcCPJZuvimTkXabnm58fDDGw7uO8MrxoYyGTbmUOmpoLN8Pg+HU1jBHj0emdJqQiIiIVMZUH4ulwFakRox1RE72gO5S5EsBHsvQ75SJTLvNlW4czfE9GK9RQ2Mdgv7BRbPZ+pvXpnSakIiIiFTWVB2LpcBWpAaUW7uZXh+bPaC7FPlSgMcy9DvdRKTdFko3Tjeeo4bGOgR9ZlNoyqcJiYiIiEwEBbYiNWAstZuv9A7xP777LG89tSXRoKiMwDbgGnxIsQ8AACAASURBVMJBh3VPvpjROXjhnPKHfjsGXGOIJUf/jGfabbFp2+M9amg8hqBP9TQhERERkYmgwFakBoyldjPmWe7fepBwwC1rtxYSXXvv3PQsnm8zOgfPagoSDjgMRBOBXClpxWfMaOT01oYJSbstNm17vEcNjecQ9KmaJiQiIiIyERTYitSAsdayej7DwWc5PN8y6J/4/Cc6B3sEnMTua+ruYtOK/+I981ne0TbuabelpG1v8i4a11FD9TQEXURERKSaKLAVqQHjVcs6EeI+GBL/pULfQmnFQcdw3uzW4WB1vNNuS0nbvtp9kkHCNBMZ8TrljhqqlyHoIiIiItVEga1IDSindrNQp99yFHo9CxiTCFpH67zsWUvPG4Ns3N7N8s5EcDueabelpG37GPLtA5c7aqhehqCLiIiIVBMFtiI1oNTazbeb7lE7/QK4jiHkGjyfjBTgSNzHS0s9LqZzsLXQHHZpCQd56Y1B/DzxrW+h540h7nz8WR7d3cN9q7uK2gktVmlp21G+6b2XK9yfj+uooXoYgi4iIiJSTRTYitSAUmo3AbaFbyqq02844PCZyxYQifnDKcANQYc7Nj07XFNbSufgSMzntGkujmPwR9m5HYz57DnSy6r123hwzUXjFtyVmra9zX8Hd8RXjnsNrLobi4iIiEweBbYiNaLY2s0rnadK6vQbiflce8lZw49Z9+SLGbu1pXQOjsR9Dvyun3haUFsohTka99nX08vGHd1cs2Ruqd+SnMpJ257IGlh1N5ZcrLXsOnyM3WlveCxqa2Vx+0y94SEiIlIGBbYiNaLY2s1SOibn6vQ7lg7MviVjp7aYFObBmM89Ww6woqt9XC7oxzJyZ8TXpxpYGWcxz2fj9mSKen+UuOdnjNA6qTnEjUvnD9efi4iISHEU2IrUkFy1m5GYj2dPBJOldEzO1el3vDowl5LC/FpflF2Hj43Lrma5I3dSQqqBlQnSH4kn35g6njGOCtJHaA1OWP25iIjIVKa/mCI1Jrt2c9Oel9mw9SDJ7OSiUm9TcnX6LSeVN5dSUpjjnmVPd++4peuWOnIn6BpOb23kQ4tnM70hqBpYGXcxz2fV+m0Zx2Q+E1V/LiIiMpXpr6VIjTLGcP6cGcx/SzOWEwFYKvW21zbRZxvwrKHPNtBrm4rq9JtK5S3n9dKNNSV6LFJp2wvntNIYLHyaaww6XNA2k//4q3fx17//Nq695CwunKs6RxlfG7d3s6/neEZQGybKlc5T3Ow+zJXOU4Q5MX85vf5cRERERqcdW5EalZ7W6GXN1ikm9TZfp99yU3mDjsHHkhohO9aU6LHSyB2pFtZa7tlyICP9uBL15yIiIlOZAluRGlRMWuNYOv2WmsobDjjMO7mZQ68PMBAtPYU5V0r0eNDIHakGuw4f47X+E7uxlao/FxERmcq0RSFSg0pNa0zXGHRYOKdwp99SU3kXzpnBt258ZxEpzGEGbIhN3kUsc7YPrzFXSvR4So3cufaSs7j5fWcr3Vgm1e7uXuLeid/VYurPU1L15yIiIlKYdmxFaky5aY0ArmP4zGUL+JPO9lFTb8tJ5S2Uwtzl/IoPuU9iMXzU/RFXuT/jDtbz5/5n+ODSKxRkypQ1lhFa411/LiIiMlUpsBWpMWNJawwHHBacPr3oetJSU3nzpTBv9ju5I7ieJhMZscb1gbWEF11b5ndDpPqNZYTWRNSfi4iITEVKRRapMZVIayw2lTdfCnOhNTYHIfjc4yWvSaRWpEZopWz2O/Hy/PmdrPpzERGRqUaBrUiNqfa0xlQK82cvP4e2WY00hVzmua/mXaOJ9sOxgxO6JpFKGssIrYmuPxcREZkqlN8kUmNqIa0xO4X5ze0HiD/7OCF/YOSDQ80w88wJX5NIpZQ7QivfSC4REREZSYGtyESKDcL+TXDsRZh5Fiy4AoINY3rJVFpj1KuesTr5pFKYOeM6eOF/knPT1nET35cxstay6/AxdqfVAS9qa2Vxu7of14qp/DMsZ4RWoZFcIvVmKp8fRGR8KLAVmSg9O2HD1eB7EO1P7Ex+7xZY+QjMvrDsl02lNQ5EB4ETaY2prsiNRBgkjIdTPWmNwQbsnz2Cd/8H8b04AW+QuNuI4wZw/+wRzBiC/Zjns3F7snNzf5S45xPzLEHXEHAdTmoOcePS+SzvbCu6aZZMrnr4Gabqz1et38a+nl4GY7lrziGxU3ve7MIjuUTqRT2cH0RkfBhr7eiPqlIdHR12x44dlV6GyEixQfjy22FoZKOmIXcaD737B5x35illv9P8wNZDGWmNkOiOPFpa42cvP4drlswt72sqU/pFSV9/H5f6v2C2PUqPOZUfOUuY1txS9kVJfySeDBSOZ3wvsjUGHc6d3cp9q7vUYbbK1NvPMOb5JY3QEqln9XZ+EJHcjDE7rbUdoz5Oga3IBNj7Ldj01xDtG3FXn23gb70/5z+dd5X9TnPM81lx79aMtMZCwgGHhXNm8MCaJZN6sTyRFyWlfg9CAYeFc1p5cM1FChiqRD3/DFNplaON0KoXSjOVbPV8fhCRTMUGtnpbS2QiHHsRG+0n1+VYIxHOsEcZiHoMRAe58/FneXR3T0lBXS2kNcY8n1XrtxV1UTIY89lzpJdV67cVfVGycXs3+3qOZ7x2atd6rjnKIXtqxq51NO6zr6eXjTu6E7vWE1D/LKUZ88+whqXqzy+cO6vSS6kopZlKPvV8fhCR8mjHVmQCxHf/G7Hv/CWNdmS3pD7bwO2x69jsdw7/ge5xTuOVM97PN65/d8k7t9Wa1pgrXXo0xaZLW2t59xd/TPexweHbzjcHhuuMmxhigIbhOuO9dv7w49pmNfLTFa2Yf82qf3bcMdc/S/HG/DP89KXayatxSjOVfHR+EJF02rEVqaBv9V/AH/kujTn+rno4vGRPYlv4psw/0K+s5wc/uJcPLLus6M+TPVanWtIarbXcs+VASUEtJHZu79lygBVd7QXXvevwMV7rjw5/HCbKhtBaWs2JcUKp8UcbQmvpitw9/K5+X18f3v0fJxA9fuIFUynjG66GW36tndtJMJaf4Wt9UXYdPlb3u521bKIzOqS26fwgIuWo2F8HY4xrjHnaGLMp+fFZxphfGGOeN8b8mzEmNNpriFQjay13P3mEldFb6bVN9NkGPGvosw302iaui36KdaEv0WoGaDFDOAZazBCtpp+Lf74GGxsc/ZNkSaU1XnvJWdz8vrO59pKzuHBu5WrTsi9KSpG6KClkd3cvce/ExfAyZzsuuS+OXXyWOduHP77U/wW+F8/9wr4H+79b+qKlZGP5GcY9y57ukY3ZpHbkSzO90nmKm92HudJ5ijAnziHpaaYy9en8ICLlqOSO7V8B+4HpyY//J/AP1tqHjDH3ANcBX63U4kTKlQrquu18uiJ3j+hUXOgPtGM9vvPNe7jsmr+q6V2J7IuSUqQuSgq9294fiRPzTpRRzDVHaco5JDdR09xuXh3+eI59haCX582DaD8cO1jWutMV2winnhvmjOVnGPN8+iN53pyQqpcroyNXmukdrM9IMy02o0Nqn84PIlKOigS2xpg5wGXA3wP/1ST+Qr0XWJF8yDeAz6HAVmpQelAXIcRj/sUZ94/2B/rF53/Jinu31nQ9WfZFSSmKuShpDgcIuoZo8nMcsqcyQMNwalq6QcIctqcMf3zEnEbMbSTkDYx4LKFmmHlmWetOrb2YRjhXL57NI7t66rphzlh+hkHXqdnfDVGaqYxO5wcRKUelrpj+EfhvMLxtdRLwhrU2dTV7BJhdiYWJjNVoQV3qD3Qug4R50TtluJ4sVuauZ6WlLkrKUcxFyaK2VgJpAd9mvxMvz+nMw2Gz3zn88Y+cJThuntd33ER35DL0R+KsuHcrdz6+n+5jgwxEPaKexQJRzzIQ9eg+Nsgdm35J19//YNTH3fn4s6y4d+uU3XkYy88w4BoWtrVO+BplYijNVEaj84OIlGPSA1tjzOXAq9banek353hozsjAGHO9MWaHMWbHb3/72wlZo0gh1lp2HnqddU++yFd++DzrnnyRnYdeJ9VhfLSgrpg/0LVeT5Z9UVKKgGs4f05rwe/x4vaZnNR8ogw/QoiV0dty1jSvjN42vNsDML1lGu7HHoWGVgi1ACbx/4bWRFfkMhpHpTfCGa1h1lDc0hfxRn1cesOcWn2Do5Cx/AxPbgmzuH1mJZYt40BppjIanR9EpByVyNW4GLjSGPNHQAOJGtt/BGYYYwLJXds5wEu5nmyt/RrwNUiM+5mcJYsUn2Z67hnTCbgOUS934JL6A52qJ2skwiDh4bEFqT/QtVxPlrooGYiW3girIeDw1w89zesDsYIpujcunZ8xTmhvnprm9AuexqDDDUvnYebMhVueS86xPZhIPx7DHNtcjXCKVa9zGY0xY/sZ1tjvhJygNFMZjc4PIlKOis6xNca8B/iUtfZyY8y3gG+nNY/aa629u9DzNcdWJksp8xYXnD6N3/y2nzcGC+8qpAKafH+gAZpCLhuu66rJerJy5tg6BhxjiPv5z0upmZb3fqyDNffvKGpcCEA44LBwzgweWLNkXOtWc81bLFa9z2WMeT4r7t1a8Z+hTK6dh15n5bptDEQT54YwUbaFb8qosU3ptU0ZNba1fE6U0uj8ICIpxc6xrabf/P9OopHUCyRqbtdVeD0iQO4003xjKQZjPk8f7qV3lKAWTjSW+ifvah7zLx4R1EJt15Mt72zj3NnTCQWKO80YwFoKBrVwIkV3zf07uPdjHSyc00pjsPDnaAwmLnjWr+4c9wueckcbpTfMyRz7NMCG0NqMUSfFjECqRUHX4b7VXRX/GcrkUpqpFEPnBxEpVUXzeay1PwF+kvz3b4CuSq5HJJfsNNPRxlLkC8sKpZzmE/V8jg/Fxvkrmhypi5LETncvg7H877gH3cQubXoCSTEpuo8/8zIPrrmIjTuSKeJ9UeKeJeb5BF2HgGs4uSXMDUvnsbxjYjoMlzvaqJiGOamO2sWMQKpVzeFAxX+GMrmUZirF0vlBREpR0VTksVIqsky07DTTUlLm0hWbcprLqdPCrLr4LGKeX5NzTmOeP8pFSYjjg7GM1O1yUnRTM2H3pM2EXdg2g8XtMyb0e/WVHz7PP3z/13nf0MjnZvdh/ibw7zg5luZZwz/E/5h/8q4GErvZ//X9b+Pm95095vVWs0r9DGXyKc1USqXzg0j9KjYVWR0YRArITjMttMvWQJTbAw9wV/yajOC2lBmNuRx9M8IX//NXWCBUg3NOg67DNUvmsqKrPedFibU+H/v6iXEe5c60NMZw4dxZk76rmd0Ip1hqmDNSpX6GMvlKyehoDDqcN1tppvVO5wcRGc3Uv1ISKUPqneF/2fIbImnNjwqNpQgR56Puj/mg+1TGzmIpKad515P8f9SzRD2PgWhizumju3u4b3VXTQQ9+S5K1j35YskzLaspRTc12ihfF+x8Nvud3MH6nPdN9lzG1PG+O+1Nh1rLDJDaozRTEREZT9V/NSwyibJH+kRiHukbcYV22YxJBLch4hk7i6XMaCxF+pzTB9dcVLMXfbU+07Lc0UbFjn2CiWuYU+wIq1rIDJDaNFpGh9JMRUSkWApsRZKKGelTaJctXfrOYikpp6WaCnNOa32mZa5GOMWqZMOcQsd7LWcGSG1SmqmIiIyV3oIXIfdIn1zSx1JEbIB8vdfSdxY3+514eX7VslNOyzEY87lnywFqtRFcKpU3pZTv10Sn6Bar1NFG6QqNfQoHErWFyzvaxnO5RR/vkJkZECuj+7OIiIjIZFBgK8LIkT6Qf1ZtapftIe9SYnmSHtJ3FkuZ0ViuWp5zOhVmWpYyb7EhYGgJB2io4FzGUo53yMwMEBEREalGGvcjdS97pA8UN26m0OifIRvk9ti1PO6/czgQS81lzZVyWmhmazHzb0Ouw60feAfXXnLWhHyPJtoDWw+NSOUt9P2CROD32cvPqaoU7PTRRn19fVzq/4I59hWOmNP4kbOE6S3TuGHpPK6+YDaPPN1TkYY55R7vkDleSURERGQyFDvuR4Gt1L2dh15n5bptDEQTQVUps2qzA4LU5b6FomfVFgoqgKICjlqfczrVZlraIzvx7v8gvhcn6A0Scxtx3ADuxx7FzLnwxOMqMJdxLMd7U8hlw3VdqoMUERGRSVNsYFt9V4Qik2x3d2/J42ZSUmnJfxf7OFGCGJPojuwYaDFDtJoBNoTWZqR1pkuf2dpihkY8b0Porrz3pb9mNTRRGotSUnknMkV3XMQGMf96NYHocULeAAZLyBsgED2O+derIXaiKVaqYc61l5zFze87m2svOYsL507siJ2xHO+p8UoiIiIi1aZ2r4RFxslYxs1AoiY0RoA4LhAb8ZxCs2oLBRXhHK+V7zWrpYnSWEyZmZb7N4GfpyGT78H+78L5H5ncNaWp9fFKIsXSfGYRkfqiwFbq3ljGzaSUEhzMbAoyvSHAS71DzCX/80IFAtvs16yWJkpjNVkzLSf0gvfYixDtz31ftB+OHRzb649RrY9XEhmN5jOLiNQnXaFI3UuNm4l6iV22QrNq843nKSU4aA67PP6X72L1fdt5+aXT8j6vUHiV/poTNee0kiZqpuWkXPDOPAtCzRDtG3lfqBlmnjmmr2GsxnK8T4XMAJnaNJ9ZRKR+6a1KqXtjGTeTUsrs1df7Yzx39E0eXHMRF/7hx7HGzfm8VL1uodecqDmntcJay85Dr7PuyRf5yg+fZ92TL7Lz0Os5Z/r2R+KsuHcrdz6+n+5jgwxEPaKexZK44B2IenQfS1zwrrh3a/kptwuuACf3zxTHTdxfQVNhvJJILprPLCJS39QVWaa+2GCi7vHYi4ndtAVXQLAh4yHljJvJlt7duJEIg4RzdjDOHs2T3kE34A1gyL1bay1ECBIhyMrobTwfOJvzZieaKNXbjkOpO6+ldl0OBRwWzmnlwTUXlbdz27MTNlydqKmN9id2ah0XVj4Csy8c/fkTbKqMVxJJV+i4zjcuTce1iEj107gfqVvp9ZPNv93NVftuxrFxQv5Q3rErpQY++RQTDOcczRMbJP7Lx/jtT9dx2uu/yBnY+hb+w1/C7XyC1mnTq7+J0gQplGqYrjHocO7sVu5b3cWjT/eMuOAdzZgveIffUDmYSD/O8YZKpUy18Uoims8sIjJ1FRvY1tc2j0xp6bt4v+uLQHyIraGbaEybzxnyBsCDN//PFWx6/0/444veStB1hsfNJAKmXgZj5QW3EUI5ux+ny9WAp98PsmprG3N/18XnzB5azMia2wEa+KHt5IyTZ/KtG99JS0OwrDXWsvRUw9ECsvRUw5ffGCwpqE09/54tB1jR1V7eBW+wsaLdjwsp5XhvDDrDmQEKaqVa7Tp8jNf6T4xASx+llpLqZbAhtDZjPvNrfVF2HT6m+cwiIjVOVykyJWTXTw7GfN5v8o/SMdZj5+ZvZNRSpsbNfPbyc2ib1UhTyCXkOhgS6cNBd3zezc9uwJMerH03emHBWt3H4x0c+F0/q+/bXpd1YRu3d7Ov53hGUBsmypXOU9zsPsyVzlMZ832jcZ+9R3o5+makrM+XuuCdikY73ptCLu2zmvjs5efwwJoldZfuLrVF85lFRERXKlLz8u3ijTaC5zTvKI8ld/RStZSFxs10vz7AA784NDwmpVzZDXgyg7VEI598tboRQhD32dfTy8Yd3XVVF2at5Z4tBzJ2XnOlGt7B+oxUw8gYUstTF7xTdSdnssYriUw0zWcWEREFtlLzcu3iQXEjeKJe7iAxfdxMqmb38OsDjLUiPXs0T65gba+dT1fk7oK1umNOk61BY0k1LFe9XPBO1Hglkcmi+cwiIqIzudS0XIEhJIKeAHEC5K6rTB/Bky9IzO68G4t7lFl6C0DINSNG82QHaynF1OrWW11YOamGo30PR6MLXpHaoPnMIiKiKzapabkCw/T01BAxUo2/LWR0xUzfzcsOEovtvFusgAOL2maOaMCTHayVYqqnyWYbS6phuXTBK1IbUvOZB6KJrsiRYso6kjSfWURkalBgKzUtOzDMlZ6aErFB/i72cTb57xyRopoeJJbSebcY4YDDZy5bwEe72kd0lc0O1kpRL2myKWNJNSyXLnhFaoMxhhuXzs8Y61VMWUd2eYiIiNQuBbZS07IDw0LpqXFcYgRy1l2mB4n5anZLFXQNbz2lhW/dkH80T3awVtrr11ea7FhSDYOuwWCIlrA7rgveqSd9xnWqSdaitlYWt8/Uz3kKWN7ZxqO7ezLelCxU1hEOOCPKQ0REpHbVz1WxTEnZgWG56anGwDM9vew4+Dpf/ckLZacfh1yHgGs4uSXMDUvnsbyjreDsz+xgrRT1liY7llTD01obOHVamL1FvmGhC96pJbtePu75xDxL0DUEXIeTmkPcuHQ+yzsL/75KddN8ZhGR+qbAVmpadmBYbnqqb+FHvzrKll//tuyd2qBruOaidi4//4yix6RkB2ulqLc02bGkGt64dD4fXDRbF7x1qFC9fNSzRD2Pgeggdz7+LI/u7uG+1V11lQkx1aTmM2/ckXwjoy9K3LPEPJ9giW88iohIbTHWjnWASeV0dHTYHTt2VHoZUkHWWt79xR/TfSwRGIaJsi18U84a217bNC4jYPIJuQ63fuAdXHvJWSU974GthzKCtWI0Bh0+e/k5dTXHFhI7byvu3Vp0/XM44LBwzgweWLOEoOskdu50wVs3Sj1eQgGHhXNah+daS21LpZ5rPrOISG0zxuy01naM9ji9LS21KzaI2b+Jf5r9NBv6Hb4bvbCk9NRxX06ZzZxy1YUVUs9psmNNNQy6DtcsmcuKrnZd8NaBXPXyYaIsc7Yz1xzlkD01Y4c/Gs8911pqk+Yzi4jUF+3YSm3q2Qkbrgbfw0b7GTJhor7Lyuit7LXzhy9e86WnToRyd2whPV2y+GCtntMltfMqo8nO5oDMUWBNDGWM/9pr5w8/rm1WIz/99KV6k0NERKQKFLtjq8BWak9sEL78dhjqHXFXr22mK/LPRQexhXZvStUUctlwXVfZuwMK1kqnVEPJZ+eh11m5bhsD0USKfyllCmP9XRYREZHxo1Rkmbr2b8L6cXKFLU0By4rwHh4aXEI07lNois7I3ZswX+BeHvEu4Rf+gpKD3LE2c1KabOmUaij5ZM+4LjQKzMVnmbN9eCxM+lxrERERqQ0KbKWmxDyfZ/c+zXnR/pyBresNctVZUf7w9zr55Utv0jcU49hAjF++dJydh14fDnTDRNkQWpuxe9NCBIAV7o/4oPsUd7B+RIpiPuM583S8gzXN7pR6lD3jupRRYOXWy4uIiEjlKLCVmpGqQ537ksPnTAMtZuRF6oAN86+/Nhzq+3XG2I6v/PB5th98ffhxhXZvjIHmZJC7IbR21E7K1drMSbM7pZ5lz7guZRRY0HXquoZdRESkFulqVmpCzPNZtX4be4708t3ohXh5Dl0Ph+9GO9hzpJdV67cRS6Yipi5yUwrt3qRLpSjm0xhMjJOptpmn/ZE4K+7dyp2P76f72CADUY+oZ7EkZncORD26jyVmd664d6t2p2TKSc24TtnsdxY8b2z2O4c/DriGhW2tE75GERERGT/VcyUuUkD62I7USJ9e20SfbcCzhj7bQK9tGh7pkz62A0Ze5KZ2b0aTnaII4BpDU8ilfVYTn738HB5Ys6SqdnfS3wQYbTbuYMwf8SaAyFSwuH0mJzWfyLQo5ryRMtZ6eREREZl81XM1LpKHtZZ7thzICNL22vl0Re4uONJnMOZzz5YDrOhqH77IHYgmRn9s9ju5g/Wjfu7sFEWAd73tZG5+79lV28xJsztFErXqNy6dz52P7x8+dxRz3hjPenkRERGZPApspertOnyM1/qjI26PEBruYprPK28Mse3F11gy7+SMi9zU7k2iK7JHMxFyXcdmpyiGXId3n/0WLpxbnbs5ud4EyDW7M7sxVvqbALqgl6lieWcbj+7uYc+R3uE3egqdN6q1Xl5ERERGp1RkqXqpsR1holzpPMXN7sNc6TxFmJHBbraYb/n0t/bSH4mzvLONc2dPJ5CstU3t3twe+3Me8N7HgA2PmqJY7bV32W8CpHd/bjFDOAZazBCtZoANobUZ38PX+qLsOnysEssWmRBB1+G+1V0snNNKY7Dwn7tqrZcXERGR4mjHVqpefyTOAv8F7g/n33UslGrb88YQq9Zv48E1F3Hf6i4+/vVfsPPQG1hO7N485l/MHfGVBVMUofpr7zS7UyRTczjAg2suYuOOZIfwvihxzxLzfIKuQ8A1nNwS5oal81jeoQ7hIiIitUqBrVS96YE494e+kDVzNtHReENoLddGP8XXQ1/KG/R61mbUkH7z+ndyy8bdfHfPy9i0zzNaanMt1N5pdqfISEHX4Zolc1nR1c6uw8fYkzbTeWHbjKqtlxcREZHiKbCVqvdubysBcnf3dfHZEPoCTeZESm160JuaQZteQxp0Hb68fBEvvzHE7u43iPk252unmx6Ic92sX/KnA3th7zxYcAUER++qPNk0u1MkP2MMF86dpawEERGRKUg5V1JVrLXsPPQ66558ka/88HnWPfki4TcP0Why7zo2MTRqqm1Keg1p0HW479ouFrXPGLX2rjP4Ij8L3sRfDvwT7pa1sOmv4ctvg56dZX6VE0ezO0VERESkHml7RqpCzPPZuD1ZA9cfJe75xDxLsxMl7O5juRMgZEamycYIECR3+mx2qm2ihvQNIFGL2h+J8/5zTmNx+wy+98wryc+bWXt3RjP8a+wLhON9EEu+ULQv8f8NV8Mtv66qndvssUaZ3Z99GokwSBgPR7M7RURERGTKUGArFdcfibNq/Tb29RwfOaYmmBjHky949XCJ4dJCZMR92am2Uc/nH3/wPHHfDgfOQdcQcB1mNQX5syVzecv0MENR70TtXe/3MZvypCr7Huz/Lpz/kbF9A8aRZneKO1nPwgAAIABJREFUiIiISD1SYCsVFfN8Vq3fljFnEjLH1GSzFvppwMPhuuinWBf6Us7Xzk61BTg+lBkgRz1L1PMYiHps2HqQc2e3ct/qrhO1plsOQrQ/9+Kj/XDsYNFf62TR7E4RERERqTeqsZWK2ri9m309xzOCWig8piZKgG9776Ircjc77DtYGb2NXts06gza0QzGfPYc6WXV+m3EUiNzZp4FoebcTwg1w8wzi379yaLZnSIiIiJSb7RjKxVjreWrP3khI/04pdCYmgAev7UzhoPWYlJtixWN+xmjgVhwBXzvltwPdtzE/VVIsztFREREpJ4osJWKiA318/jGr/GhN/dx0Dk1IxANE+Vk00ucAKEctbXZtbMw+gzaUqSPBjLBBlj5SKJRlO8l0o9DzYmgduUjVdU4Kptmd4qIiIhIvTDWjj7Ds1p1dHTYHTt2VHoZUqLBF7fh3X81+HGaGGIgWS+7MnobQLKDr0czEXLFXb22aXg+7URpCrlsuK7rxLzL2CDs35SoqZ15ZtXOsRURERERmUqMMTuttR2jPU47tjKpYkP9ePdfTYvtg2TQ2pJMOd4QWgtYWs3giOelN4wqtXa2HInRQL0nAttgY1V1PxYRERERkRNUWCeTJub5PPiNfwY/9+ieMDHCecb6pDeM2mvnF/w8rjE0hVxaG4NjWmt/JPdaRERERESkuiiwlUnRH4mz4mtbee3wc3mbQoWIESKW877shlH5BF3Dx945lw3XLeHm976VkFteDWnQdU6M/BERERERkaqmK3eZcKlZtbuPvMHp9lQGaBhOP07n4+BjCDGyS3KuhlG5nN7ayN9ecU6yKZIl4DpEvZGvN5qAa1jY1lry80REREREZPJpx1YmXGpWbcyzbPY78fIcdi4+wRxBLYCHw2a/s+DnaQw63LB03nCn38XtMzmpeeQOb5goVzpPcbP7MFc6TxEmOuIxJ7eEWdw+c7QvTUREREREqoACW5lQ1lru2XJgeFZthBAro7fRa5vosw2kN+U2huEuyNaCZ6HPNtBrm0ZtGBUOOJw3ewbLO9rSXs9w49L5NAbd4dvONwfYFr6Ju4Lr+JvAv3NXcB3bwjdxvjkw/JjsAFlERERERKqbAluZENZadh56nc9/91leOZ6ZdrzXzqcrcjff9t5FNE82fIQg/+Et4fbYdaM2jAq6hoVzZrB+dSdBN/OQXt7ZxrmzpxMKOISJsiG0llYzQIsZwjHQYoZoNQNsCK0lTDRngCwiIiIiItVNNbYyrmKez8bt3dyz5QCv9UeJxDy8HKOSI4T4nW0lmKcLcpA4v7LtPOZfXPDzhQMOn7lsAR/tah8R1EKiCdR9q7tYtX4bc196Ehc/5+u4+FwR2sHhMy7PGSCLiIiIiEj1mvTA1hjTBtwPnAb4wNestf/bGDML+DfgTOAgsNxae2yy1yflsdby1IHfcdu3n+Hl3iHifo5oNsuhAo2kRmsWFXQMbz2lhW/d+E5aGgqP9WkOB3hwzUU8+9Ammp7P3ZG5yURY+TY450+XKKgVEREREakxldixjQO3WGt3GWOmATuNMd8HVgE/tNZ+wRhzK3Ar8N8rsD4pQWqH9qs/eYGXeocoIp4dttnv5A7W57wvV7OokOsQcA0nt4S5Yek8lne0FR2EBl2HheddgD3UDNH+EfebUDMLz1sECmpFRERERGrOpAe21tqXgZeT/37TGLMfmA1cBbwn+bBvAD9BgW1V64/EWbV+G/t6jg83hypFqpHUhtBaXHwaiTBIGA9nuFmU68DsGU18aPFspjcEWdg2g8XtM8pr7LTgCsz3bsl5l3FcWHBF6a8pMsVZa9l1+Bi7u3vpj8RpDgdY1NbK4vaZarAmIiIiVcNYW8IW23h/cmPOBH4KnAscttbOSLvvmLV2xLwVY8z1wPUA7e3tFx46dGhyFisZYp7Pinu3sudIL9F47rrVMFGWOduZa45yyJ7KZr8zZ2fj1OPazasctqcMP84AHXNnct+1XTSHx+k9mJ6dsOFq8L3Ezm2oGRwXVj4Csy8cn88hMgVk18vHPZ+YZwm6hoDrcFJziBuXzmd5Z/GZEyIiIiKlMsbstNZ2jPq4SgW2xpgWYAvw99bah40xbxQT2Kbr6OiwO3bsmOilSg4PbD3EnY/vz7tTe745MLwT28QQAzQM78QW6nCcYoArF53Olz6yaPwvmmODsH8THDsIM89M7NQGG8b3c4jUsGKzMRqDDufObuW+1eP45pOIiIhImqoObI0xQWATsNla+7+Stz0HvMda+7Ix5nTgJ9batxd6HQW2ky8xxucYf/6NHbwxGMv5mDBRtoVvotUMjLiv1zbRFbm74EzaoGO4oH0GD6y5SDtBIpOsmGyMdKGAw8I5rTyo31cRERGZAMUGtpN+FWISRVnrgP2poDbpMeDjyX9/HPjOZK9N8ot5Pg9sPcS7v/hjrvk/v8gb1AIsc7YXHKuzzNme97mNQYcL2meyfnWXLpJFKmDj9m729RzPCGrDRLnSeYqb3Ye50nmKMNHh+6Jxn309vWzc0V2J5YqIiIgAlemKfDGwEnjGGLM7edvtwBeAjcaY64DDwEcqsDYhs1lM31CM374Z4Ylnj/J6f7SoMT5zzVGacozwAWgkQrt5deTtQZe3TCu927GIjB9rLfdsOZCRfpyrrOAO1meUFQzGfO7ZcoAVXe1qKCUiIiIVUYmuyE+SKKHM5X2TuRbJlN0sJhL38EbPRByh1Pm0joEzT2riO5+8mFDALXf5IjJGuw4f47X+E7uxYaJsCK3NKCtI/V5vCK3NKCt4rS/KrsPHuHDurMldtIiIiAiV2bGVKlTK6J583Y5Tt88zL+GQe2c313xa38LB1/r51s4jXLNk7rh9TSJyQjFje3Z39xJPezermLKCx/yLAYh7lj3dvQpsRUREpCIU2Aoxz2fV+m1FNYvJl5b4+dhK/i64Yfj2IUL4FoYIESY2Yj5tNqUyikyMUsb29EfixLwTb0qVUlYQ83z6I/EJ/3pEREREclFgW6fSd29+9sLv2N39RsYFbS6F0hK/FPwXnLR4tCnVXMbC/xe/mt/Y0/POsU1RKqPI+CqUiRH1LFHPYyA6yJ2PP8uju3t47ztOIegaoslzQSllBUHX0cgfERERqRhdhdSZ7N2bWNwjVmQdbaG0xHx7rD4Ov7GnD6crFqJURpHxU0omxmDMZ8+RXt4cihNwHaJeIgje7HdyB+tzPie7rCDgGha2tY7fFyAiIiJSAgW2daTcOtqX7ElY4MPu/583LTGfVLpivrrcdEplFBk/+cb25Ps9jMZ9Dv6uj8ZQgIFo4vwQIcTK6G3D5QeNRPKWFZzcEmZx+8zJ/SJFREREkhTY1olo3OPDX/0Zz7/ahzfKyJ7sOtrUbqwl/85sPoOEAcu28E0Fx4WAUhlFxku5Y3uG4paGkKUx6A4/d6+dT1fkbpY522k3r3LYnjLijanGoMMNS+epPl5EREQqRlHEFJdKPf7SE89xbCA26uNz1dGmFLpkzRf0ehjWBL5X1LgQpTKKjI+xjO2JxHzOPKmZA7/rH97tjRDKW04QDjicN3sGyzvaJurLERERERmVAtspbLTU41zpxu9znibM6AGwtYlgdoAGHCxbvPNY6u7Fx9BIdDhd8d74H3FjYFPO18geF6JURpHxMZaxPZ4PVy2azQ9/dZR9Pb0MFijCbwwmgtr1qzsJus74fhEiIiIiJVBgO0WN1jhmrOnGFtjrz+NtzhF8DMvcHQwSxgG+6b2Xbf472Ox3cr27qahxIUplFBk/Yx3bE/N8HlxzERt3JBvN9UWJe5aY5xN0HQKu4eSWMDcsncfyjjYFtSIiIlJxCmynqFyNY1LKTTdON0CYtzk9NJkT6Y7NRAC4wv05d8RXEiFU1LgQpTKKjK/mcGDMY3uCrsM1S+ayoqudXYePsae7l/5InOZwgIVtM1jcPkNvRImIiEjVUGA7BeVqHJOuUFpisRwsNk8YnJ7aONq4kC3uEhYqlVFkXC1qax23sT3GGC6cO0tjuERERKSqKZKYgrIbx2QrlJaYztrM/zwLfbaBXtvEI94lNCZ3aLOlpzZGCPHx+O302mb6bAOeNcnXaObTDZ/nv12+iAfWLFE3ZJFxtLh9Jic1n+hanBrb02ubsn4PmzS2R0RERKYERRM1yFrLrsPH2J2WGriorZXF7TMxxoxoHJOtUFpiughBfuAt5sf+Iixwhnl9eNTHMmc7V7k/GzW1sTHo8MeXXcGBt3yY408/QvjNw0SmtTP9gg/xL/NOUyqjyAQwxnDj0vnc+fh+je0RERGRuqDAtoakRvfcs+UAr/VHiXs+Mc8SdA0B1+Gk5hA3Lp3P8cFYRuOYbIXSEtNFCHJL/C8yLnyLeY1UamOqdvZPOtsTacbzP1H8FysiY7K8s41Hd/dkNJDT2B4RERGZqpSKXCP6I3FW3LuVOx/fT/exQQaiHlHPYoGoZxmIenQfG+TOx5/l2zu7KbThkp2W6OdJN85OUQw48GdL2llw2jScYEPB1EYn2MDCOaqdFamUoOtw3+ouFs5ppTFY+HewMejo91VERERqmrE2/85etevo6LA7duyo9DImXMzzWXHv1ryje8qVmmPbbl7lZTtrRLpx9k5t+6wmtnz6PcR9OzwGpK+vj0v9XzDbHqXHnMqPnCVMb5mmMSAiVSLm+RrbIyIiIjXLGLPTWtsx6uMU2Fa/B7YeyqiVq4TGoMNnLz+Ha5bMHb4tVeurMSAi1U+/ryIiIlKLig1sVWNb5UYb3VOK1A7tXHOUQ/bUnLuyOZ+Xp/ZOY0BEaod+X0VERGQqU2Bb5UYb3VOs880BNoTW4uLTxBADNHAH61kZvY29dn7e5zUGE0Gtau9ERERERKRaKbCtcqON7ilGmCgbQmtpNQPDt6XG9GwIraUrcjdRQgQcQ9y3qr2TKWG0sVgiIiIiMnUosK1y/ZF4wdE9owkT5fbAAzSQe9fXxecDgR20dn6UuSc1q/ZOal6xY7GWd+oNGxEREZGpQoFtlWsOBwi6hmhWcFtMvWwq/biRKEHiOV+/kQht9iihljDXXnLWhH0dIpOhPxJn1fpt7Os5PqIuPepZop7HQDQxFuvR3T3ct7qL5rBOgyIiIiK1Tld0VW5RWysB1yHqnbhIL6ZeNlf6cS6DhOkxp3KuLu6lxsU8n1XrtxU1Fmsw5rPnSC+r1m/jwTUXaedWREREpMbpaq7KLW6fyUnNJ3Zi0wPWFjOEY6DFDNFqBtgY+h982NnCNPoKph+n83D4kbOEhW2tE/lliEy4jdu72ddzPCOoDRPlSucpbnYf5krnKcJpvxPRuM++nl427uiuxHJFREREZBwpsK1yxhhuXDqfxqALwDJnOy65d6PCxFgbXMee8PWscH9EKE/6sbUQsQF6bRMro7cxvWUai9tnTtjXIDLRco3FOt8cYFv4Ju4KruNvAv/OXcF1bAvfxPnmwPBjBmM+92w5QC3P8xYRERERBbY1YXlnG+fOno7rGOaaozQlOxpnMwZCJo5jIGg88vV9ihLgIe9SuiJ383zgbG5YOk9NoqSmZY/FKpTZsCG0NmPn9rW+KLsOH6vEskVERERknCiwrQFB1+G+1V2c0drAIXsqAzSM6fWGCHFX/BqsG+a82TNY3tE2TisVqYzssViFMhtcfJY524c/jnuWPd29E75GEREREZk4CmxrgLWWX71ynEvfcQpP2E68Mn5s2enHnhNiUdtM1q/uVOMcqXnZY7EKZTY0EqHdvDr8cczz6Y/kTtsXERERkdqgVrhVLHseZyzuEbMhVkZvS6ZTxggTy5tynC6VfnxX/BoINPC3ly3go13tCmplSsgei5XKbGjJEdwOEuawPWX446DraOSPiIiISI3T1VyV6huK8ZF7fs4Lv+3L2IkC2Gvn0xW5m8ucn3NX8Os0EBv19YYI8UX7Z8w7fRbfuuGdtDQEJ2rpIpMueyzWZr+TO1if87EeDpv9zuGPA65RV3ARERGRGqftuioT83zu/9lBFt/xffa/8uaIoDYlQoiH/aUsj/4tvbaJPtuAZw0DNoRvYcCG8KyhzzbQa5v4VMPnuP3KC3jsk5coqJUpJ3ssVoREZkP670bqd2Fl9DYinHjsyS1hdQUXERERqXHasa0i/ZE4q9Zv4+nDbxD3ixs/ktq9XeZsp928ymF7Cj/2F3Kps4cznVfpa5rD+z68hq+97Qx1PpYpKzUW687H9w+P/Mn1u7HZ78wIahuDjrqCi4iIiEwBCmyrRDTu8eGv/oxfH32TImPaYRFCPOZfDEDIdQiEDLtb3s+SpfO4uaNNdbRSF5Z3tvHo7h72HOklGk90RE7/3cgWDjjqCi4iIiIyRSiwrbBUg6gvPfEcxwby18qGibLM2c5cc5RD9tQRO08AQddwzUXtXH7+GSxun6FdKKkrqbFYq9ZvY19PL4Ox3ON+ILFTe97sGeoKLiIiIjJFKLCtoFTq8b6e48Ppk7mcbw6wIbQWF58mhhiggTtYz8robey184cfZzC0zWziwrmqF5T61BwO8OCai9i4I9lNvC9K3LPEPJ+g6xBwDSe3hLlh6TyWK5tBREREZMpQYFshMc9n1fptGWmTuYSJsiG0llYzMHxbaoTJhtBauiJ3D+/cah6nSGLn9polc1nR1c6uw8fY091LfyROczjAwrYZymYQERERmYIU2FbIxu3dPFNEUHt74AEaiea838VnmbN9uIZQ8zhFTjDGcOHcWVw4d1allyIiIiIiE0xRUAVE4x7/7+ZfMVQgqE2lHzcQJUjuXdhGIrSbV4c/1jxOERERERGpRwpsJ1l/JM4ff/VnvDGYP2U4V/pxLoOEOWxPGf5Y8zhFRERERKQeKbCdRKm62l+/2pfz/lTn42XOdsLk75Cc4uGw2e8ENI9TRERERETqlwLbSbRxezf7eo7j5RhUm975uDnZHCoXayFKgCFCrIzeRoSQ5nGKiIiIiEhdU2A7SaJxjy898VzOsT7Fph5DIqh9yLuUu+LXECFE0DUsnKN5nCIiIiIiUr8U2E6C/kicD3/1ZxwbyJ1evMzZjkv+RlLphggNB7XhgMNnLlvAR7vaFdSKiIiIiEjdUmA7wVJ1tc+PUlfblCf92FqwwAANeDisjN6GZ0IsOHUa37rxnbQ0BCdw9SIiIiIiItVPge0E+7dth9l7pLdgXW2YGPlaPkUI8gNvMU/4HWz2O2lqaubzy97O8o427dKKiIiIiIigwHZCWGvZ9uJrrH/qIJufPYodGdMWXVcbIcgt8b8gakK84/RpfOcTFxMKuBO0chERERERkdqjwHYcxTyfjdu7ufsnL/By7xA5NmmBRFB7e+ABGonmvN/aREAbITjc+XjBqdP49xt/T0GtiIiIiIhIFgW246Q/EmfV+m08c6SXoXj+RlCp9OMGogSJ53yMBX7gLeaW+F8QIcSs5iDf+aR2akVERERERHJRYDsOUg2i9hzpJVogqC02/XiABp7wO4gQojHocMsfvF1BrYiIiIiISB4KbMfBxu3d7Os5njeoTXU+XuZsJ0zukT/pPBw2+524juG82TNY3tE23ksWERERERGZMhTYjpG1lnu2HGAw5uW8P5V67OLTxFDe7sfWQpQAQ4TS6mpbWL+6U92PRUREREREClBgO0a7Dh/jtf7cTaCKTT2GRFD7kHcpd8WvIUKImU1BdUAWEREREREpgrYCx2h3dy9xL3cK8jJnOy75a27TDREaDmobAoZPLVNdrYiIiIiISDG0YztG/ZE4MW/kXJ9UXW0zQzmfZ22i+/EADXg4w+nH4YDD+XNUVysiIiIiIlIsBbZj1BwOEHQN0bTgNlVXW6hRVIQgP/AW84TfwWa/czioXThnhupqRURERERESqDAdowWtbUScB2iXqJ5VLF1tRGCw3NqAVzH8LeXL2B5Z7uCWhERERERkRJUXQRljPlDY8xzxpgXjDG3Vno9o1ncPpOTmkPDHxeqq7UWhmyQXts0nHoMEHINn7/yHK656EwFtSIiIiIiIiWqqijKGOMC/wx8ADgH+Kgx5pzKrqowYww3Lp1PYzDR6GmuOUpTvrpa4AfeYroid7PXzgcgHHBY1DaTP+lsn6wli4iIiIiITClVFdgCXcAL1trfWGujwEPAVRVe06iWd7Zx7uzphAIOh+ypDNCQ83EDNPCE3zG8U9sYVE2tiIiIiIjIWFVbNDUb6E77+EjytqoWdB3uW93FwjmtbHGX4OX5tno4bPY7cQzMmdnIZy8/hwfWLKE5rFJnERERERGRclVbRGVy3JYxS8cYcz1wPUB7e/Wk7zaHAzy45iI27ujmUz/6HF8a+jwuHo1EGCSMh8tfmM/y++e18/HfO5POM2dhTK4vV0REREREREphrB05g7VSjDHvBD5nrV2W/Pg2AGvt2lyP7+josDt27JjEFRbHWsvTv3mZ408/QvjNw0SmtTP9gg9xwbzTFMyKiIiIiIgUyRiz01rbMdrjqm3HdjtwtjHmLKAH+FNgRWWXVDpjDIvnnwHzP1HppYiIiIiIiEx5VRXYWmvjxphPApsBF/i6tfaXFV6WiIiIiIiIVLGqCmwBrLXfA75X6XWIiIiIiIhIbai2rsgiIiIiIiIiJVFgKyIiIiIiIjVNga2IiIiIiIjUNAW2IiIiIiIiUtMU2IqIiIiIiEhNU2ArIiIiIiIiNU2BrYiIiIiIiNQ0BbYiIiIiIiJS0xTYioiIiIiISE1TYCsiIiIiIiI1TYGtiIiIiIiI1DQFtiIiIiIiIlLTFNiKiIiIiIhITVNgKyIiIiIiIjXNWGsrvYayGWN+Cxyq9DpGcTLwu0ovQqQIOlalVuhYlVqhY1VqiY5XqVZzrbVvGe1BNR3Y1gJjzA5rbUel1yEyGh2rUit0rEqt0LEqtUTHq9Q6pSKLiIiIiIhITVNgKyIiIiIiIjVNge3E+1qlFyBSJB2rUit0rEqt0LEqtUTHq9Q01diKiIiIiIhITdOOrYiIiIiIiNQ0BbYTxBjzh8aY54wxLxhjbq30ekSyGWMOGmOeMcbsNsbsSN42yxjzfWPM88n/z6z0OqX+GGO+box51RizL+22nMemSfhK8ly71xizuHIrl3qT51j9nDGmJ3lu3W2M+aO0+25LHqvPGWOWVWbVUo+MMW3GmB8bY/YbY35pjPmr5O06t8qUocB2AhhjXOCfgQ8A5wAfNcacU9lVieR0qbV2UVp7/1uBH1przwZ+mPxYZLLdB/xh1m35js0PAGcn/7se+OokrVEEch+rAP+QPLcustZ+DyB5HfCnwH9JPufu5PWCyGSIA7dYaxcAFwGfSB6TOrfKlKHAdmJ0AS9Ya39jrY0CDwFXVXhNIsW4CvhG8t/fAD5YwbVInbLW/hR4PevmfMfmVcD9NmErMMMYc/rkrFTqXZ5jNZ+rgIestRFr7YvACySuF0QmnLX2ZWvtruS/3wT2A7PRuVWmEAW2E2M20J328ZHkbSLVxAJPGGN2GmOuT952qrX2ZUj8EQROqdjqRDLlOzZ1vpVq9Mlk+ubX00o6dKxKVTDGnAlcAPwCnVtlClFgOzFMjtvUflqqzcXW2sUk0o0+YYx5d6UXJFIGnW+l2nwVmA8sAl4Gvpy8XceqVJwxpgX4NvDX1trjhR6a4zYdr1LVFNhOjCNAW9rHc4CXKrQWkZystS8l//8q8AiJlLijqVSj5P9frdwKRTLkOzZ1vpWqYq09aq31rLU+cC8n0o11rEpFGWOCJILaB6y1Dydv1rlVpgwFthNjO3C2MeYsY0yIRLOIxyq8JpFhxphmY8y01L+BPwD2kThOP5582MeB71RmhSIj5Ds2HwM+luzgeRHQm0qrE6mErDrEq0mcWyFxrP6pMSZsjDmLRFOebZO9PqlPxhgDrAP2W2v/V9pdOrfKlBGo9AKmImtt3BjzSWAz4AJft9b+ssLLEkl3KvBI4u8cAeBBa+1/GmO2AxuNMdcBh4GPVHCNUqeMMd8E3gOcbIw5Avwd8AVyH5vfA/6IRCOeAWD1pC9Y6laeY/U9xphFJNI2DwI3AFhrf2mM2Qg8S6JD7SestV4l1i116WJgJfCMMWZ38rbb0blVphBjrdLlRUREREREpHYpFVlERERERERqmgJbERERERERqWkKbEVERERERKSmKbAVERERERGRmqbAVkRERERERGqaAlsREZExMMbMMcZ8xxjzvDHmgDHmfydnmI/2vNsL3HfQGPNM8r9njTF3GmPC47tyERGRqUOBrYiISJlMYhj0w8Cj1tqzgbcBLcDfF/H0vIFt0qXW2vOALmAe8LWxrDXFGKMZ9iIiMuUosBURESnfe4Eha+16AGutB/wNcK0xpskYs8oY80+pBxtjNhlj3mOM+QLQaIzZbYx5oNAnsNb2ATcCHzTGzEq+zqeNMduNMXuNMZ9Pe/3/xxjzK2PM940x3zTGfCp5+0+MMXcZY7YAf2WMeYsx5tvJ19hujLk4+bhmY8zXk7c9bYy5aly/WyIiIhNE79qKiIiU778AO9NvsNYeN8YcBt6a70nW2luNMZ+01i4q5pMkX/NF4GxjTCtwNomdXAM8Zox5NzAAfBi4gMTf911Za5thrV0KYIx5EPgHa+2Txph2YDOwAPgM8CNr7bXGmBnANmPMD6y1/cWsU0REpFIU2IqIiJTPALaE28f6uQD+IPnf08mPW0gEutOA71hrBwGMMd/Nev6/pf3794FzEpnUAEw3xkxLvu6VqZ1eoAFoB/aP49chIiIy7hTYioiIlO+XJHZJhxljpgNtwAFgIZllPw3lfJJk0Hkm8GsSAe5aa+2/ZD3mb0Z5mfRdVwd4ZyoITnsNA3zYWvtcOesUERGpFNXYioiIlO+HQJMx5mMAxhgX+DJwn7V2ADgILDLGOMaYNhLpwykxY0xwtE9gjGkB7ibRoOoYibTha5O3Y4yZbYw5BXgSuMIY05C877ICL/sE8Mm0z5FKid7xJ+MUAAABAElEQVQM3JwMcDHGXDDqd0BERKQKKLAVEREpk7XWAlcDHzHGPE9iR3WIEx2PnwJeBJ4BvkSi7jXla8DeAs2jfmyM2QdsAw4DNyQ/5xPAg8DPjTHPAP8OTLPWbgceA/aQ6NS8A+jN89p/CXQkm089S6I5FcAdQDC5rn3Jj0VERKqeSfxNFhERkVpnjGmx1vYZY5qAnwLXW2t3jfY8ERGRWqcaWxERkanja8aYc0jU8n5DQa2IiNQL7diKiIiIiIhITVONrYiIiIiIiNQ0BbYiIiIiIiJS0xTYioiIiIiISE1TYCsiIiIiIiI1TYGtiIiIiIiI1DQFtiIiIiIiIlLT/i8I2ezDQKyeJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "assi = fig.gca()\n",
    "assi.plot(x,y_mean,marker='o', ms=15, linestyle='None')\n",
    "assi.plot(x,y_median,marker='o', ms=7, linestyle='None')\n",
    "assi.set_xlabel('Out Degree')\n",
    "assi.set_ylabel('In Degree')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio guidato**: Possiamo anche chiederci quali nodi hanno un comportamento 'particolare'. Nello specifico vogliamo identificare, se esistono, i nodi con una elevata discrepanza tra l'attività in uscita e quella in entrata.\n",
    "\n",
    "Calcoliamo quindi la differenza tra la strength dei nodi, in entrata e uscita"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "differenza_in_out = [np.abs(v['in']-v['out']) for v in in_and_out4nodes.values()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estriamo i valori della differenza, calcoliamo la CDF e la visualizzaziamo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f053dd1aac8>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = ECDF(differenza_in_out)\n",
    "x = np.unique(differenza_in_out)\n",
    "y = cdf(x)\n",
    "fig = plt.figure(figsize=(16,9))\n",
    "assi = fig.gca()\n",
    "assi.plot(x,y,linestyle='None', marker='o', ms=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Come abbiamo visto per l'identificazione degli hub dobbiamo estrarre un valore di soglia che identifica un comportamento 'anomalo'. Possiamo calcolare il quantile 0.99."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56.01999999999998"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "soglia = np.percentile(differenza_in_out, 99)\n",
    "soglia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Oppure calcolare la media e sommare 3 deviazioni standard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "39.35453398824574\n"
     ]
    }
   ],
   "source": [
    "soglia2 = np.mean(differenza_in_out) + 3 * np.std(differenza_in_out)\n",
    "print(soglia2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infine identifichiamo i nodi con un comportamento anomalo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Identificazione nodi outlier\n",
    "node2diff = {k: np.abs(v['in']-v['out']) for k,v in in_and_out4nodes.items()}\n",
    "nodi_anomali = set([k for k,v in node2diff.items() if v >= soglia])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'36', '400', '9', '67', '266', '3', '41', '105', '176', '321', '770', '871', '1543', '12', '19', '1598', '103', '249', '357'}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "19"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(nodi_anomali)\n",
    "len(nodi_anomali)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Altre misure di centralità (Zafarani)\n",
    "\n",
    "Per confrontare la degree centrality in due reti differenti posso normalizzare il grado, secondo i seguenti schemi:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalizzazione del grado\n",
    "<img src='figures/degree_norm.png'>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 0.12486828240252898)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_degree_sample = list(dict(ucirvine_graph.out_degree()).values())\n",
    "max_out_degree = np.max(out_degree_sample)\n",
    "sum_out_degree = np.sum(out_degree_sample)\n",
    "order_norm = ucirvine_graph.order() - 1\n",
    "out_degree_norm = [e/order_norm for e in out_degree_sample]\n",
    "out_degree_max = [e/max_out_degree for e in out_degree_sample]\n",
    "out_degree_sum = [e/sum_out_degree for e in out_degree_sample]\n",
    "min(out_degree_norm), max(out_degree_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvector centrality\n",
    "L'idea di questa centralità è molto semplice: un nodo è importante se ha molti amici importanti\n",
    "<img src='figures/eig.jpg'>\n",
    "\n",
    "In NetworkX la computazione della eigenvector centrality è eseguita dal metodo:\n",
    "\n",
    "**eigenvector_centrality(G, max_iter=100, tol=1e-06, nstart=None, weight=None)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fatto 1\n",
      "Fatto 2\n",
      "Fatto 3\n"
     ]
    }
   ],
   "source": [
    "eigen_con_pesi = nx.eigenvector_centrality(ucirvine_graph, weight='peso')\n",
    "print('Fatto 1')\n",
    "eigen_senza_pesi = nx.eigenvector_centrality(ucirvine_graph, weight=None)\n",
    "print('Fatto 2')\n",
    "eigen_senza_pesi_numpy = nx.eigenvector_centrality_numpy(ucirvine_graph)\n",
    "print('Fatto 3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0015769463599309445\n",
      "0.008194725751443355\n",
      "0.008195008397299315\n"
     ]
    }
   ],
   "source": [
    "print(eigen_con_pesi['270'])\n",
    "print(eigen_senza_pesi['270'])\n",
    "print(eigen_senza_pesi_numpy['270'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Estrarre i nodi con centralità massima nei casi di eigenvectort centrality pesata e non."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('1624', 0.469127802110353) ('32', 0.153518668255088)\n"
     ]
    }
   ],
   "source": [
    "max_weight = sorted(eigen_con_pesi.items(),key= lambda x:x[1], reverse=True)[0]\n",
    "max_noweight = sorted(eigen_senza_pesi.items(),key= lambda x:x[1], reverse=True)[0]\n",
    "print(max_weight,max_noweight)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 1.8832407348632722e-11, 1: 3.0686146707563375e-06, 3: 3.068627147808309e-06, 2: 0.9999999999905835}\n"
     ]
    }
   ],
   "source": [
    "toy = nx.DiGraph()\n",
    "toy.add_edges_from([(0,1),(0,3),(1,2),(3,2)])\n",
    "print(nx.eigenvector_centrality_numpy(toy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Katz centrality\n",
    "Per ovviare al problema evidenziato dal grafo 'giocattolo' nella Katz centrality viene introdotto il fattore $\\beta$, grazie al quale si evitano valori di centralità uguali a 0.\n",
    "<img src='figures/katz.png'>\n",
    "\n",
    "In NetworkX la Katz centrality è calcolata dal metodo:\n",
    "\n",
    "**katz_centrality(G, alpha=0.1, beta=1.0, max_iter=1000, tol=1e-06, nstart=None, normalized=True, weight=None)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "grafo_matrice = nx.to_numpy_matrix(ucirvine_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zigno/anaconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.02259649781622392"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = 1/(float(np.max(np.linalg.eig(nx.to_numpy_matrix(ucirvine_graph))[0]))+10)\n",
    "alpha"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "katz_cent = nx.katz_centrality(ucirvine_graph, alpha=alpha, beta=1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('1', 0.028136881923964508),\n",
       " ('2', 0.013532940041570638),\n",
       " ('3', 0.04149167487224097),\n",
       " ('4', 0.009764598715730682),\n",
       " ('5', 0.0088270327461842),\n",
       " ('6', 0.04648165022668076),\n",
       " ('7', 0.013289097108751171),\n",
       " ('8', 0.0599998657416455),\n",
       " ('9', 0.053713964473916895),\n",
       " ('10', 0.010245470812410508)]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(katz_cent.items())[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Page rank\n",
    "<img src='figures/page.png'>\n",
    "**Esercizio**: Calcoliamo il pagerank sul grafo di UCIrvine utilizzando o meno i pesi degli archi. Si identifichino i nodi con pagerank maggiore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "pr_centrality = nx.pagerank_numpy(ucirvine_graph,weight='peso')\n",
    "pr_centrality_senza_peso = nx.pagerank_numpy(ucirvine_graph,weight=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('32', 0.006860894208174804)\n",
      "('32', 0.005997514282124588)\n"
     ]
    }
   ],
   "source": [
    "max_weight = sorted(pr_centrality.items(),key= lambda x:x[1], reverse=True)[0]\n",
    "max_noweight = sorted(pr_centrality_senza_peso.items(),key= lambda x:x[1], reverse=True)[0]\n",
    "print(max_weight,max_noweight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il nodo con PageRank piu' elevato rimane lo stesso, indipendentemente dal peso associato agli archi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Betweenness centrality\n",
    "<img src='figures/bet.png'>\n",
    "<img src='figures/bet_norm.png'>\n",
    "\n",
    "In NetworkX questa centralita' e' calcolata dal metodo\n",
    "```python\n",
    "betweenness_centrality(G, k=None, normalized=True, weight=None, endpoints=False, seed=None)\n",
    "```\n",
    "Il coefficiente di normalizzazione dipende dal tipo di grafo (non orientato/orientato)\n",
    "\n",
    "Il parametro $k$ restringe il numero di nodi $\\in V$ tra cui calcolare i cammini minimi. Nello specifico vengono estratti $k$ nodi in modo casuale da $V$. Questa modalita' e' utile quando il tempo di computazione applicando l'algoritmo standard e' elevato\n",
    "\n",
    "E' possibile calcolare la betweenness centrality valutando il numero di cammini minimi che passano gli archi, anziche' sui nodi. In questo caso il metodo da utilizzare e':\n",
    "```python\n",
    "edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None)\n",
    "```\n",
    "Viene restituito un dictionary che associa ad ogni arco del grafo il corrispettivo valore di betweenness.\n",
    "\n",
    "La betweenness centrality sugli archi puo' essere utilizzata per valutare la quantita' di informazione che puo' passare attraverso una relazione, ipotizzando che l'informazione si propaghi nella rete solo attraverso i cammini minimi. \n",
    "\n",
    "\n",
    "**Esercizio da svolgere in aula**: Si trovi il nodo con betweenness centrality maggiore nel grafo UCIrvine considerando o meno l'orientamento degli archi. Per estrarre la versione non orientata di un grafo orientato $D$ si puo' utilizzare il metodo di NetworkX **to_undirected()**. Si individui anche l'arco con edge betweenness centrality più elevata nel grafo UCIrvine non orientato."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ucirvine_graph = nx.DiGraph()\n",
    "with open('data/out.opsahl-ucsocial') as f:\n",
    "    f.readline()\n",
    "    f.readline()\n",
    "    for line in f:\n",
    "        sorgente, destinazione, _ , _ = line.strip().split()\n",
    "        if ucirvine_graph.has_edge(sorgente,destinazione):\n",
    "            ucirvine_graph[sorgente][destinazione]['peso'] += 1\n",
    "        else:\n",
    "            ucirvine_graph.add_edge(sorgente,destinazione,peso=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "bc_orientato = nx.betweenness_centrality(ucirvine_graph)\n",
    "bc_nonorientato = nx.betweenness_centrality(ucirvine_graph.to_undirected())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('32', 0.04116792473108579)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(bc_orientato.items(), key = lambda x:x[1], reverse = True)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('9', 0.06464919453079458)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted(bc_nonorientato.items(), key = lambda x:x[1], reverse = True)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Closeness centrality\n",
    "<img src='figures/close.png'>\n",
    "\n",
    "Piu' i valori della closeness centrality sono elevati piu' il nodo e' centrale.\n",
    "\n",
    "Il metodo per il calcolo della closeness centrality in NetworkX e':\n",
    "```python\n",
    "closeness_centrality(G, u=None, distance=None, wf_improved=True, reverse=False)\n",
    "```\n",
    "_distance_ ha lo stesso significato del classico attributo _weight_ utilizzato nei metodi finora visti. \n",
    "\n",
    "Il metodo utilizza una versione migliorata della closeness centrality:\n",
    "$$ C_{+}(u) = \\frac{n-1}{N-1}C_c(u) $$\n",
    "dove $N$ indica il numero di nodi del grafo e $n$ il numero di nodi raggiungibili da $u$.\n",
    "\n",
    "**Esercizio da svolgere in aula**: Si calcoli la closeness centrality utilizzando o meno la versione migliorata dell'indice. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "cc_migliorata = nx.closeness_centrality(ucirvine_graph)\n",
    "cc_nonmigliorata = nx.closeness_centrality(ucirvine_graph, wf_improved=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('32', 0.31788579872505657)\n",
      "('187', 1.0)\n"
     ]
    }
   ],
   "source": [
    "print(sorted(cc_migliorata.items(), key = lambda x: x[1], reverse=True)[0])\n",
    "print(sorted(cc_nonmigliorata.items(), key = lambda x: x[1], reverse=True)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structural equivalence\n",
    "<img src='figures/jaccard_cosine.png'>\n",
    "\n",
    "**Esercizio da svolgere in aula**: Si implementino due funzioni *structural_equivalence_jaccard(graph,nodo1,nodo2)* e *structural_equivalence_cosine(graph,nodo1,nodo2)* che calcolano l'equivalenza strutturale dei due nodi passati come argomento. Si calcolino le equivalenza strutturali di un nodo estratto a caso ed un suo vicino estratto a caso"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "set(ucirvine_graph['32'].keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def structural_equivalence_jaccard(graph, u, v):\n",
    "    vicinato_u = set(graph[u].keys())\n",
    "    vicinato_v = set(graph[v].keys())\n",
    "    numeratore = len(vicinato_u.intersection(vicinato_v)) # calcolo intersezione\n",
    "    denominatore = len(vicinato_u.union(vicinato_v)) # calcolo unione\n",
    "    return numeratore/denominatore\n",
    "    \n",
    "def structural_equivalence_cosine(graph, u, v):\n",
    "    vicinato_u = set(graph[u].keys())\n",
    "    vicinato_v = set(graph[v].keys())\n",
    "    numeratore = len(vicinato_u.intersection(vicinato_v)) # calcolo intersezione\n",
    "    denominatore = np.sqrt(len(vicinato_u)*len(vicinato_v))\n",
    "    return numeratore/denominatore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zigno/anaconda3/lib/python3.6/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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Il19+qbCwMK1atUp9+vQxHQcAbun999/Xz3/+c3300UcKCQkxHadKsEL2IU2aNNGSJUs0YcIEff3116bjAMAtjR49Wn/5y180ZMgQZWZmmo5TJVgh+6Bnn31WR48e1YYNG2S705dWAEAVWL16tZ5++mlt2bJFQV7+GllWyD7olVde0ZkzZ/SXv/zFdBQAuK2HH35Yc+bM0aBBg5SVlWU6TqViheyjjh8/ru7du2vLli0++8wfAM/x3nvv6Ze//KUSEhLUuXNn03EqBStkH3X//fdr3rx5iouL0+XLl03HAYDbiouL0xtvvKFBgwbp8OHDpuNUClbIPu7xxx9XUVGR3nnnHdNRAOAHrVy5Ur/+9a+1detWdezY0XQct2KF7OPmzZunffv2afny5aajAMAPGjdunGbPnq0BAwYoOzvbdBy3qmE6AMyqU6eOVq1apQEDBqh79+5q06aN6UgAcFvjx4+X3W7XwIEDtXXrVnXo0MF0JLdghQyFhIToxRdf1NixY3Xt2jXTcQDgBz3yyCP685//rAEDBuiTTz4xHcctuIcMSY5XNcbGxqpVq1Z64403TMcBgDJZvny5fvOb32jbtm1q37696TgVwpY1JEk2m02LFy9WaGio+vfvr5iYGNORAOAHPfroo7Lb7erfv7/HlzKFjBINGjTQihUrNHr0aKWnp6tZs2amIwHAD5o4caLsdrsGDBigbdu2qV27dqYj3RHuIcNFr1699OSTT2rChAm6ceOG6TgAUCaPPfaYXn75ZfXv319Hjx41HeeOUMgo5YUXXpAkvfrqq4aTAEDZTZo0Sf/7v/+r/v3769NPPzUdp9zYskYp1atX17vvvquuXbuqb9++ioyMNB0JAMpk8uTJJfeUt2/fXvpRztxcaelSKTNTunhRCgyUgoOlyZOlu+82ktmJKWvc0qZNm/Szn/1MBw4cUIMGDUzHAYAye/vtt/Xiiy9q+/btat26tZSaKs2cKcXHO76hoODbb/b3l+x2KSpKev55qVs3I5kpZNzWM888oxMnTuiDDz7gVY0APMrixYv10ksvKe3//T81+vOfpfx8R/Heis3mKOfZs6Xp06suqPPHU8i4nWvXrikiIkJTpkzRk08+aToOAJRL8oQJCvv73xVQnqoLCDBSyhQyftCxY8cUERGhrVu3KiQkxHQcACib1FSpb18pL6/8nw0IkHbulMLD3R7rVpiyxg9q06aN3njjDcXFxenq1aum4wBA2cyc6dimvhP5+Y7PVyFWyCizxx57TDVq1NDixYtNRwGA28vNlVq2dB3eKi8/P+nkySqbvmaFjDKbP3++kpOTtXLlStNRAOD2li6t+DVsNvdcp4woZJRZ3bp1tWrVKj311FM6fvy46TgAcGuZmRVbHUuObeusLPfkKQMKGeUSGhqq3/3udxo7dqwKCwtNxwGA73fxonuuc/68e65TBhQyyu0Xv/iFmjRpov/5n/8xHQUAvldRnTruuVD9+u65ThlwdCbKzWaz6e2331ZoaKj69eunqKgo05EA+Lhz585p165dSkxMVFJSkvrv36/f2Wzyq8jcsr+/FBTkvpA/gClr3LGdO3dq7Nix2r9/v5o0aWI6DgAf8sUXXygpKank14kTJ9S9e3f17t1bkZGR+q9WreTfvr1HTVlTyKiQP/zhD9q1a5e2bNmiatW4AwLA/ex2uz777LOS8k1MTNTFixcVGRlZ8is0NFQ1anxn0zc2Vlq//vbHZd6KzSaNHCmtXeuev0RZfiSFjIooKioq2bZ+/vnnTccB4AWKi4uVlZVVUr5JSUmqUaNGyeq3d+/eat++/Q8vAjzspC4KGRWWk5Oj8PBwrV+/Xj169DAdB4CHKSwsVHp6ekn57tq1S40bNy4p38jISLVs2fLOXnCzYIE0Y0b5SpmzrOHJNmzYoKeffloZGRn60Y9+ZDoOAAu7evWq9uzZU1LAqampatOmTUn59urVS40bN3bfD3SWMm97gq/4xS9+oS+//FJr1qzhVY0ASpw7d07JycklW9CHDx9Wly5dSgo4IiJCgYGBlRsiLc1xNvXmzY7ivfmMa+f7kKOjHe9DrsJt6ptRyHCbgoICde/eXdOnT9dPf/pT03EAGOKcgHaugD///HP16NGjZAu6W7du8vf3NxPu7FnHcZhZWY5DP+rXdzzaNGlSlU1T3wqFDLc6evSoevXqpR07dqhz586m4wCoZM4JaGf5JiYm6tKlSyXTz71791aXLl1KT0CjFAoZbrd06VLNmjVLqampCggIMB0HgBvduHGjZALaWcC1atVyGcAq0wQ0SqGQ4XZ2u10TJkxQ3bp1tXDhQtNxAFRAYWGh0tLSSso3JSVFjRs3dnkEqWXLlqZjegUKGZXi0qVLCgsL08yZMzVmzBjTcQCU0ZUrV1wmoNPS0tS2bduSLWi3T0CjBIWMSpOWlqbo6Gjt3btX9957r+k4AL7HN998UzIBnZSUpMOHDys0NLRk9RsREaG77rrLdEyfQCGjUr3++utavXq1kpKSVLNmTdNxAJ936tQpl/u/OTk5rmdA/9d/yc/Pz3RMn0Qho1IVFxcrJiZGISEhmjlzpuk4gE+x2+06duyYyyNIly9fdjkDmglo66CQUelyc3MVFhamJUuWaODAgabjAF7r5gloZwHXqlWr1BnQHNxjTRQyqsT27ds1YcIEHThwgIEQwE2cE9A3nwHdpEmTUmdAwzNQyKgyv/3tb5Wamqr4+HieUQTuwJUrV7R79+6SFXB6enrJBHTv3r3Vq1cvNWrUyHRM3CEKGVWmqKhIffr00YgRI/Tss8+ajgNY3s0T0ImJicrOzlZoaKjLGdBMQHsPChlV6vPPP1e3bt20ceNGPfDAA6bjAJbinIB2bkHn5OSUOgOaCWjvRSGjyn3wwQeaMWOGDhw4UPlveAEsyjkB7Szf705A9+7dWyEhIUxA+xAKGUb87Gc/07lz57Ry5UomPuETbty4oczMzJLyTUpKUu3atUudAc1/D76LQoYR+fn5euCBB/T000/r8ccfNx0HcLtr1665TECnpKSoSZMmJeXLBDS+i0KGMdnZ2erTp4927typjh07mo4DVIhzAvrmM6Dbt2/vcgY0E9C4HQoZRi1atEjz5s3T3r17zb2wHLgDX3/9tcsE9CeffKKwsLCSLegePXowAY1yoZBhlN1u17hx49SgQQO9+eabpuMAt5STk+NyBvSpU6fUo0ePki1oJqBRURQyjLt48aJCQ0M1e/ZsxcbGmo4DyG6369NPP3V5BOnKlSsu93+ZgIa7UciwhL1792ro0KFKTU1l0AVVzjkBffMjSH5+fi5nQLdr144JaFQqChmW8dprr2nDhg3auXMnKw9UqmvXrik1NbWkfFNSUtS0aVOXR5BatGhhOiZ8DIUMyyguLlZUVJS6deuml19+2XQceJHLly+XOgPaOQHtPAP67rvvNh0TPo5ChqV89dVXCg0N1bvvvqt+/fqZjgMP5ZyAdm5BOyegnatfJqBhRRQyLCchIUGTJ0/WgQMHWLWgTHJyclzu/546dUoRERElK+Dw8HAmoGF5FDIs6Te/+Y2ysrK0ceNGXtUIF84JaGcBJyYmKi8vz+UM6ODgYOYQ4HEoZFjS9evXFRkZqbi4OD3zzDOm48CgGzdu6ODBgyXlm5ycLH9/f5cBLCag4Q0oZFjWv//9bz3wwAOKj49X165dTcdBFbl5AjoxMVG7d+9W06ZNXZ4BZgIa3ohChqWtWbNGL7zwgtLT0xnC8VKXL19WSkpKyf3f9PR0dejQweUMaGYJ4AsoZFjetGnTlJeXp+XLl7Mt6QXOnj3rcgb0kSNH1LVrV5czoOvVq2c6JlDlKGRYXl5enrp166bnnntOjz32mOk4KKeTJ0+6HEH5xRdfKCIiwuUM6Nq1a5uOCRhHIcMjHDp0SA8++KCSk5PVrl0703FwC3a7XUePHnV5BMk5Ae0s4JCQEFWvXt10VMByKGR4jIULF+qtt97S7t27eabUIpwT0DcXcEBAgMsZ0G3btuVWA1AGFDI8ht1u15gxY9S0aVPNmzfPdByfVFBQUGoC+ic/+YnLCrh58+amYwIeiUKGRzl//rxCQ0M1b948DRs2zHQcr+ecgHaugPfv318yAe08A7phw4amYwJegUKGx0lJSdHIkSOVnp6un/zkJ6bjeBXnBLSzgJ0T0DefAc0ENFA5KGR4pFdffVX//Oc/tX37do5IrICTJ0+6HEF5+vRp9ezZs+QZYCaggapDIcMj3bhxQ4MHD1avXr304osvmo7jEex2u44cOVIyfJWYmKiCgoJSZ0AzAQ2YQSHDY3355ZcKCwvTqlWr1KdPH9NxLKeoqKjUGdB16tRxGcBiAhqwDgoZHi0+Pl7Tpk1TRkaGfvzjH5uOY5RzAtq5Be2cgL75DGgmoAHropDh8WbMmKFPP/1UGzZs8KnV3qVLl1zOgHZOQDsLmAlowLNQyPB4hYWF6tmzpx599FE99dRTpuNUmrNnz7rc/z169KjCw8NLtqC7d+/OBDTgwShkeIXjx4+re/fu2rJli0JDQ03HcYvPP//c5QzoL7/80uUM6PDwcCagAS9CIcNrrFy5Ui+++KLS09NVt25d03HKxTkBffMRlM4JaGcBMwENeDcKGV5lypQpKi4u1tKlS01Hua2ioiJlZGSUlG9SUpLq1q3rcgZ0mzZtfOqeOODrKGR4latXr6pr16767W9/qwkTJjj+MDdXWrpUysyULl6UAgOl4GBp8mSpil58X1BQoH379pVsQe/Zs0fNmzcvmX5mAhoAhQyvc/DgQQ0YMEDpb72lFitWSPHxji8UFHz7Tf7+kt0uRUVJzz8vdevm1gzOCWjnFvSBAwfUsWPHktVvz549mYAG4IJChlf6eOxYPbB6tfwk2W73r7jN5ijn2bOl6dPv+Ofl5ua6bD87J6BvPgPa0+5rA6haFDK8z4IFss+YIVteXtk/ExBQrlL+/PPPXc6APnPmjMsZ0ExAAygvChneJTVV6ttXKk8ZOwUESDt3SuHhLn9st9v1ySefuDyCdO3aNZcBrKCgICagAVQIhQzvEhsrrV/vuD9cXjabNHKkit57TxkZGSXlm5ycrHr16rk8gsQENAB3o5DhPXJzpZYtXYe3yulatWpq7++vOq1auZwBzXuXAVQ2XiQL7+GGZ4+r16ihQ88+qzp/+EPF8wBAOVDI8B6ZmRVaHUtSjcJC1Th+3E2BAKDsqpkOALjNxYvuuc758+65DgCUA4UM7xEY6J7r1K/vnusAQDlQyPAewcGSn1/FruHvLwUFuScPAJQDU9bwHm6Yspafn3TyZJWdcQ0ATqyQ4T0aNZKiomS/0+eDbTYpOpoyBmAEhQyvsqt3b+Xf6aaPv7/jRRMAYACFDK+xePFijfrTn/TljBmOYzDLw3mW9XeOzQSAqsJzyPB4drtdL730kpYtW6bExETd37atdN990owZUn7+7Y/RdNPbngCgohjqgkcrKirSE088oYyMDH344Ye65557vv1iWpo0c6a0ebOjePPzv/2a833I0dGObWpWxgAMo5Dhsa5cuaK4uDgVFxdrzZo1t37f8NmzjmM1s7Ich37Ur+94tGnSJAa4AFgGhQyPlJubq4ceekhBQUFauHChatasaToSAFQIQ13wOMeOHVNERISio6O1ePFiyhiAV2CoCx5l7969GjFihP74xz9q6tSppuMAgNtQyPAYGzdu1JQpU7RkyRLFxMSYjgMAbsWWNTzCwoULNW3aNG3atIkyBuCVWCHD0ux2u37/+99r5cqVSkpKUuvWrU1HAoBKQSHDsq5fv66pU6cqOztbKSkpatSokelIAFBpKGRY0uXLlzV69GjVrFlTO3bsUJ06dUxHAoBKxT1kWM6ZM2fUp08ftWzZUuvXr6eMAfgEChmWcvToUUVERGjkyJFauHChatRgEweAb+D/drCMlJQUxcbGaubMmZo8ebLpOABQpShkWMK6des0bdo0LVu2TFFRUabjAECVo5Bh3Pz58/XKK68oPj5e4bx1CYCPopBhTHFxsV544QWtW7dOycnJuu+++0xHAgBjKGQYUVhYqClTpuj48ePatWuXGjZsaDoSABhFIaPKXbp0SbGxsapbt662bdtxSvE7AAAJFklEQVSmgIAA05EAwDgee0KVOn36tCIjI9W2bVutXbuWMgaA/6CQUWWys7MVERGhsWPHav78+apevbrpSABgGWxZo0okJSVp9OjRmjVrliZOnGg6DgBYDoWMSvf+++9r+vTpWrFihQYNGmQ6DgBYEoWMSjV37lzNmjVLCQkJ6tKli+k4AGBZFDIqRXFxsZ577jlt2rRJycnJatWqlelIAGBpFDLc7tq1a5o0aZJycnK0a9cuNWjQwHQkALA8pqzhVhcuXNCQIUNUWFiohIQEyhgAyohChtucOnVKkZGRCgoK0urVq+Xv7286EgB4DAoZbnHo0CFFRERo4sSJmjt3Ls8YA0A5cQ8ZFbZjxw7FxcVpzpw5Gj9+vOk4AOCRKGRUyKpVq/TUU09p1apV6tevn+k4AOCxKGTcEbvdrtdff11z5szR1q1bFRwcbDoSAHg0ChnlVlxcrF/96ldKSEjQrl271KJFC9ORAMDjUcgol4KCAj366KPKzc1VcnKy6tevbzoSAHgFpqxRZufPn9egQYNUrVo1ffTRR5QxALgRhYwyOXnypHr27Knw8HCtXLlSfn5+piMBgFehkPGDDh48qIiICE2dOlWvv/66qlXjXxsAcDfuIeO2tm3bpnHjxumvf/2rHn74YdNxAMBrsdTBLa1YsULjx4/XmjVrKGMAqGSskFGK3W7Xa6+9pjfffFPbt29Xp06dTEcCAK9HIcPFjRs39PTTTysxMVEpKSlq1qyZ6UgA4BMoZJTIz8/XI488ogsXLigpKUmBgYGmIwGAz+AeMiRJ33zzjQYMGCA/Pz/Fx8dTxgBQxShk6N///rd69uypnj176t1331Xt2rVNRwIAn0Mh+7j9+/erV69eevLJJ/Xaa6/xjDEAGMI9ZB/20UcfacKECXrrrbc0atQo03EAwKexHPJR77zzjiZOnKh169ZRxgBgAayQfYzdbterr76qRYsW6eOPP1aHDh1MRwIAiEL2KUVFRfr5z3+uvXv3KiUlRU2aNDEdCQDwHxSyj8jLy9PYsWNVUFCgnTt36q677jIdCQBwE+4h+4CzZ8+qX79++tGPfqQPP/yQMgYAC6KQvdzx48fVs2dP9evXT++8845q1aplOhIA4HtQyF4sNTVVkZGReuaZZ/Tqq6/KZrOZjgQAuAXuIXupzZs367HHHtOiRYs0fPhw03EAAD+AFbIXWrx4saZMmaJ//OMflDEAeAhWyF7EbrfrpZde0rJly5SYmKi2bduajgQAKCMK2UsUFRXpiSeeUEZGhlJSUnTPPfeYjgQAKAcK2QtcuXJFcXFxKi4u1scff6y6deuajgQAKCfuIXu43NxcPfjgg2rcuLH+8Y9/UMYA4KEoZA927NgxRUREKDo6WosXL1bNmjVNRwIA3CG2rD3U3r17NWLECP3xj3/U1KlTTccBAFQQheyBNm7cqClTpmjJkiWKiYkxHQcA4AZsWXuYhQsXatq0adq0aRNlDABehBWyh7Db7fr973+vlStXKikpSa1btzYdCQDgRhSyB7h+/bqmTp2q7OxspaSkqFGjRqYjAQDcjEK2uMuXL2vMmDGqUaOGduzYoTp16piOBACoBNxDtrAzZ86ob9++atGihdavX08ZA4AXo5At6ujRo4qIiNCIESO0cOFC1ajBZgYAeDP+L29BKSkpio2N1cyZMzV58mTTcQAAVYBCtph169Zp2rRpWrZsmaKiokzHAQBUEQrZQubPn69XXnlF8fHxCg8PNx0HAFCFKGQLKC4u1gsvvKB169YpOTlZ9913n+lIAIAqRiEbVlhYqClTpuj48ePatWuXGjZsaDoSAMAACtmgS5cuKTY2VnXr1tW2bdsUEBBgOhIAwBAeezLk9OnTioyMVNu2bbV27VrKGAB8HIVsQHZ2tiIiIjR27FjNnz9f1atXNx0JAGAYW9ZVLCkpSaNHj9asWbM0ceJE03EAABZBIVeh999/X9OnT9eKFSs0aNAg03EAABZCIVeRuXPnatasWUpISFCXLl1MxwEAWAyFXMmKi4v13HPPadOmTUpOTlarVq1MRwIAWBCFXImuXbumSZMmKScnR7t27VKDBg1MRwIAWBRT1pXkwoULGjJkiAoLC5WQkEAZAwBui0KuBKdOnVJkZKSCgoK0evVq+fv7m44EALA4CtnNDh06pIiICE2cOFFz587lGWMAQJlwD9mNduzYobi4OM2ZM0fjx483HQcA4EEo5FvJzZWWLpUyM6WLF6XAQCk4WJo8Wbr77lLfvmrVKj311FNatWqV+vXrV/V5AQAezWa32+2mQ1hKaqo0c6YUH+/4fUHBt1/z95fsdikqSnr+ealbN9ntdr3++uuaM2eONm3apODgYDO5AQAejUK+2YIF0owZUn6+o3hvxWaT/P1VPGuWfvXpp0pISFB8fLxatGhRdVkBAF6FQnZylnFeXpk/UlC9uubfe6+m7Nun+vXrV2I4AIC3o5AlxzZ1377lKmMne0CAbDt3SuHh7s8FAPAZPPYkOe4Z5+ff0Udt+fmOzwMAUAGskHNzpZYtXYe3ysvPTzp58nunrwEAKAtWyEuXVvwaNpt7rgMA8FkUcmZmxVbHkmO7OyvLPXkAAD6JQr540T3XOX/ePdcBAPgkCjkw0D3X4bEnAEAFUMjBwY6hrIrw95eCgtyTBwDgk5iyZsoaAGABrJAbNXKcTW2z3dnnbTYpOpoyBgBUCCtkqUIndSkgQOKkLgBABbFClqRu3aTZsx3lWh4BAY7PUcYAgArifchO06c7/lmOtz1p9uxvPwcAQAWwZf1daWmOs6k3b3YU781nXDvfhxwd7XgfMitjAICbUMi3cvas4zjMrCzHoR/16zsebZo0iQEuAIDbUcgAAFgAQ10AAFgAhQwAgAVQyAAAWACFDACABVDIAABYAIUMAIAFUMgAAFgAhQwAgAVQyAAAWACFDACABVDIAABYAIUMAIAFUMgAAFgAhQwAgAVQyAAAWACFDACABVDIAABYAIUMAIAFUMgAAFgAhQwAgAVQyAAAWACFDACABVDIAABYAIUMAIAFUMgAAFgAhQwAgAVQyAAAWACFDACABVDIAABYAIUMAIAFUMgAAFjA/weRyUcWong2ngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gioco = nx.Graph()\n",
    "gioco.add_edges_from([(0,1),(0,2),(1,3),(2,3),(3,4)])\n",
    "nx.draw(gioco)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n",
      "0.6666666666666666\n",
      "1.0\n",
      "0.8164965809277261\n"
     ]
    }
   ],
   "source": [
    "print(structural_equivalence_jaccard(gioco,2,1))\n",
    "print(structural_equivalence_jaccard(gioco,0,3))\n",
    "print(structural_equivalence_cosine(gioco,2,1))\n",
    "print(structural_equivalence_cosine(gioco,0,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Componenti\n",
    "<img src='figures/compo.png'>\n",
    "\n",
    "## Grafi non orientati\n",
    "Per verificare se un grafo non orientato e' connesso posso utilizzare il metodo di NetworkX:\n",
    "```python\n",
    "is_connected(G)\n",
    "```\n",
    "Per calcolare il numero di componenti connesse posso utilizzare il metodo\n",
    "```python\n",
    "number_connected_components(G)\n",
    "```\n",
    "Mentre il metodo\n",
    "```python\n",
    "connected_components(G)\n",
    "```\n",
    "restituisce un generatore di insiemi di nodi, uno per ogni componente connessa.\n",
    "\n",
    "**Esercizio da svolgere in aula:** Generare una lista contenente la dimensione delle componenti connesse nella versione non orientata del grafo di UCIrvine.\n",
    "\n",
    "**Esercizio da svolgere in aula:** Ottenere l'insieme dei nodi appartenenti alla componente connessa principale. Utilizzare la funzione **max** e specificare l'argomento key che accetta una funzione di comparazione. Per esempio \n",
    "```python\n",
    "max([(2,3),(4,5,4,3),(2,)],key=len)\n",
    "```\n",
    "restituisce la tupla (4,5,4,3) perchè è la più lunga.\n",
    "\n",
    "Per estrarre i sottografi delle componenti connesse è consigliabile utilizzare il seguente codice:\n",
    "```python\n",
    "G.subgraph(c).copy() for c in connected_components(G)\n",
    "```\n",
    "\n",
    "## Grafi orientati\n",
    "Per verificare se un grafo orientato è fortemente connesso posso utilizzare il metodo\n",
    "```python\n",
    "is_strongly_connected(G)\n",
    "```\n",
    "Per calcolare il numero di componenti fortemente connesse utilizzo il metodo\n",
    "```python\n",
    "number_strongly_connected_components(G)\n",
    "```\n",
    "Mentre il metodo\n",
    "```python\n",
    "strongly_connected_components(G)\n",
    "```\n",
    "restituisce un generatore di insiemi di nodi appartenenti alle componenti fortemente connesse\n",
    "\n",
    "Rispetto ai metodi per i grafi non orientati, esiste un metodo che restituisce una rappresentazione compatta della rete in cui le componenti fortemente connesse sono i nodi del grafo ed esiste una arco tra le componenti A e B se esiste un arco tra un nodo $a\\in A$ e$b\\in B$\n",
    "\n",
    "I corrispettivi metodi che estraggono le componenti debolmente connesse hanno la stessa signature in cui _weakly_ sostituisce _strongly_.\n",
    "\n",
    "**Esercizio da svolgere in aula**: Si contino il numero di componenti fortemente e debolmente connesse nel grafo di UCIrvine e si estragga la componente fortemente connessa principale (giant strongly connected component)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "ucirvine_non_orientato = ucirvine_graph.to_undirected()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1893, 2, 2, 2]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[len(e) for e in list(nx.connected_components(ucirvine_non_orientato))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodi_componente_principale = max(nx.connected_components(ucirvine_non_orientato), key = len)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sottografo della componente principale\n",
    "ucirvine_giant_comp = ucirvine_non_orientato.subgraph(nodi_componente_principale).copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1893, 13835, 13838)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ucirvine_giant_comp.order(), ucirvine_giant_comp.size(), ucirvine_non_orientato.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La visite di una rete vengono definite **Traversal**\n",
    "\n",
    "# Depth-First Search - Visita in profondita'\n",
    "<img src='figures/dfs.png'>\n",
    "\n",
    "Utilizzando il metodo di NetworkX\n",
    "```python\n",
    "dfs_tree(G[, source, depth_limit])\n",
    "```\n",
    "ottengo l'albero della visita in profondita'. Posso specificare un nodo sorgente (radice dell'albero) da cui iniziare la visita mediante il parametro _source_ e fissare la profondita' della visita (quanti hop dalla sorgente) mediante il parametro *depth_limit*\n",
    "\n",
    "**Esercizio da svolgere in aula:** Calcolare l'albero dfs partendo da un nodo estratto in maniera casuale dal grafo di UCIrvine e limitando la profondita' a 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Breadth-first Search BFS - Visita in ampiezza\n",
    "<img src='figures/bfs.png'>\n",
    "\n",
    "Anche in questo caso posso farmi restituire l'albero della visita in ampiezza tramite il metodo\n",
    "```python\n",
    "bfs_tree(G, source, reverse=False)\n",
    "```\n",
    "che restituisce un grafo orientato (albero)\n",
    "\n",
    "La visita in ampiezza si relaziona con il calcolo dei cammini minimi.\n",
    "\n",
    "# Cammini minimi - Grafo non pesato\n",
    "\n",
    "I metodi principali per il calcolo dei cammini minimi in un grafo non pesato sono\n",
    "```python\n",
    "single_source_shortest_path(G, source[, cutoff])\n",
    "```\n",
    "e\n",
    "```python\n",
    "all_pairs_shortest_path(G[, cutoff])\n",
    "```\n",
    "Il primo metodo calcola i cammini minimi fissando un nodo sorgente ed eventualmente bloccando la visita del grafo se il cammino minimo ha lunghezza maggiore di _cutoff_. Il secondo metodo calcola i cammini minimi per ogni coppia di nodi del grafo.\n",
    "\n",
    "**Esercizio da svolgere in aula:** Calcolare il cammino minimo tra due nodi estratti in modo casuale dal grafo UCIrvine. Si utilizzi solo il primo metodo, in quanto il secondo ha una complessita' elevata $O(n^2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cammini di peso minimo - Grafo pesato\n",
    "\n",
    "Nel caso di grafo pesato si utilizza l'algoritmo di Dijkstra\n",
    "<img src='figures/dijkstra.png'>\n",
    "implementato dal metodo\n",
    "```python\n",
    "single_source_dijkstra(G, source, target=None, cutoff=None, weight='weight')\n",
    "```\n",
    "dove posso specificare un nodo obiettivo se voglio calcolare il peso del cammino di peso minimo dal nodo _source_ al nodo _target_, oppure limitare il calcolo del peso del cammino utilizzando il parametro _cutoff_. Come per molti metodi visti finora, il parametro weight specifica quale attributo utilizzare per il peso dall'arco"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network con attributi sui nodi\n",
    "\n",
    "In questa parte del notebook analizzeremo alcune proprietà della rete dei blog politici durante le elezioni americane del 2004.\n",
    "Il grafo è orientato ed etichettato. Ad ogni nodo è associato un orientamento politico (destra/sinistra)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Caricamento del grafo\n",
    "I link sono salvati nel file out.moreno_blogs_blogs. Il file contiene una edge list (prime due righe sono commenti). In ogni riga gli estremi dell'arco (sorgente e destinazioni) sono separati da un carattere di tabulazione.\n",
    "\n",
    "**Esercizio da svolgere in aula**: Tenendo in considerazione le precedenti indicazioni si costruisca il grafo orientato tra i blog."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "blog_graph = nx.DiGraph()\n",
    "with open('data/out.moreno_blogs_blogs','r') as file_grafo:\n",
    "    file_grafo.readline()\n",
    "    file_grafo.readline()\n",
    "    for line in file_grafo:\n",
    "        source, destination = line.strip().split()\n",
    "        blog_graph.add_edge(source, destination)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1224, 19025, '1')"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blog_graph.order(), blog_graph.size(), min(blog_graph.nodes())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il file ent.moreno_blogs_blogs.blog.orientation contiene gli attributi da assegnare ai nodi. Il file è testuale.<br>\n",
    "La riga i-esima contiene l'attributo da assegnare al nodo con identificatore i.\n",
    "\n",
    "**Esercizio da svolgere in aula:**: Si assegni ad ogni nodo del grafo precedentemente costruito il relativo attributo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "count_line = 1\n",
    "with open('data/ent.moreno_blogs_blogs.blog.orientation','r') as file_orientation:\n",
    "    for line in file_orientation:\n",
    "        value = line.strip()\n",
    "        blog_graph.node[str(count_line)]['orientamento_politico'] = value\n",
    "        count_line += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'orientamento_politico': 'right-leaning'}"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blog_graph.node['15']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio da svolgere in aula:**: Si contino quanti nodi hanno un determinato attributo. Nel caso dei blog, quanti sono i blog orientati a 'Destra'?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({'left-leaning': 588, 'right-leaning': 636})"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lista_orientamenti = [data['orientamento_politico'] for node, data in blog_graph.nodes(data=True)]\n",
    "Counter(lista_orientamenti)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reciprocità\n",
    "<img src='figures/reciprocity.png'>\n",
    "che equivale alla seguente formula\n",
    "<img src='figures/reciprocity_formula.png.jpg'>\n",
    "Con questa formulazione il calcolo del numeratore diventa più semplice.<br>\n",
    "Praticamente si deve verificare se, dato un arco (a,b), esiste corrispettivo (b,a). In tal caso si incrementa il contatore degli archi reciproci di una unità\n",
    "\n",
    "**Esercizio**: si definisca la funzione _reciprocity(graph)_ che restituisce la reciprocità di un grafo orientato"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reciprocity(graph):\n",
    "    count = 0\n",
    "    for edge in graph.edges():\n",
    "        if graph.has_edge(edge[1],edge[0]):\n",
    "            count = count + 1\n",
    "    return count/graph.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.24268068331143233"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reciprocity(blog_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esiste una seconda formulazione della reciprocità.\n",
    "<img src='figures/reciprocity_formula2.jpg'>\n",
    "dove (a) corrisponde al numeratore della formula utilizzata per la prima formulazione della reciprocità, mentre (b) corrisponde al numero di link nel grafo non orientato ottenuto da quello orientato<br>\n",
    "**Esercizio**: si definisca la funzione _reciprocity2(graph)_ che restituisce la reciprocità di un grafo orientato, secondo la seconda formulazione"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reciprocity2(graph):\n",
    "    count = 0\n",
    "    for edge in graph.edges():\n",
    "        if graph.has_edge(edge[1],edge[0]):\n",
    "            count = count + 1\n",
    "    return (count/2)/graph.to_undirected().size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Esercizio**: Calcolare la reciprocità (entrambe le definizioni) dell rete dei blog politici."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1380846991266898"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reciprocity2(blog_graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Clustering Coefficient\n",
    "<img src='figures/transitivity.png'>\n",
    "La formula per il calcolo del clustering coefficient è:\n",
    "<img src='figures/cc_formula.png'>\n",
    "\n",
    "In NetworkX la funzione per il calcolo del clustering coefficient è **transitivity**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2259585173589758"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E' possibile anche contare il numero di triangoli mediante la funzione **triangle**\n",
    "\n",
    "**Esercizio**: Si contino il numero di triangoli nel grafo non orientato relativo al grafo dei blog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "101043.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Local Clustering Coefficient\n",
    "<img src='figures/lcc_formula.png'>\n",
    "\n",
    "In NetworkX il metodo per il calcolo del cc locale è **clustering**\n",
    "\n",
    "**Esercizio**: Si calcoli il cc locale di un nodo estratto casualmente dal grafo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "890\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.41534391534391535"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Assortatività\n",
    "<img src='figures/assorta_nominal.png'>\n",
    "<img src='figures/modularity.png'>\n",
    "\n",
    "In NetworkX si calcola l'assortatività su attributi nominali mediante il metodo **attribute_assortativity_coefficient**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8229242280560486"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.attribute_assortativity_coefficient(blog_graph, attribute='orientamento_politico')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src='figures/assorta_ordinal_1.png'>\n",
    "<img src='figures/assorta_ordinal_2.png'>\n",
    "In NetworkX l'assortatività su attributi ordinali viene calcolata mediante il metodo **numeric_assortativity_coefficient**\n",
    "\n",
    "**Esercizio**: Dal momento che il grafo dei blog contiene attributi nominali, dobbiamo introdurre un attributo ordinale. Nel nostro caso l'aatributo età o age. Per imporre una correlazione positiva assumiamo che i blogger schierati a sinistra siano più giovani di quelli schierati a destra. Ad ogni blogger schierato a sinistra assegniamo un'età casuale tra 18 e 30, mentre ad ogni blogger schierato a destra assegniamo un'età casuale tra 40 e 50. Si calcoli l'assortatività sull'attributo age o età."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "for n in blog_graph.nodes(data=True):\n",
    "    if n[1]['orientamento_politico'] == 'left-leaning':\n",
    "        blog_graph.node[n[0]]['age'] = random.randint(18,30)\n",
    "    else:\n",
    "        blog_graph.node[n[0]]['age'] = random.randint(40,50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'orientamento_politico': 'left-leaning', 'age': 24},\n",
       " {'orientamento_politico': 'right-leaning', 'age': 46})"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "blog_graph.node['1'], blog_graph.node['15']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7516437102832811"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.numeric_assortativity_coefficient(blog_graph,attribute='age')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Community detection\n",
    "In quest'ultima parte del notebook verranno presentati tre algoritmi per individuare le community in reti sociali.\n",
    "Louvain e Label Propagation restituiscono community non sovrapposte, mentre CPM (Clique Percolation Method) restituisce community sovrapposte.\n",
    "\n",
    "### Louvain\n",
    "Per utilizzare l'algoritmo di Louvain si deve installare il relativo modulo tramite **pip install python-louvain**. Il modulo installato si chiama **community**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import community"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per eseguire l'algoritmo invoco il metodo **best_partition**. Il metodo restituisce un dictionary in cui ad ogni nodo viene associato la community di appartenenza.\n",
    "\n",
    "**Esercizio da svolgere in aula**: Si estraggano le community dal grafo non orientato dei blog."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "communities_louvain = community.best_partition(blog_graph.to_undirected())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({0: 522, 1: 651, 2: 2, 3: 38, 4: 2, 5: 3, 6: 2, 7: 2, 8: 2})"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Counter(communities_louvain.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il modulo community mette a disposizione anche il metodo **generate_dendogram** che ci permette di ottenere la gerarchia delle community. Il metodo, infatti, è gerarchico in quanto al passaggio $pass(i)$ aggrega le community identificate al passaggio $pass(i-1)$, come mostrato nell'esempio presentato nelle slide di teoria:\n",
    "<img src='figures/louvain_steps.png'>\n",
    "La corrispondente gerarchia è la seguente:\n",
    "<img src='figures/hierarchy_louvain.png'>\n",
    "\n",
    "Il metodo generate_dendogram restituisce una lista di dictionary, dove ogni dictionary rappresenta una partizione dei nodi. Ogni dictionary corrisponde ad un livello del dendogramma (albero)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'1': 0,\n",
       "  '2': 0,\n",
       "  '3': 0,\n",
       "  '4': 0,\n",
       "  '5': 0,\n",
       "  '6': 0,\n",
       "  '7': 1,\n",
       "  '8': 0,\n",
       "  '9': 0,\n",
       "  '10': 0,\n",
       "  '11': 0,\n",
       "  '12': 0,\n",
       "  '13': 0,\n",
       "  '14': 0,\n",
       "  '15': 2,\n",
       "  '16': 2,\n",
       "  '17': 0,\n",
       "  '18': 0,\n",
       "  '19': 0,\n",
       "  '20': 0,\n",
       "  '21': 0,\n",
       "  '22': 0,\n",
       "  '23': 0,\n",
       "  '24': 0,\n",
       "  '25': 0,\n",
       "  '26': 0,\n",
       "  '27': 0,\n",
       "  '28': 0,\n",
       "  '29': 0,\n",
       "  '30': 0,\n",
       "  '31': 0,\n",
       "  '32': 0,\n",
       "  '33': 0,\n",
       "  '34': 0,\n",
       "  '35': 0,\n",
       "  '36': 0,\n",
       "  '37': 0,\n",
       "  '38': 0,\n",
       "  '39': 0,\n",
       "  '40': 0,\n",
       "  '41': 0,\n",
       "  '42': 0,\n",
       "  '43': 0,\n",
       "  '44': 0,\n",
       "  '45': 0,\n",
       "  '46': 0,\n",
       "  '47': 0,\n",
       "  '48': 0,\n",
       "  '49': 0,\n",
       "  '50': 0,\n",
       "  '51': 0,\n",
       "  '52': 3,\n",
       "  '53': 0,\n",
       "  '54': 3,\n",
       "  '55': 2,\n",
       "  '56': 0,\n",
       "  '57': 0,\n",
       "  '58': 0,\n",
       "  '59': 0,\n",
       "  '60': 0,\n",
       "  '61': 0,\n",
       "  '62': 0,\n",
       "  '63': 0,\n",
       "  '64': 0,\n",
       "  '65': 0,\n",
       "  '66': 0,\n",
       "  '67': 0,\n",
       "  '68': 0,\n",
       "  '69': 0,\n",
       "  '70': 0,\n",
       "  '71': 0,\n",
       "  '72': 0,\n",
       "  '73': 0,\n",
       "  '74': 0,\n",
       "  '75': 0,\n",
       "  '76': 0,\n",
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       " {0: 0,\n",
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       "  3: 3,\n",
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       "  11: 10,\n",
       "  12: 11}]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dendo = community.generate_dendrogram(blog_graph.to_undirected())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32\n",
      "13\n",
      "12\n"
     ]
    }
   ],
   "source": [
    "for level in dendo:\n",
    "    print(len(set(level.values())))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Infine per valutare la modularity di una partizione in community posso utilizzare il metodo **modularity**\n",
    "\n",
    "Nell'esempio valutiamo la modularity delle partizioni generate dai diversi passaggi dell'algoritmo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0.42424197450796386\n",
      "1 0.4270263290703586\n",
      "2 0.42706862373400645\n"
     ]
    }
   ],
   "source": [
    "for level in range(len(dendo)):\n",
    "    partition = community.partition_at_level(dendo,level)\n",
    "    print(level, community.modularity(partition, blog_graph.to_undirected()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Label propagation\n",
    "Label propagation individua le community mediante un processo diffusivo su grafo. Il processo è definito dai seguenti passi:\n",
    "1. Inizializzo ogni nodo con un'etichetta (id community) diversa\n",
    "2. Per ogni nodo sostituisco la sua etichetta con quella più frequente tra i suoi vicini. In caso di parità scelgo un'etichetta a caso tra quelle più frequenti.\n",
    "3. Il processo termina quando l'etichetta di ogni nodo corrisponde con l'etichetta più frequente trai suoi vicini.\n",
    "\n",
    "In NetworkX l'algoritmo è implementato dal metodo **label_propagation_communities** il quale restituisce un generatore di insiemi che corrispondono alle community di nodi.\n",
    "\n",
    "\n",
    "**Esercizio da svolgere in aula:**: Si valuti la modularity della partizione identificata da Label Propagation. Si può utilizzare il metodo enumerate il quale, dato una lista $l$, restituisce una lista di coppie (i,v) tale che $l_i=v$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.001314998733199665"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({0: 1208, 1: 4, 2: 2, 3: 2, 4: 2, 5: 2, 6: 2, 7: 2})"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CPM (Clique Percolation Method)\n",
    "L'algoritmo si basa sulla definizione di $k$-clique community. Una $k$-clique community  è l'unione di tutte le $k$-clique che possono essere raggiunte attraverso una sequenza di $k$-clique adiacenti. Due $k$-clique sono adiacenti se hanno in comune $k-1$ nodi.\n",
    "\n",
    "L'algoritmo:\n",
    "1. estrae tutte le k-clique\n",
    "2. costruisce un grafo non orientato i cui sono le k-clique ed esiste un arco $(u,v)$ sse le k-clique $u$ e $v$ sono adiacenti.\n",
    "3. ogni componente connessa del grafo corrisponde ad una $k$-clique community\n",
    "\n",
    "In NetworkX l'algoritmo CPM è implementato dal metodo **clique_communities(graph, k)** il quale restituisce un generatore di insiemi corrispondenti alla nodi appartenenti alle $k$-clique community identificate.\n",
    "\n",
    "**Esercizio da svolgere in aula:**: Identificare le $k$-clique community nel grafo dei blog americani."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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