multiNetX v2.3

multiNetX is a python package for the manipulation and visualization of multilayer networks. The core of this package is a MultilayerGraph, a class that inherits all properties from networkx.Graph().

This allows for:

• Creating networks with weighted or unweighted links (only undirected networks are supported in this version)
• Analysing the spectral properties of adjacency or Laplacian matrices
• Visualizing dynamical processes by coloring the nodes and links accordingly

How to install multiNetX

You have to execute the following command in your terminal:

pip install git+https://github.com/nkoub/multinetx.git

Or

1. Clone the repository of multinetx into your system:

   git clone https://github.com/nkoub/multinetx.git

2. Enter in the multinetx directory:

   cd multinetx

3. and then simply write:

   pip install .

How to use multiNetX

Import standard libraries for numerics

import numpy as np

Import the package MultiNetX

import multinetx as mx

Create a multiplex 1st way

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 5
g1 = mx.generators.erdos_renyi_graph(N,0.5,seed=218)
g2 = mx.generators.erdos_renyi_graph(N,0.6,seed=211)
g3 = mx.generators.erdos_renyi_graph(N,0.7,seed=208)

Create an 3Nx3N lil sparse matrix. It will be used to describe the layers interconnection

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

Define the type of interconnection among the layers (here we use identity matrices thus connecting one-to-one the nodes among layers)

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
    
# use symmetric inter-adjacency matrix
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3],
                        inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

Create a multiplex 2nd way

mg = mx.MultilayerGraph()

Add layers

mg.add_layer(mx.generators.erdos_renyi_graph(N,0.5,seed=218))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.6,seed=211))
mg.add_layer(mx.generators.erdos_renyi_graph(N,0.7,seed=208))

Create an instance of the MultilayerGraph class

mg.layers_interconnect(inter_adjacency_matrix=adj_block)

Weights can be added to the edges

mg.set_edges_weights(intra_layer_edges_weight=2,
                     inter_layer_edges_weight=3)

The object mg inherits all properties from Graph of networkX, so that we can calculate adjacency or Laplacian matrices, their eigenvalues, etc.

How to plot multiplex networks

Import standard libraries

import numpy as np
import matplotlib.pyplot as plt

Import the package MultiNetX

import multinetx as mx

Create three Erd"os- R'enyi networks with N nodes for each layer

N = 50
g1 = mx.erdos_renyi_graph(N,0.07,seed=218)
g2 = mx.erdos_renyi_graph(N,0.07,seed=211)
g3 = mx.erdos_renyi_graph(N,0.07,seed=208)

Edge colored nertwork (no inter-connected layers)

Create the multiplex network

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3])

Set weights to the edges

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('edge colored network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(g1),
					  layer_vertical_shift=0.2,
					  layer_horizontal_shift=0.0,
					  proj_angle=47)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

Regular interconnected multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*3,N*3)))

adj_block[0:  N,  N:2*N] = np.identity(N)    # L_12
adj_block[0:  N,2*N:3*N] = np.identity(N)    # L_13
#adj_block[N:2*N,2*N:3*N] = np.identity(N)    # L_23
adj_block += adj_block.T

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3], 
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=4)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('regular interconnected network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=1.4,
					  layer_horizontal_shift=0.0,
					  proj_angle=7)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

General multiplex multiplex

Define the type of interconnection between the layers

adj_block = mx.lil_matrix(np.zeros((N*4,N*4)))

adj_block[0  :  N ,   N:2*N] = np.identity(N)   # L_12
adj_block[0  :  N , 2*N:3*N] = np.random.poisson(0.005,size=(N,N))   # L_13
adj_block[0  :  N , 3*N:4*N] = np.random.poisson(0.006,size=(N,N))   # L_34
adj_block[3*N:4*N , 2*N:3*N] = np.random.poisson(0.008,size=(N,N))   # L_14
adj_block += adj_block.T
adj_block[adj_block>1] = 1

Create an instance of the MultilayerGraph class

mg = mx.MultilayerGraph(list_of_layers=[g1,g2,g3,g1],
						inter_adjacency_matrix=adj_block)

mg.set_edges_weights(inter_layer_edges_weight=5)

mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_intra_edges_weights(layer=2,weight=3)
mg.set_intra_edges_weights(layer=3,weight=4)

Plot the adjacency matrix and the multiplex networks

fig = plt.figure(figsize=(15,5))
ax1 = fig.add_subplot(121)
ax1.imshow(mx.adjacency_matrix(mg,weight='weight').todense(),
		  origin='upper',interpolation='nearest',cmap=plt.cm.jet_r)
ax1.set_title('supra adjacency matrix')

ax2 = fig.add_subplot(122)
ax2.axis('off')
ax2.set_title('general multiplex network')
pos = mx.get_position(mg,mx.fruchterman_reingold_layout(mg.get_layer(0)),
					  layer_vertical_shift=.3,
					  layer_horizontal_shift=0.9,
					  proj_angle=.2)
mx.draw_networkx(mg,pos=pos,ax=ax2,node_size=50,with_labels=False,
				 edge_color=[mg[a][b]['weight'] for a,b in mg.edges()],
				 edge_cmap=plt.cm.jet_r)
plt.show()

How to plot 3D multiplex networks

Import specific libraries

import numpy as np #  to use matrix
import matplotlib.pyplot as plt # to use plot
import networkx as nx # to use graphs
import multinetx as mx # to use multinet
import math # to use floor
import matplotlib.cm as cmx # to use cmap (for data color values)
import matplotlib.colors as colors # to use cmap (for data color values)
import matplotlib.cbook as cb # to test if an object is a string

from mpl_toolkits.mplot3d import Axes3D # to use 3D plot

Create multinet

N1 = 10
g1 = nx.cycle_graph(N1)
N2 = 2*N1
g2 = nx.cycle_graph(N2)

adj_block = mx.lil_matrix(np.zeros((N1+N2,N1+N2)))

for i in range(N1):
    adj_block[i,N1+2*i] = 1

adj_block += adj_block.T

mg = mx.MultilayerGraph(list_of_layers=[g1,g2],inter_adjacency_matrix=adj_block)

Plot multiplex networks by layer

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')

pos = mx.get_position3D(mg)


intra_c = ['b','r']
inter_c = 'grey'
layer_c = ['b','r']

mg.set_edges_weights(inter_layer_edges_weight=1, intra_layer_edges_weight=1)
edge_color=[mg[a][b]['weight'] for a,b in mg.edges()]


mx.FigureByLayer(mg, pos, ax, intra_edge_color=intra_c,node_color=layer_c, inter_edge_color=inter_c)
ax.axis('off')

(-1.0999999812245371,
 1.0999999991059304,
 -1.0999999595281706,
 1.0999999980727702)

Plot multiplex networks by nodes and edges

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')
# Get position of all nodes
pos = mx.get_position3D(mg)
# Set edges weights
mg.set_intra_edges_weights(layer=0,weight=1)
mg.set_intra_edges_weights(layer=1,weight=2)
mg.set_edges_weights(inter_layer_edges_weight=3)

# Get edges and nodes color
edge_color=[mg.edges.get((a,b))['weight'] for a,b in mg.edges()]
node_color=[i for i in mg.nodes]

# Plot multiplex network using options
mx.Figure3D(mg, pos, ax, edge_color=edge_color, node_color=node_color, 
         node_shape = 'D', edge_linewidth = 0.5, node_linewidth = 0,
         edge_style = 'dashed', label = 'Node', with_labels = True,
         font_size = 8, font_color = 'red', font_weight = 'heavy', 
         font_family = 'fantasy')
# Print legend
ax.legend(scatterpoints=1)

/home/icarrasco/fnh_k/multinetx_display/multinetx/draw.py:439: MatplotlibDeprecationWarning: The is_string_like function was deprecated in version 2.1.
  if not cb.is_string_like(label):





<matplotlib.legend.Legend at 0x7fcc9b69fbe0>

Plot partial multiplex networks by nodes and edges

# Create the figure
fig = plt.figure()
# Create 3D axes
ax = fig.add_subplot(111, projection='3d')

# Get position of nodes
pos = mx.get_position3D(mg)
# Choose some edges
edge_list = [(0, 1),(0, 10),(0, 9),(1, 2),(1, 12),(2, 3),(2, 14),(3, 16),(3, 4),(4, 18),(4, 5),(5, 20),(5, 6),(6, 22),(6, 7),(7, 8),(7, 24)]
# Choose the edges color
edge_color = [np.random.randint(1,100) for i in edge_list]
# Choose some nodes
node_list = [0,2,4,6,8,10,12,14,16,18,20]
# Choose the nodes color
node_color = [0,2,4,6,8,10,12,14,16,18,20]
# Plot the partial mutiplex network
mx.Figure3D(mg, pos, ax, node_list=node_list, node_color=node_color, edge_list=edge_list, edge_color = edge_color)

How to cite multiNetX

If multiNetX was useful and facilitated your research and work flow you can use a reference in your publications by citing either of the following papers for which multiNetX was originally developed:

• R. Amato, N. E Kouvaris, M. San Miguel and A. Diaz-Guilera, Opinion competition dynamics on multiplex networks, New J. Phys. DOI: https://doi.org/10.1088/1367-2630/aa936a
• N. E. Kouvaris, S. Hata and A. Diaz-Guilera, Pattern formation in multiplex networks, Scientific Reports 5, 10840 (2015). http://www.nature.com/srep/2015/150604/srep10840/full/srep10840.html
• A. Sole-Ribata, M. De Domenico, N. E. Kouvaris, A. Diaz-Guilera, S. Gomez and A. Arenas, Spectral properties of the Laplacian of a multiplex network, Phys. Rev. E 88, 032807 (2013). http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.032807

Copyright

(C) Copyright 2013-2019, Nikos E Kouvaris

Each file in this folder is part of the multiNetX package.

multiNetX v1.0 is part of the deliverables of the LASAGNE project (multi-LAyer SpAtiotemporal Generalized NEtworks), EU/FP7-2012-STREP-318132 (http://complex.ffn.ub.es/~lasagne/)

multiNetX v2.0 is an extension of the version 1.0 and has the additions made by Ines Carrasco (https://github.com/InesCarrasco) during her internship in the University of Namur and the Namur Institute for Complex Systems (naXys) the summer of 2018.

multiNetX v2.3 provides is buid on the previous versions and provides an easy installation m,ethod via pypip

multiNetX is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

multiNetX is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.