demo/K-Truss.ipynb

{
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   "source": [
    "# K-Truss\n",
    "\n",
    "\"The output matrix C is the k-truss subgraph of A.  Its edges are a subset of\n",
    "A.  Each edge in C is part of at least k-2 triangles in C.  The pattern of C\n",
    "is the adjacency matrix of the k-truss subgraph of A.  The edge weights of C\n",
    "are the support of each edge.  That is, C(i,j)=nt if the edge (i,j) is part\n",
    "of nt triangles in C.  All edges in C have support of at least k-2.  The\n",
    "total number of triangles in C is sum(C)/6.  The number of edges in C is\n",
    "nnz(C)/2.  C is returned as symmetric with a zero-free diagonal.\" - LAGraph_ktruss()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pygraphblas import *\n",
    "from pygraphblas.gviz import draw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
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   "source": [
    "def ktruss(A, k=3):\n",
    "    assert k >= 3\n",
    "    Support = Scalar.from_value(k-2)\n",
    "    last_nz = A.nvals\n",
    "    while True:\n",
    "        A = A.mxm(A, semiring=UINT32.PLUS_LAND, mask=A)\n",
    "        A = A.select('>=', Support)\n",
    "        if A.nvals == last_nz:\n",
    "            break\n",
    "        last_nz = A.nvals\n",
    "    return A\n",
    "\n",
    "karate = list(Matrix.ssget('Newman/karate'))[-1][1]\n",
    "\n",
    "draw(karate, show_weight=False, directed=False, graph_attr=dict(layout='sfdp'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
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       "<g id=\"a_edge37\"><a xlink:title=\"2\">\n",
       "</a>\n",
       "</g>\n",
       "</g>\n",
       "<!-- 29&#45;&#45;23 -->\n",
       "<g id=\"edge35\" class=\"edge\">\n",
       "<title>29&#45;&#45;23</title>\n",
       "<g id=\"a_edge35\"><a xlink:title=\"2\">\n",
       "</a>\n",
       "</g>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Graph at 0x7ffa89207130>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draw(ktruss(karate, 4).select('>', 1), graph_attr=dict(layout='sfdp'), directed=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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