sde-test-cliques.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graphical Models: Similarity Distribution Experimentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import necessary libraries\n",
    "from sde import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### make directed graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OutEdgeView([(0, 8), (1, 5), (2, 10), (3, 12), (5, 14), (8, 7), (8, 13), (9, 5), (9, 10), (9, 13), (9, 2), (11, 10), (11, 0), (12, 3), (13, 4)])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g = makeDirectedGraph(15, 17)\n",
    "nx.edges(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_networkx(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 8): 0.10705481082284529,\n",
       " (1, 5): 0.33789950082167586,\n",
       " (2, 10): 0.20042539272764914,\n",
       " (3, 12): 0.0027635293534530314,\n",
       " (5, 14): 0.9337957965416462,\n",
       " (8, 7): 0.3165671855854175,\n",
       " (8, 13): 0.6306370273480687,\n",
       " (9, 5): 0.6652249756886771,\n",
       " (9, 10): 0.04034587693959979,\n",
       " (9, 13): 0.021458901906325933,\n",
       " (9, 2): 0.9665335215008626,\n",
       " (11, 10): 0.7037568337021488,\n",
       " (11, 0): 0.9247423800060931,\n",
       " (12, 3): 0.7322693029704619,\n",
       " (13, 4): 0.9243059023924293}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.get_edge_attributes(g, 'weight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# clique size\n",
    "import itertools as it\n",
    "from networkx.algorithms import approximation\n",
    "from networkx.algorithms.approximation import clique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{9, 13}\n"
     ]
    }
   ],
   "source": [
    "max_clique = clique.max_clique(g)\n",
    "print(max_clique)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding the largest size clique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Similarity Implementation: Edit-Distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "13\n"
     ]
    }
   ],
   "source": [
    "list_max_clique  = list(max_clique)\n",
    "A = list_max_clique[0]\n",
    "B = list_max_clique[1]\n",
    "\n",
    "print(A)\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.17432437623921526,\n",
       " 12: 0.141006931853849,\n",
       " 2: 0.9665335215008626,\n",
       " 9: 0.26879426888764013,\n",
       " 5: 0.6652249756886771,\n",
       " 14: 0.6211842860526054,\n",
       " 10: 0.1937178606312481,\n",
       " 13: 0.021458901906325933,\n",
       " 4: 0.019834589690877213}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = get_all_children(g, A)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.17432437623921526,\n",
       " 12: 0.141006931853849,\n",
       " 2: 0.9665335215008626,\n",
       " 9: 0.26879426888764013,\n",
       " 5: 0.6652249756886771,\n",
       " 14: 0.6211842860526054,\n",
       " 10: 0.1937178606312481,\n",
       " 13: 0.021458901906325933,\n",
       " 4: 0.9243059023924293}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = get_all_children(g,B)\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Edit distance by a node's child"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_immediate_similarity(g, A, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_most_immediate_similar(g, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#find_most_immediate_similar(g, B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Node: 0\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 1\n",
      "Similarity: 0.8318313687167503\n",
      "\n",
      "Node: 2\n",
      "Similarity: 0.7900198789470123\n",
      "\n",
      "Node: 3\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 4\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 5\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 6\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 7\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 8\n",
      "Similarity: 0.9022945313604357\n",
      "\n",
      "Node: 10\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 11\n",
      "Similarity: 0.9158527391906373\n",
      "\n",
      "Node: 12\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 13\n",
      "Similarity: 1.0\n",
      "\n",
      "Node: 14\n",
      "Similarity: 1.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "nodes = list(g.nodes)\n",
    "nodes.remove(A)\n",
    "\n",
    "for node in nodes:\n",
    "    node_similarity = get_immediate_similarity(g, A, node)\n",
    "    print(\"Node:\", node)\n",
    "    print(\"Similarity:\", node_similarity)\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Edit-distance similarity implementation based on all descendants of a node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{5: 0.6652249756886771,\n",
       " 14: 0.6211842860526054,\n",
       " 10: 0.1937178606312481,\n",
       " 13: 0.021458901906325933,\n",
       " 4: 0.019834589690877213,\n",
       " 2: 0.9665335215008626}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_desc = get_descendants(g, A)\n",
    "A_desc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{5: 0.6652249756886771,\n",
       " 14: 0.6211842860526054,\n",
       " 10: 0.1937178606312481,\n",
       " 13: 0.021458901906325933,\n",
       " 4: 0.9243059023924293,\n",
       " 2: 0.9665335215008626}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B_desc = get_descendants(g, B)\n",
    "B_desc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9840785521169253"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_full_similarity(g, A, B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding all maximal cliques"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 4, 6, 7, 9, 11, 14}\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.approximation import independent_set\n",
    "mis = independent_set.maximum_independent_set(g)\n",
    "print(mis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "({0, 1, 2, 3, 4, 6, 7, 9, 11, 14}, [{9, 10, 2}, {8, 0}, {1, 5}, {3, 12}, {4, 13}, {6}, {7}, {11}, {14}])\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.approximation import clique\n",
    "cliq_rem = clique.clique_removal(g)\n",
    "print(cliq_rem)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{9, 10, 2}, {8, 0}, {1, 5}, {3, 12}, {4, 13}, {6}, {7}, {11}, {14}]\n"
     ]
    }
   ],
   "source": [
    "cliques = cliq_rem[1]     #retrieve list of maximal cliques in the graph\n",
    "print(cliques)"
   ]
  }
 ],
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