Weisfeiler Lehman Isomorphism Test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Weisfeiler-Lehman Isomorphism Test\n",
    "\n",
    "The Weisfeiler-Lehman Isomorphism Test, also called WL-Test, is a classical result from the graph theory. It is an heuristic to find out if two graphs are isomorphic. The problem of the graph isomorphism does not have a definitive solution in polinomial time yet, making some people say it may be NP-Complete. The WL-Test offers one alternative that allows us to estimate it.\n",
    "\n",
    "However, since this is an heuristic, the test is not perfect. Therefore, it fail in some simple cases and because of that new versions of this test were proposed.\n",
    "\n",
    "In this notebook we will explore a little about the theory of the test and implement it in its classical form and also some newer versions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "Gvaav4nXDvdl"
   },
   "outputs": [],
   "source": [
    "import copy\n",
    "import pprint\n",
    "import itertools\n",
    "import hashlib\n",
    "import networkx as nx\n",
    "\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def base_WL(G_, k, verbose, n_set, initial_colors_func, find_neighbors_func):    \n",
    "    if verbose:\n",
    "        print('-----------------------------------')\n",
    "        print('Starting the execution for the graph')\n",
    "    G, n = n_set(G_)\n",
    "    colors = initial_colors_func(n)\n",
    "\n",
    "    old_colors = copy.deepcopy(colors)\n",
    "    \n",
    "    if verbose:\n",
    "        print(f'Initial Color hashes: \\n {colors} \\n')\n",
    "\n",
    "    for i in range(len(n)):\n",
    "        for node in n:\n",
    "            neigh_colors = \"\".join([colors[i][0] for i in find_neighbors_func(G, n, node)])\n",
    "            \n",
    "            colors[node].extend([neigh_colors])\n",
    "            colors[node].sort()\n",
    "\n",
    "        # Update with the hash\n",
    "        if verbose:\n",
    "            print(f'Colors before hashes at iteration {i}: {colors} \\n')\n",
    "        colors = {i: [hashlib.sha224(\"\".join(colors[i]).encode('utf-8')).hexdigest()] for i in colors}\n",
    "                \n",
    "        if verbose:\n",
    "            print(f'Colors hashes at iteration {i}: \\n {colors} \\n')\n",
    "            print(f'Histogram: \\n {sorted(Counter([item for sublist in colors.values() for item in sublist]).items())} \\n')\n",
    "        \n",
    "        if list(Counter([item for sublist in colors.values() for item in sublist]).values()) == list(Counter([item for sublist in old_colors.values() for item in sublist]).values()) and i != 0:\n",
    "            if verbose:\n",
    "                print(f'Converged at iteration {i}!')\n",
    "            break\n",
    "        \n",
    "        old_colors = copy.deepcopy(colors)\n",
    "\n",
    "    canonical_form = sorted(Counter([item for sublist in colors.values() for item in sublist]).items())\n",
    "    if verbose:\n",
    "        print(f'Canonical Form Found: \\n {canonical_form} \\n')\n",
    "\n",
    "    return canonical_form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "xSj97eqCD2qA"
   },
   "outputs": [],
   "source": [
    "def WL(G, k=2, verbose=False):\n",
    "    def n_set(G):\n",
    "        G = nx.convert_node_labels_to_integers(G)\n",
    "        return G, list(G.nodes())\n",
    "    \n",
    "    def set_initial_colors(n):\n",
    "        return {i: [hashlib.sha224(\"1\".encode('utf-8')).hexdigest()] for i in n}\n",
    "    \n",
    "    def find_neighbors(G, n, node):\n",
    "        return G.neighbors(node)\n",
    "    \n",
    "    return base_WL(G, k, verbose, n_set, set_initial_colors, find_neighbors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "id": "9VEc1kyapDao"
   },
   "outputs": [],
   "source": [
    "def kWL(G, k, verbose=False):\n",
    "    def n_set(G):\n",
    "        G = nx.convert_node_labels_to_integers(G)\n",
    "        V = list(G.nodes())\n",
    "        V_k = [comb for comb in itertools.combinations(V, k)]\n",
    "        return G, V_k\n",
    "\n",
    "    def set_initial_colors(n):\n",
    "        return {i: [hashlib.sha224(str(i).encode('utf-8')).hexdigest()] for i in n}\n",
    "\n",
    "    def find_neighbors(G, V_k, node):\n",
    "        print([n for n in V_k if len(set(n) - set(V_k[V_k.index(node)])) == 1])\n",
    "        return [n for n in V_k if len(set(n) - set(V_k[V_k.index(node)])) == 1]\n",
    "\n",
    "    return base_WL(G, k, verbose, n_set, set_initial_colors, find_neighbors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "id": "UytqtTezslYV"
   },
   "outputs": [],
   "source": [
    "def fkWL(G, k, verbose=False):\n",
    "    def n_set(G):\n",
    "        G = nx.convert_node_labels_to_integers(G)\n",
    "        V = list(G.nodes())\n",
    "        V_k = [comb for comb in itertools.product(V, repeat=k)]\n",
    "        return G, V_k\n",
    "\n",
    "    def set_initial_colors(n):\n",
    "        return {i: [hashlib.sha224(str(i).encode('utf-8')).hexdigest()] for i in n}\n",
    "\n",
    "    def find_neighbors(G, V_k, node):\n",
    "        V = list(G.nodes())\n",
    "        vals = []\n",
    "        for i in range(k):\n",
    "            w = []\n",
    "            nodes_to_add = [u for u in V if u != V_k[V_k.index(node)][i]]\n",
    "            for u in nodes_to_add:\n",
    "                aux = list(V_k[V_k.index(node)])\n",
    "                aux[i] = u\n",
    "                w.append(tuple(aux))\n",
    "            vals.extend(w)\n",
    "        return vals\n",
    "\n",
    "    return base_WL(G, k, verbose, n_set, set_initial_colors, find_neighbors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "id": "-pF5hq6i_y_J"
   },
   "outputs": [],
   "source": [
    "def compare_graphs(G1, G2, method='WL', k=2, verbose=False):\n",
    "    methods = {\n",
    "        'WL': WL,\n",
    "        'kWL': kWL,\n",
    "        'fkWL': fkWL\n",
    "    }\n",
    "\n",
    "    # If two graphs have different numbers of nodes they cannot be isomorphic\n",
    "    if len(G1.nodes()) != len(G2.nodes()):\n",
    "        if verbose:\n",
    "            print('Non-Isomorphic by different number of nodes!')\n",
    "        return False\n",
    "    \n",
    "    c1 = methods[method](G1, k, verbose)\n",
    "    c2 = methods[method](G2, k, verbose)\n",
    "\n",
    "    return c1 == c2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing the Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------------------------\n",
      "Starting the execution for the graph\n",
      "Initial Color hashes: \n",
      " {(0, 1): ['dd1ff31c7034df9b181dec11a0ae633bf9bee80662d76e1b5f655c2e'], (0, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5'], (1, 2): ['efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3']} \n",
      "\n",
      "Colors before hashes at iteration 0: {(0, 1): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3', 'dd1ff31c7034df9b181dec11a0ae633bf9bee80662d76e1b5f655c2e'], (0, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5', 'af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3'], (1, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5', 'efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3']} \n",
      "\n",
      "Colors hashes at iteration 0: \n",
      " {(0, 1): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf'], (0, 2): ['c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee'], (1, 2): ['f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613']} \n",
      "\n",
      "Histogram: \n",
      " [('946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf', 1), ('c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee', 1), ('f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 1)] \n",
      "\n",
      "Colors before hashes at iteration 1: {(0, 1): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf', 'c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baeef5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613'], (0, 2): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcff5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 'c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee'], (1, 2): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcff5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 'f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613']} \n",
      "\n",
      "Colors hashes at iteration 1: \n",
      " {(0, 1): ['0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38'], (0, 2): ['40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd'], (1, 2): ['43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7']} \n",
      "\n",
      "Histogram: \n",
      " [('0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38', 1), ('40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd', 1), ('43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7', 1)] \n",
      "\n",
      "Converged at iteration 1!\n",
      "Canonical Form Found: \n",
      " [('0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38', 1), ('40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd', 1), ('43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7', 1)] \n",
      "\n",
      "-----------------------------------\n",
      "Starting the execution for the graph\n",
      "Initial Color hashes: \n",
      " {(0, 1): ['dd1ff31c7034df9b181dec11a0ae633bf9bee80662d76e1b5f655c2e'], (0, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5'], (1, 2): ['efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3']} \n",
      "\n",
      "Colors before hashes at iteration 0: {(0, 1): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3', 'dd1ff31c7034df9b181dec11a0ae633bf9bee80662d76e1b5f655c2e'], (0, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5', 'af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3'], (1, 2): ['af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3af78931ab7820443f0986de9ef1f276363014d89b9dd587f16b5f3e5', 'efc8967f524c37abb64097ebc4ca64c6c9a47e4ae3f6bd4bda7a52a3']} \n",
      "\n",
      "Colors hashes at iteration 0: \n",
      " {(0, 1): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf'], (0, 2): ['c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee'], (1, 2): ['f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613']} \n",
      "\n",
      "Histogram: \n",
      " [('946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf', 1), ('c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee', 1), ('f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 1)] \n",
      "\n",
      "Colors before hashes at iteration 1: {(0, 1): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf', 'c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baeef5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613'], (0, 2): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcff5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 'c229b1e4d137cac51864bc1340783d63f573156b9fa91a2ea577baee'], (1, 2): ['946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcf946dbe927789cffad1e35be6686a4bc3fa664ff51ad0ed7190480dcff5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613', 'f5abc44f56ff8f111a99c562174f02c5c0e105dfdd05cb228681e613']} \n",
      "\n",
      "Colors hashes at iteration 1: \n",
      " {(0, 1): ['0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38'], (0, 2): ['40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd'], (1, 2): ['43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7']} \n",
      "\n",
      "Histogram: \n",
      " [('0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38', 1), ('40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd', 1), ('43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7', 1)] \n",
      "\n",
      "Converged at iteration 1!\n",
      "Canonical Form Found: \n",
      " [('0be3e678a6d1445e96b6584de1f531a9fedeb8d39f1ba8d2616dbe38', 1), ('40d5304d6ff744d2184aaeb108b5bfa3aad94d7afac23b219c81c8fd', 1), ('43a464a76a0950ea1caec50ad27a0539e59b4d24009572d1db09cce7', 1)] \n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "G_edge_list = [(1, 2), (2, 3), (3, 1)]\n",
    "G.add_edges_from(G_edge_list)\n",
    "\n",
    "compare_graphs(G, G, k=2, verbose=True, method='kWL')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When evaluating, we must know that our implementation works besides the node naming. Also, we must test to some non-isomorphic graphs that cannot be distinguished by the WL test."
   ]
  },
  {
   "attachments": {
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"
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"
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"
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example of Two Non-Isomorphic Graphs that fail the WL-Test <br>\n",
    "![image.png](attachment:69bf6397-f73e-437d-a78b-566b639deda7.png)\n",
    "![image.png](attachment:5af3da87-a5f4-4d44-8293-e5dfd9dd3ad3.png) <br>\n",
    "\n",
    "Another Example of Two Non-Isomorphic Graphs that fail the WL-Test <br>\n",
    "![image.png](attachment:8329f627-9d3f-4ec8-8d49-cc8858b98f2b.png)\n",
    "![image.png](attachment:82fdb576-e925-4a47-90d1-d4ed9206af5f.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "id": "pcueX9I4s3_n"
   },
   "outputs": [],
   "source": [
    "def evaluation(method, k):\n",
    "    print(f'Method: {method}')\n",
    "    \n",
    "    # Generates two non-isomorphic graphs\n",
    "    G = nx.Graph()\n",
    "    G_edge_list = [(1, 2), (2, 3), (1, 3), (4, 5), (5, 6), (4, 6)]\n",
    "    G.add_edges_from(G_edge_list)\n",
    "\n",
    "    H = nx.Graph()\n",
    "    H_edge_list = [(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 1)]\n",
    "    H.add_edges_from(H_edge_list)\n",
    "    \n",
    "    G_ = nx.Graph()\n",
    "    G_edge_list = [(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 1), (3, 7), (7, 8), (8, 9), (9, 10), (10, 4)]\n",
    "    G_.add_edges_from(G_edge_list)\n",
    "\n",
    "    H_ = nx.Graph()\n",
    "    H_edge_list = [(1, 2), (2, 3), (3, 4), (4, 5), (5, 1), (3, 6), (6, 7), (7, 8), (8, 9), (9, 10), (10, 6)]\n",
    "    H_.add_edges_from(H_edge_list)\n",
    "    \n",
    "    \n",
    "    G1 = nx.davis_southern_women_graph()\n",
    "    G2 = nx.karate_club_graph()\n",
    "    G3 = nx.les_miserables_graph()\n",
    "    G4 = nx.convert_node_labels_to_integers(G3)\n",
    "\n",
    "    G5 = nx.convert_node_labels_to_integers(G3)\n",
    "    G5.remove_edge(0, 1)\n",
    "\n",
    "    print(f'Expected: False, got: {compare_graphs(G, H, method, k)}')\n",
    "    print(f'Expected: False, got: {compare_graphs(G_, H_, method, k)}')\n",
    "    print(f'Expected: True, got: {compare_graphs(G1, G1, method, k)}')\n",
    "    print(f'Expected: True, got: {compare_graphs(G2, G2, method, k)}')\n",
    "    print(f'Expected: True, got: {compare_graphs(G3, G3, method, k)}')\n",
    "    print(f'Expected: True, got: {compare_graphs(G4, G4, method, k)}')\n",
    "    print(f'Expected: True, got: {compare_graphs(G5, G5, method, k)}')\n",
    "    \n",
    "    print(f'Expected: True, got: {compare_graphs(G3, G4, method, k)}')\n",
    "    print(f'Expected: False, got: {compare_graphs(G3, G5, method, k)}')\n",
    "    print(f'Expected: False, got: {compare_graphs(G4, G5, method, k)}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected: False, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: False, got: False\n",
      "Expected: False, got: False\n"
     ]
    }
   ],
   "source": [
    "evaluation('WL', k=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected: False, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: True, got: True\n",
      "Expected: False, got: False\n",
      "Expected: False, got: False\n"
     ]
    }
   ],
   "source": [
    "evaluation('kWL', k=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'evaluation' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[1;32mIn [53]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mevaluation\u001b[49m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfkWL\u001b[39m\u001b[38;5;124m'\u001b[39m, k\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m3\u001b[39m)\n",
      "\u001b[1;31mNameError\u001b[0m: name 'evaluation' is not defined"
     ]
    }
   ],
   "source": [
    "evaluation('fkWL', k=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "name": "Weisfeiler-Lehman isomorphism test.ipynb",
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   "language": "python",
   "name": "python3"
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