{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import os\n",
    "import wget\n",
    "import zipfile\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import networkx as nx\n",
    "import plotly.graph_objects as go\n",
    "from utils import *\n",
    "from collections import Counter\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "import geopandas as gpd\n",
    "import gdown # for downloading files from google drive\n",
    "import shutil\n",
    "import warnings\n",
    "import sys\n",
    "from pyvis.network import Network\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocessing\n",
    "import random\n",
    "import networkx as nx\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "def parallel_omega(G, nrand=10, seed=None):\n",
    "\n",
    "    random.seed(seed)\n",
    "    if not nx.is_connected(G):\n",
    "        G = G.subgraph(max(nx.connected_components(G), key=len))\n",
    "\n",
    "    if len(G) == 1:\n",
    "        return 0\n",
    "\n",
    "    niter_lattice_reference = nrand\n",
    "    niter_random_reference = nrand * 2\n",
    "    \n",
    "    def worker(queue):\n",
    "        while True:\n",
    "            task = queue.get()\n",
    "            if task is None:\n",
    "                break\n",
    "            random_graph = nx.random_reference(G)\n",
    "            lattice_graph = nx.lattice_reference(G)\n",
    "            random_shortest_path = nx.average_shortest_path_length(random_graph)\n",
    "            lattice_clustering = nx.average_clustering(lattice_graph)\n",
    "            queue.put((random_shortest_path, lattice_clustering))\n",
    "               \n",
    "    n_processes = multiprocessing.cpu_count()\n",
    "    manager = multiprocessing.Manager()\n",
    "    queue = manager.Queue()\n",
    "    processes = [multiprocessing.Process(target=worker, args=(queue,)) for _ in range(n_processes)]\n",
    "    for process in processes:\n",
    "        process.start()\n",
    "    \n",
    "    for _ in range(nrand):\n",
    "        queue.put(1)\n",
    "    \n",
    "    for _ in range(n_processes):\n",
    "        queue.put(None)\n",
    "    \n",
    "    for process in processes:\n",
    "        process.join()\n",
    "    \n",
    "    shortest_paths = []\n",
    "    clustering_coeffs = []\n",
    "    while not queue.empty():\n",
    "        random_shortest_path, lattice_clustering = queue.get()\n",
    "        shortest_paths.append(random_shortest_path)\n",
    "        clustering_coeffs.append(lattice_clustering)\n",
    "    \n",
    "    L = nx.average_shortest_path_length(G)\n",
    "    C = nx.average_clustering(G)\n",
    "\n",
    "    # kill the process\n",
    "    for process in processes:\n",
    "        process.terminate()\n",
    "        process.join()\n",
    "\n",
    "    omega = (np.mean(shortest_paths) / L) - (C / np.mean(clustering_coeffs))\n",
    "\n",
    "\n",
    "    return omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Graph with 200 nodes and 584 edges'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = nx.erdos_renyi_graph(200, 0.03)\n",
    "G = G.subgraph(max(nx.connected_components(G), key=len))\n",
    "nx.info(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6776975801779451"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omega = parallel_omega(G, nrand=10, seed=42)\n",
    "omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[4], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m standard_omega \u001b[39m=\u001b[39m nx\u001b[39m.\u001b[39;49momega(G, nrand\u001b[39m=\u001b[39;49m\u001b[39m10\u001b[39;49m, seed\u001b[39m=\u001b[39;49m\u001b[39m42\u001b[39;49m)\n\u001b[1;32m      2\u001b[0m standard_omega\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/utils/decorators.py:845\u001b[0m, in \u001b[0;36margmap.__call__.<locals>.func\u001b[0;34m(_argmap__wrapper, *args, **kwargs)\u001b[0m\n\u001b[1;32m    844\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mfunc\u001b[39m(\u001b[39m*\u001b[39margs, __wrapper\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs):\n\u001b[0;32m--> 845\u001b[0m     \u001b[39mreturn\u001b[39;00m argmap\u001b[39m.\u001b[39;49m_lazy_compile(__wrapper)(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m<class 'networkx.utils.decorators.argmap'> compilation 14:6\u001b[0m, in \u001b[0;36margmap_omega_9\u001b[0;34m(G, niter, nrand, seed)\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39minspect\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mitertools\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mre\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mcollections\u001b[39;00m \u001b[39mimport\u001b[39;00m defaultdict\n\u001b[1;32m      8\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mcontextlib\u001b[39;00m \u001b[39mimport\u001b[39;00m contextmanager\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/smallworld.py:367\u001b[0m, in \u001b[0;36momega\u001b[0;34m(G, niter, nrand, seed)\u001b[0m\n\u001b[1;32m    363\u001b[0m niter_random_reference \u001b[39m=\u001b[39m niter \u001b[39m*\u001b[39m \u001b[39m2\u001b[39m\n\u001b[1;32m    365\u001b[0m \u001b[39mfor\u001b[39;00m _ \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(nrand):\n\u001b[1;32m    366\u001b[0m     \u001b[39m# Generate random graph\u001b[39;00m\n\u001b[0;32m--> 367\u001b[0m     Gr \u001b[39m=\u001b[39m random_reference(G, niter\u001b[39m=\u001b[39;49mniter_random_reference, seed\u001b[39m=\u001b[39;49mseed)\n\u001b[1;32m    368\u001b[0m     randMetrics[\u001b[39m\"\u001b[39m\u001b[39mL\u001b[39m\u001b[39m\"\u001b[39m]\u001b[39m.\u001b[39mappend(nx\u001b[39m.\u001b[39maverage_shortest_path_length(Gr))\n\u001b[1;32m    370\u001b[0m     \u001b[39m# Generate lattice graph\u001b[39;00m\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/utils/decorators.py:845\u001b[0m, in \u001b[0;36margmap.__call__.<locals>.func\u001b[0;34m(_argmap__wrapper, *args, **kwargs)\u001b[0m\n\u001b[1;32m    844\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39mfunc\u001b[39m(\u001b[39m*\u001b[39margs, __wrapper\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, \u001b[39m*\u001b[39m\u001b[39m*\u001b[39mkwargs):\n\u001b[0;32m--> 845\u001b[0m     \u001b[39mreturn\u001b[39;00m argmap\u001b[39m.\u001b[39;49m_lazy_compile(__wrapper)(\u001b[39m*\u001b[39;49margs, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m<class 'networkx.utils.decorators.argmap'> compilation 24:6\u001b[0m, in \u001b[0;36margmap_random_reference_19\u001b[0;34m(G, niter, connectivity, seed)\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39minspect\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mitertools\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[39mimport\u001b[39;00m \u001b[39mre\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mcollections\u001b[39;00m \u001b[39mimport\u001b[39;00m defaultdict\n\u001b[1;32m      8\u001b[0m \u001b[39mfrom\u001b[39;00m \u001b[39mcontextlib\u001b[39;00m \u001b[39mimport\u001b[39;00m contextmanager\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/smallworld.py:100\u001b[0m, in \u001b[0;36mrandom_reference\u001b[0;34m(G, niter, connectivity, seed)\u001b[0m\n\u001b[1;32m     97\u001b[0m G\u001b[39m.\u001b[39mremove_edge(c, d)\n\u001b[1;32m     99\u001b[0m \u001b[39m# Check if the graph is still connected\u001b[39;00m\n\u001b[0;32m--> 100\u001b[0m \u001b[39mif\u001b[39;00m connectivity \u001b[39mand\u001b[39;00m local_conn(G, a, b) \u001b[39m==\u001b[39m \u001b[39m0\u001b[39m:\n\u001b[1;32m    101\u001b[0m     \u001b[39m# Not connected, revert the swap\u001b[39;00m\n\u001b[1;32m    102\u001b[0m     G\u001b[39m.\u001b[39mremove_edge(a, d)\n\u001b[1;32m    103\u001b[0m     G\u001b[39m.\u001b[39mremove_edge(c, b)\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/connectivity/connectivity.py:649\u001b[0m, in \u001b[0;36mlocal_edge_connectivity\u001b[0;34m(G, s, t, flow_func, auxiliary, residual, cutoff)\u001b[0m\n\u001b[1;32m    646\u001b[0m \u001b[39melif\u001b[39;00m flow_func \u001b[39mis\u001b[39;00m boykov_kolmogorov:\n\u001b[1;32m    647\u001b[0m     kwargs[\u001b[39m\"\u001b[39m\u001b[39mcutoff\u001b[39m\u001b[39m\"\u001b[39m] \u001b[39m=\u001b[39m cutoff\n\u001b[0;32m--> 649\u001b[0m \u001b[39mreturn\u001b[39;00m nx\u001b[39m.\u001b[39;49mmaximum_flow_value(H, s, t, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/flow/maxflow.py:307\u001b[0m, in \u001b[0;36mmaximum_flow_value\u001b[0;34m(flowG, _s, _t, capacity, flow_func, **kwargs)\u001b[0m\n\u001b[1;32m    304\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m callable(flow_func):\n\u001b[1;32m    305\u001b[0m     \u001b[39mraise\u001b[39;00m nx\u001b[39m.\u001b[39mNetworkXError(\u001b[39m\"\u001b[39m\u001b[39mflow_func has to be callable.\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[0;32m--> 307\u001b[0m R \u001b[39m=\u001b[39m flow_func(flowG, _s, _t, capacity\u001b[39m=\u001b[39;49mcapacity, value_only\u001b[39m=\u001b[39;49m\u001b[39mTrue\u001b[39;49;00m, \u001b[39m*\u001b[39;49m\u001b[39m*\u001b[39;49mkwargs)\n\u001b[1;32m    309\u001b[0m \u001b[39mreturn\u001b[39;00m R\u001b[39m.\u001b[39mgraph[\u001b[39m\"\u001b[39m\u001b[39mflow_value\u001b[39m\u001b[39m\"\u001b[39m]\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/flow/edmondskarp.py:237\u001b[0m, in \u001b[0;36medmonds_karp\u001b[0;34m(G, s, t, capacity, residual, value_only, cutoff)\u001b[0m\n\u001b[1;32m    120\u001b[0m \u001b[39mdef\u001b[39;00m \u001b[39medmonds_karp\u001b[39m(\n\u001b[1;32m    121\u001b[0m     G, s, t, capacity\u001b[39m=\u001b[39m\u001b[39m\"\u001b[39m\u001b[39mcapacity\u001b[39m\u001b[39m\"\u001b[39m, residual\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m, value_only\u001b[39m=\u001b[39m\u001b[39mFalse\u001b[39;00m, cutoff\u001b[39m=\u001b[39m\u001b[39mNone\u001b[39;00m\n\u001b[1;32m    122\u001b[0m ):\n\u001b[1;32m    123\u001b[0m \u001b[39m    \u001b[39m\u001b[39m\"\"\"Find a maximum single-commodity flow using the Edmonds-Karp algorithm.\u001b[39;00m\n\u001b[1;32m    124\u001b[0m \n\u001b[1;32m    125\u001b[0m \u001b[39m    This function returns the residual network resulting after computing\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    235\u001b[0m \n\u001b[1;32m    236\u001b[0m \u001b[39m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 237\u001b[0m     R \u001b[39m=\u001b[39m edmonds_karp_impl(G, s, t, capacity, residual, cutoff)\n\u001b[1;32m    238\u001b[0m     R\u001b[39m.\u001b[39mgraph[\u001b[39m\"\u001b[39m\u001b[39malgorithm\u001b[39m\u001b[39m\"\u001b[39m] \u001b[39m=\u001b[39m \u001b[39m\"\u001b[39m\u001b[39medmonds_karp\u001b[39m\u001b[39m\"\u001b[39m\n\u001b[1;32m    239\u001b[0m     \u001b[39mreturn\u001b[39;00m R\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/flow/edmondskarp.py:104\u001b[0m, in \u001b[0;36medmonds_karp_impl\u001b[0;34m(G, s, t, capacity, residual, cutoff)\u001b[0m\n\u001b[1;32m    101\u001b[0m     \u001b[39mraise\u001b[39;00m nx\u001b[39m.\u001b[39mNetworkXError(\u001b[39m\"\u001b[39m\u001b[39msource and sink are the same node\u001b[39m\u001b[39m\"\u001b[39m)\n\u001b[1;32m    103\u001b[0m \u001b[39mif\u001b[39;00m residual \u001b[39mis\u001b[39;00m \u001b[39mNone\u001b[39;00m:\n\u001b[0;32m--> 104\u001b[0m     R \u001b[39m=\u001b[39m build_residual_network(G, capacity)\n\u001b[1;32m    105\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    106\u001b[0m     R \u001b[39m=\u001b[39m residual\n",
      "File \u001b[0;32m/usr/lib/python3.10/site-packages/networkx/algorithms/flow/utils.py:139\u001b[0m, in \u001b[0;36mbuild_residual_network\u001b[0;34m(G, capacity)\u001b[0m\n\u001b[1;32m    135\u001b[0m \u001b[39mif\u001b[39;00m \u001b[39mnot\u001b[39;00m R\u001b[39m.\u001b[39mhas_edge(u, v):\n\u001b[1;32m    136\u001b[0m     \u001b[39m# Both (u, v) and (v, u) must be present in the residual\u001b[39;00m\n\u001b[1;32m    137\u001b[0m     \u001b[39m# network.\u001b[39;00m\n\u001b[1;32m    138\u001b[0m     R\u001b[39m.\u001b[39madd_edge(u, v, capacity\u001b[39m=\u001b[39mr)\n\u001b[0;32m--> 139\u001b[0m     R\u001b[39m.\u001b[39;49madd_edge(v, u, capacity\u001b[39m=\u001b[39;49m\u001b[39m0\u001b[39;49m)\n\u001b[1;32m    140\u001b[0m \u001b[39melse\u001b[39;00m:\n\u001b[1;32m    141\u001b[0m     \u001b[39m# The edge (u, v) was added when (v, u) was visited.\u001b[39;00m\n\u001b[1;32m    142\u001b[0m     R[u][v][\u001b[39m\"\u001b[39m\u001b[39mcapacity\u001b[39m\u001b[39m\"\u001b[39m] \u001b[39m=\u001b[39m r\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "standard_omega = nx.omega(G, nrand=10, seed=42)\n",
    "standard_omega"
   ]
  }
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