CollaborationNetwork.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2bbbea64-1d2e-40ec-bdff-2b5271af3733",
   "metadata": {},
   "source": [
    "# Clustering Stefano Boccaletti's collaboration network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74c37386-1440-462a-96fd-a1faf4667500",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import pandas as pd\n",
    "import xgi\n",
    "from scipy.cluster import hierarchy\n",
    "from collections import defaultdict\n",
    "from itertools import combinations, product\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots\n",
    "plt.style.use(['science', 'no-latex'])\n",
    "\n",
    "from hyperfunctions import *\n",
    "from modularity_functions import *"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50c476a3-a4b0-4f05-a364-e1e328dcfe9b",
   "metadata": {},
   "source": [
    "##  Constructing the Hypergraph"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9cec0e30-76e7-4cd1-ae70-f3cd9e98870e",
   "metadata": {},
   "source": [
    "We create the hypergraph with Stefano's coauthors and their respective coauthors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8ab67f79-4426-4054-bbe7-1e5aecb7ee8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15237 20227\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('Datasets/boccaletti_and_cocoauthors.csv', sep = ';')\n",
    "\n",
    "hyperedge_dict = {}\n",
    "for paper, ID in enumerate(df['Author(s) ID']):\n",
    "    hyperedge_dict[paper] = ID.split(';')[:-1]\n",
    "\n",
    "H = xgi.Hypergraph(hyperedge_dict)\n",
    "print(len(H.edges), len(H.nodes))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fadf904a-d82b-43be-aca5-5a918bae3a37",
   "metadata": {},
   "source": [
    "We create the hypergraph with only Stefano's coauthors. We can apply some restrictions to the number of papers with him to be considered a coauthor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "79c3019d-c632-450d-b3f4-5eb6b5782481",
   "metadata": {},
   "outputs": [],
   "source": [
    "restriction_papers = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dc619c5c-4002-478a-bf6d-ee139c3fc638",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "338 414\n",
      "338 69\n"
     ]
    }
   ],
   "source": [
    "dg = pd.read_csv('Datasets/boccaletti_coauthors.csv', sep = ',')\n",
    "\n",
    "hyperedge_dic = {}\n",
    "for paper, ID in enumerate(dg['Author(s) ID']):\n",
    "    hyperedge_dic[paper] = ID.split(';')[:-1]\n",
    "\n",
    "E = xgi.Hypergraph(hyperedge_dic)\n",
    "\n",
    "print(len(E.edges), len(E.nodes))\n",
    "\n",
    "for node in list(E.nodes):\n",
    "    if E.degree(node) < restriction_papers:\n",
    "        E.remove_node(node)     \n",
    "\n",
    "print(len(E.edges), len(E.nodes))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2cd788d-b6ce-4dbf-bba5-289656ecbd84",
   "metadata": {},
   "source": [
    "Keep from the first hypergraph (H) the nodes from the second hypergraph (E)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4096da1b-bc7a-46d3-84d8-75b0b7f642c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "for node in list(H.nodes):\n",
    "    if node in list(E.nodes):\n",
    "        continue\n",
    "    else:\n",
    "        H.remove_node(node)\n",
    "        \n",
    "# Also remove Stefano Boccaletti\n",
    "H.remove_node('7006291912')\n",
    "\n",
    "# Also remove outlier (Soregaroli, not a coauthor)\n",
    "H.remove_node('15133256400')\n",
    "\n",
    "H.remove_edges_from(H.edges.singletons())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ef07d9a0-8b84-4565-93c6-55006267a5b6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "67 1685\n"
     ]
    }
   ],
   "source": [
    "print(len(H.nodes), len(H.edges))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "48c56c74-7f98-4900-947e-ca2cbf03d467",
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes_list = list(H.nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "db9ac775-e964-4397-bd9d-806f7dacfc69",
   "metadata": {},
   "outputs": [],
   "source": [
    "Authors_list = []\n",
    "IDs_list = []\n",
    "for author, ID in zip(dg['Authors'],dg['Author(s) ID']):\n",
    "    Authors_list.append(author.split(', '))\n",
    "    IDs_list.append(ID.split(';')[:-1])\n",
    "\n",
    "authors_dict = {}\n",
    "IDs_dict={}\n",
    "for cont, authors in enumerate(Authors_list):\n",
    "    for cont_2, author in enumerate(authors):\n",
    "        IDs_dict[IDs_list[cont][cont_2]] = author\n",
    "        authors_dict[author] = IDs_list[cont][cont_2]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7beb7ce9-dd8b-4dc9-978e-66c4eec81493",
   "metadata": {},
   "source": [
    "## Communities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2641af8e-7557-4c05-8b7c-92262faf3615",
   "metadata": {},
   "outputs": [],
   "source": [
    "derivative = derivative_list(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3c7f9e0b-2ed7-4a3d-9bf5-aaf35adefaab",
   "metadata": {},
   "outputs": [],
   "source": [
    "method = \"average\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "56db2793-e800-4a87-8a98-3afd2b4d8d0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1, figsize=(8,6))\n",
    "\n",
    "Z = hierarchy.linkage(derivative, method)\n",
    "dn = hierarchy.dendrogram(Z, labels = nodes_list, orientation='top', count_sort='ascending', ax=ax)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc022328-2642-4d43-8887-9b5d5ceadefb",
   "metadata": {},
   "source": [
    "## General (us)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4961071d-a9df-40be-bb35-7192f7f6ae06",
   "metadata": {},
   "outputs": [],
   "source": [
    "h_cut, num_fusion = height_based_cut(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dcaedf97-c290-4f7c-acbd-18cc998236f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "cuttree = hierarchy.cut_tree(Z, height = h_cut)\n",
    "\n",
    "# Assign each node to its community\n",
    "node_community_dict = {}\n",
    "for index, node in enumerate(H.nodes):\n",
    "    node_community_dict[node] = cuttree[index][0]\n",
    "\n",
    "# Assign each community its nodes\n",
    "communities_dict = defaultdict(set)\n",
    "for node, comm in node_community_dict.items():\n",
    "    communities_dict[comm].add(node)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c5fcd357-5137-4a92-b296-92643f3869cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n"
     ]
    }
   ],
   "source": [
    "Num_communities = len(set(node_community_dict.values()))\n",
    "print(Num_communities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "4b486379-3c48-418d-9ef1-36c59a1845ef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Li D.', 'Havlin S.']\n",
      "###\n",
      "['Bragard J.', 'Mendoza C.']\n",
      "###\n",
      "['Kurths J.', 'Arecchi F.T.', 'Meucci R.', 'Zhou C.S.', 'Allaria E.']\n",
      "###\n",
      "['Mancini H.', 'Maza D.']\n",
      "###\n",
      "['Bortolozzo U.', 'Residori S.']\n",
      "###\n",
      "['Li X.', 'Dai X.', 'Shen C.', 'Guo H.', 'Shi L.', 'Wang Z.', 'Jusup M.', 'Perc M.', 'Jia D.']\n",
      "###\n",
      "['Sevilla-Escoboza R.', 'Sousa P.A.C.', 'Jaimes-Reátegui R.', 'Zanin M.', 'Papo D.', 'Menasalvas E.']\n",
      "###\n",
      "['Koronovskii A.A.', 'Hramov A.E.', 'Moskalenko O.I.', 'Makarov V.V.', 'Maksimenko V.A.']\n",
      "###\n",
      "['Raigorodskii A.M.', 'Romance M.', 'Criado R.', 'Alfaro-Bittner K.', 'del Genio C.I.', 'Musatov D.']\n",
      "###\n",
      "['Gómez-Gardeñes J.', 'Latora V.', 'Frasca M.', 'Moreno Y.']\n",
      "###\n",
      "['Qiu T.', 'Liu Z.', 'Guan S.', 'Zou Y.', 'Bonamassa I.']\n",
      "###\n",
      "['Barzel B.', 'Zhang X.']\n",
      "###\n",
      "['Sendiña-Nadal I.', 'Leyva I.', 'del-Pozo F.', 'Buldú J.', 'Almendral J.A.', 'Navas A.', 'Bajo R.', 'Maestú F.', 'Gutiérrez R.']\n",
      "###\n",
      "['Amann A.', 'Hwang D.-U.', 'Chavez M.']\n",
      "###\n",
      "['Pampaloni E.', 'Giaquinta A.', 'Ramazza P.L.']\n",
      "###\n",
      "['Pecora L.M.', 'Valladares D.L.']\n",
      "###\n"
     ]
    }
   ],
   "source": [
    "nodeset_list = []\n",
    "nodeset_list_names = []\n",
    "for nodeset in communities_dict.values():\n",
    "    nodeset_list.append(nodeset)\n",
    "    nodeset_list_names.append([IDs_dict[ID] for ID in nodeset])\n",
    "    print([IDs_dict[ID] for ID in nodeset])\n",
    "\n",
    "    print(\"###\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7f3cd62a-2fd6-48e1-a138-7d550e5354f3",
   "metadata": {},
   "outputs": [],
   "source": [
    "partition_general = nodeset_list"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bcaa7e9-6ef1-4e2a-9bfe-d182bcc961e7",
   "metadata": {},
   "source": [
    "## Modularity (us)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1f03f58b-f4f5-4555-b0b5-283660326b49",
   "metadata": {},
   "outputs": [],
   "source": [
    "A, G, mapping = reduced_adjacency_matrix(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a37897d5-9600-48bc-8d01-0b4d7f34678e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- 0.0% --\n",
      "-- 0.746268656716418% --\n"
     ]
    }
   ],
   "source": [
    "Modularity = calculate_modularities(H, G, Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b83976c2-1531-44a9-90cb-f537126ca0e0",
   "metadata": {},
   "source": [
    "*Conclusion*: the general method coincides with our modularity maximization in this example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0f83c1d5-b07e-4543-8def-3c47d56dfae7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of communities maximizing the modularity is: 9,\n",
      "with modularity: 0.6779792723843422\n"
     ]
    }
   ],
   "source": [
    "m = max(Modularity)\n",
    "num_fusion = [i for i, j in enumerate(Modularity) if j == m]\n",
    "index_max = num_fusion[0]\n",
    "\n",
    "print(f'Number of communities maximizing the modularity is: {index_max},')\n",
    "print(f'with modularity: {m}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fc456164-0c32-48ae-bef0-6b1854ffa191",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "#plt.title(\"Modularity score vs Number of communities\")\n",
    "plt.plot(range(len(H.nodes)), Modularity, label='$Q$')\n",
    "#plt.grid()\n",
    "plt.axvline(Num_communities, color='r', label='$ Q(h=h_{cut}) $ ')\n",
    "plt.axvline(index_max, color='g', label='$ Q_{\\max}=\\max(Q) $ ')\n",
    "\n",
    "plt.ylabel('Modularity')\n",
    "plt.xlabel('$ n $')\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.savefig('Figures/modularity_collab.svg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "906e690d-b214-4f2b-abe5-4f1588eab975",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Li D.', 'Havlin S.', 'Barzel B.', 'Zhang X.']\n",
      "###\n",
      "['Kurths J.', 'Arecchi F.T.', 'Mancini H.', 'Mendoza C.', 'Allaria E.', 'Meucci R.', 'Maza D.', 'Zhou C.S.', 'Bragard J.']\n",
      "###\n",
      "['Giaquinta A.', 'Residori S.', 'Pampaloni E.', 'Ramazza P.L.', 'Bortolozzo U.']\n",
      "###\n",
      "['Li X.', 'Dai X.', 'Shen C.', 'Guo H.', 'Shi L.', 'Wang Z.', 'Jusup M.', 'Perc M.', 'Jia D.']\n",
      "###\n",
      "['Sevilla-Escoboza R.', 'Sendiña-Nadal I.', 'Leyva I.', 'Sousa P.A.C.', 'Buldú J.', 'del-Pozo F.', 'Almendral J.A.', 'Navas A.', 'Jaimes-Reátegui R.', 'Zanin M.', 'Bajo R.', 'Maestú F.', 'Gutiérrez R.', 'Papo D.', 'Menasalvas E.']\n",
      "###\n",
      "['Koronovskii A.A.', 'Hramov A.E.', 'Moskalenko O.I.', 'Makarov V.V.', 'Maksimenko V.A.']\n",
      "###\n",
      "['Raigorodskii A.M.', 'Romance M.', 'Frasca M.', 'Criado R.', 'Latora V.', 'Alfaro-Bittner K.', 'del Genio C.I.', 'Moreno Y.', 'Gómez-Gardeñes J.', 'Musatov D.']\n",
      "###\n",
      "['Qiu T.', 'Liu Z.', 'Guan S.', 'Zou Y.', 'Bonamassa I.']\n",
      "###\n",
      "['Valladares D.L.', 'Amann A.', 'Pecora L.M.', 'Chavez M.', 'Hwang D.-U.']\n",
      "###\n"
     ]
    }
   ],
   "source": [
    "communities_dict = communities(H, derivative, method, n_clusters=index_max)\n",
    "\n",
    "nodeset_list = []\n",
    "nodeset_list_names = []\n",
    "for nodeset in communities_dict.values():\n",
    "    nodeset_list.append(nodeset)\n",
    "    nodeset_list_names.append([IDs_dict[ID] for ID in nodeset])\n",
    "    print([IDs_dict[ID] for ID in nodeset])\n",
    "\n",
    "    print(\"###\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "50056de4-0ed0-40c9-ab7b-811cfb184ad9",
   "metadata": {},
   "outputs": [],
   "source": [
    "partition_modularity = nodeset_list"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c2abd67-2e1a-498e-b3cb-cc571c996c26",
   "metadata": {},
   "source": [
    "### Iterate again over the communities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "919df67b-6044-4ae5-89bb-56df3840f603",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Li D.', 'Havlin S.']\n",
      "#######\n",
      "['Barzel B.', 'Zhang X.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Bragard J.', 'Mendoza C.']\n",
      "#######\n",
      "['Zhou C.S.', 'Kurths J.']\n",
      "#######\n",
      "['Mancini H.', 'Maza D.']\n",
      "#######\n",
      "['Meucci R.', 'Allaria E.', 'Arecchi F.T.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Giaquinta A.', 'Residori S.', 'Pampaloni E.', 'Ramazza P.L.', 'Bortolozzo U.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Li X.', 'Dai X.', 'Wang Z.', 'Jusup M.', 'Perc M.']\n",
      "#######\n",
      "['Shi L.', 'Guo H.', 'Jia D.', 'Shen C.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Menasalvas E.', 'Sousa P.A.C.']\n",
      "#######\n",
      "['Buldú J.', 'Papo D.', 'Zanin M.']\n",
      "#######\n",
      "['Gutiérrez R.', 'Bajo R.', 'del-Pozo F.', 'Maestú F.']\n",
      "#######\n",
      "['Sevilla-Escoboza R.', 'Jaimes-Reátegui R.']\n",
      "#######\n",
      "['Sendiña-Nadal I.', 'Leyva I.', 'Almendral J.A.', 'Navas A.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Moskalenko O.I.', 'Hramov A.E.', 'Koronovskii A.A.']\n",
      "#######\n",
      "['Maksimenko V.A.', 'Makarov V.V.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Raigorodskii A.M.']\n",
      "#######\n",
      "['Gómez-Gardeñes J.', 'Latora V.', 'Frasca M.', 'Moreno Y.']\n",
      "#######\n",
      "['Romance M.', 'Alfaro-Bittner K.', 'del Genio C.I.', 'Criado R.']\n",
      "#######\n",
      "['Musatov D.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Qiu T.', 'Bonamassa I.']\n",
      "#######\n",
      "['Liu Z.', 'Zou Y.', 'Guan S.']\n",
      "#######\n",
      "------NEXT------\n",
      "['Amann A.', 'Hwang D.-U.', 'Chavez M.']\n",
      "#######\n",
      "['Pecora L.M.', 'Valladares D.L.']\n",
      "#######\n",
      "------NEXT------\n"
     ]
    }
   ],
   "source": [
    "iterated_partition = []\n",
    "for comm in nodeset_list:\n",
    "    \n",
    "    if len(comm) == 1:\n",
    "        iterated_partition.append(list(comm))\n",
    "        print([IDs_dict[list(comm)[0]]])\n",
    "        \n",
    "        continue\n",
    "    \n",
    "    # Obtain the subhypergraph of the community\n",
    "    subH = xgi.subhypergraph(H, nodes = comm)\n",
    "    \n",
    "    # Compute the derivatives and dendrogram\n",
    "    sub_derivative = derivative_list(subH)\n",
    "    subZ = hierarchy.linkage(sub_derivative, method)\n",
    "        \n",
    "    # Compute the reduced graph and adjacency matrix\n",
    "    subA, subG, sub_mapping = reduced_adjacency_matrix(subH)\n",
    "    \n",
    "    # Calculate the modularity, and its max\n",
    "    sub_Modularity = calculate_modularities(subH, subG, subZ, verbose=False)\n",
    "    \n",
    "    m = max(sub_Modularity)\n",
    "    num_fusion = [i for i, j in enumerate(sub_Modularity) if j == m]\n",
    "    index_max = num_fusion\n",
    "    \n",
    "    # Obtain the partition of the subhypergraph\n",
    "    communities_dict = communities(subH, sub_derivative, method, n_clusters=index_max)\n",
    "    \n",
    "    # Print it\n",
    "    for nodeset in communities_dict.values():\n",
    "        iterated_partition.append(list(nodeset))\n",
    "        \n",
    "        print([IDs_dict[ID] for ID in nodeset])\n",
    "        print(\"#######\")\n",
    "        \n",
    "        \n",
    "    print(\"------NEXT------\")    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4d4752d7-dcf6-4ab8-a790-2c5bf1a96fc6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(iterated_partition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "cd637013-95e2-40bb-918f-bb208f8864da",
   "metadata": {},
   "outputs": [],
   "source": [
    "q = nx.community.modularity(G, iterated_partition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "aa9b4dd3-b5d3-43f3-acd7-e5bab9501cba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5639540632374226\n"
     ]
    }
   ],
   "source": [
    "print(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b9a87f83-b6ca-4d94-aa89-1867a627dc0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "partition_modularity_iterated = iterated_partition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46350aa9-fc3a-4a61-8897-46673ac6bbaa",
   "metadata": {},
   "source": [
    "## Modularity (Kumar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "80603ff6-1bfc-4926-bd61-dfb2236537e5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "It converged after 987 iterations\n",
      "['Maza D.', 'Bragard J.', 'Giaquinta A.', 'Mancini H.', 'Meucci R.', 'Allaria E.', 'Mendoza C.', 'Arecchi F.T.']\n",
      "['Navas A.', 'Sousa P.A.C.', 'Menasalvas E.', 'Buldú J.', 'Jaimes-Reátegui R.', 'Papo D.', 'Sendiña-Nadal I.', 'Sevilla-Escoboza R.', 'Leyva I.', 'Bajo R.', 'del-Pozo F.', 'Zanin M.', 'Maestú F.', 'Almendral J.A.', 'Gutiérrez R.']\n",
      "['Hramov A.E.', 'Makarov V.V.', 'Moskalenko O.I.', 'Maksimenko V.A.', 'Koronovskii A.A.']\n",
      "['Dai X.', 'Li X.', 'Jusup M.', 'Raigorodskii A.M.', 'Guo H.', 'Wang Z.', 'Jia D.', 'Alfaro-Bittner K.', 'Musatov D.', 'Perc M.', 'Shi L.', 'Shen C.']\n",
      "['Criado R.', 'Romance M.']\n",
      "['Havlin S.', 'Guan S.', 'Kurths J.', 'Zou Y.', 'Liu Z.', 'Bonamassa I.', 'Barzel B.', 'Li D.', 'Qiu T.', 'Valladares D.L.', 'Zhang X.', 'Zhou C.S.']\n",
      "['Frasca M.', 'Amann A.', 'del Genio C.I.', 'Moreno Y.', 'Chavez M.', 'Gómez-Gardeñes J.', 'Latora V.', 'Pecora L.M.', 'Hwang D.-U.']\n",
      "['Ramazza P.L.', 'Pampaloni E.', 'Residori S.', 'Bortolozzo U.']\n",
      "The modularity for this partition is: 0.714021349642142\n"
     ]
    }
   ],
   "source": [
    "clusters = IRMM_algorithm(H, tol=1e-3)\n",
    "Communities_K = []\n",
    "for comm in clusters:\n",
    "    Community_K = []\n",
    "    Community_IDs = []\n",
    "    for node in comm:\n",
    "        Community_K.append(mapping[node])\n",
    "        Community_IDs.append(IDs_dict[mapping[node]])\n",
    "    Communities_K.append(Community_K)\n",
    "    \n",
    "    print(Community_IDs)\n",
    "\n",
    "q = nx.community.modularity(G,Communities_K)\n",
    "print(f'The modularity for this partition is: {q}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "90e01e4c-b58e-4bc1-816e-7a401144b296",
   "metadata": {},
   "outputs": [],
   "source": [
    "partition_Kumar = Communities_K"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d33428f5-d43e-45a6-829d-86060fd8e360",
   "metadata": {},
   "source": [
    "## Index between partitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "acff347b-bd8e-4aee-bcb6-e65fe8ae8ea9",
   "metadata": {},
   "outputs": [],
   "source": [
    "partition_list = [partition_general, partition_modularity, partition_modularity_iterated, partition_Kumar]\n",
    "partition_names = [\"general\", \"modularity\", \"iterated\", \"Kumar\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "77ac2d57-e903-43be-9efa-acdca591c0ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ind_geom = np.zeros((4,4))\n",
    "Ind_arit = np.zeros((4,4))\n",
    "for i, part_1 in enumerate(partition_list):\n",
    "    for j, part_2 in enumerate(partition_list):\n",
    "        \n",
    "        Sim_geom, Sim_arit = similarity_partitions(part_1, part_2) \n",
    "        \n",
    "        Ind_geom[i,j] = Sim_geom\n",
    "        Ind_arit[i,j] = Sim_arit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e228cb0a-9540-449b-a2fb-05aefb9b87c8",
   "metadata": {},
   "source": [
    "### Geometric index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d63587da-38cf-4873-a184-50d434259f30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Ind_geom)\n",
    "\n",
    "ax.set_xticks(np.arange(len(partition_names)), labels=partition_names, rotation=45)\n",
    "ax.set_yticks(np.arange(len(partition_names)), labels=partition_names)\n",
    "\n",
    "for (j, i), label in np.ndenumerate(np.round(Ind_geom,2)):\n",
    "    ax.text(i, j, label, ha='center', va='center')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36782060-167a-442f-8a3f-9547333c53f9",
   "metadata": {},
   "source": [
    "### Arithmetic index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "4675399f-f243-4eb4-8e1b-5113b704b820",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(Ind_arit)\n",
    "\n",
    "ax.set_xticks(np.arange(len(partition_names)), labels=partition_names, rotation=45)\n",
    "ax.set_yticks(np.arange(len(partition_names)), labels=partition_names)\n",
    "\n",
    "for (j, i), label in np.ndenumerate(np.round(Ind_arit,2)):\n",
    "    ax.text(i, j, label, ha='center', va='center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "de3aecd9-d378-4cff-ab24-a15bb424c162",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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