All_topological_properties.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "All topological properties 2.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# ***Here we calculate and explorate some topological properties of funtional networks***\n",
        "\n",
        "# ***`First let's load everything we're going to need`***"
      ],
      "metadata": {
        "id": "HugnjWBrc5DZ"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FjhtvdcgYweV"
      },
      "outputs": [],
      "source": [
        "#import libraries\n",
        "import networkx as nx\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import json\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/gdrive')\n",
        "%cd /gdrive"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7taJU2WwdFl2",
        "outputId": "a96bc8bf-ee56-4bb3-853e-2e665c8c9338"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /gdrive\n",
            "/gdrive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Load FC, feedback type, mouse name and brain areas per sesion (sesions 9,12,14,17,21,30,32)\n",
        "sessions = [9,12,14,17,21,30,32]\n",
        "FCSS = []\n",
        "f_types = []\n",
        "areass = []\n",
        "trialss = []\n",
        "names = ['Henchde','Lederbergde','Lederbergde','Lederbergde','Mullerde','Richardsde','Richardsde']\n",
        "for session in sessions:\n",
        "  FCS = np.load('/gdrive/Shareddrives/NoNameGroup - NMA/Results/Functional Networks/FC_' + str(session) + '.npy')\n",
        "  f_type = np.load('/gdrive/Shareddrives/NoNameGroup - NMA/Results/Functional Networks/feedbacktype_' + str(session) +'.npy')\n",
        "  area = np.load('/gdrive/Shareddrives/NoNameGroup - NMA/Results/Functional Networks/brainareas_' + str(session) + '.npy')\n",
        "  trials = np.load('/gdrive/Shareddrives/NoNameGroup - NMA/Results/Functional Networks/trials_' + str(session) +'.npy')\n",
        "\n",
        "  FCSS.append(FCS)\n",
        "  f_types.append(f_type)\n",
        "  areass.append(area)\n",
        "  trialss.append(trials)"
      ],
      "metadata": {
        "id": "k7HgMZA9dDyy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def entropy_dist(measure,nbins):\n",
        "  hist = np.histogram(measure,bins= nbins)[0]\n",
        "  prob = hist/np.sum(hist)\n",
        "  prob = prob[np.nonzero(prob)]\n",
        "  S = -np.sum(prob*np.log(prob)) \n",
        "  return S\n",
        "\n",
        "def node_degree(graph):\n",
        "  degree = list(graph.degree())\n",
        "  degree2 = np.ones(len(degree))\n",
        "  for i in range(len(degree)):\n",
        "    degree2[i] = degree[i][1]\n",
        "  return degree2\n",
        "\n",
        "\n",
        "def super_areas(brain_areas):\n",
        "  '''\n",
        "  from the list with brain areas, this function construct a list with super brain areas\n",
        "  input: \n",
        "  list of brain areas\n",
        "\n",
        "  output:\n",
        "  list of super brain areas\n",
        "  '''\n",
        "  visual = [\"VISa\", \"VISam\", \"VISl\", \"VISp\", \"VISpm\", \"VISrl\"]  # visual cortex\n",
        "  talamo = [\"CL\", \"LD\", \"LGd\", \"LH\", \"LP\", \"MD\", \"MG\", \"PO\", \"POL\", \"PT\", \"RT\", \"SPF\", \"TH\", \"VAL\", \"VPL\", \"VPM\"] # thalamus\n",
        "  hipocampo = [\"CA\", \"CA1\", \"CA2\", \"CA3\", \"DG\", \"SUB\", \"POST\"]  # hippocampal\n",
        "  no_visual = [\"ACA\", \"AUD\", \"COA\", \"DP\", \"ILA\", \"MOp\", \"MOs\", \"OLF\", \"ORB\", \"ORBm\", \"PIR\", \"PL\", \"SSp\", \"SSs\", \"RSP\",\"TT\"]  # non-visual cortex\n",
        "  midbrain = [\"APN\", \"IC\", \"MB\", \"MRN\", \"NB\", \"PAG\", \"RN\", \"SCs\", \"SCm\", \"SCig\", \"SCsg\", \"ZI\"]  # midbrain\n",
        "  basal_g = [\"ACB\", \"CP\", \"GPe\", \"LS\", \"LSc\", \"LSr\", \"MS\", \"OT\", \"SNr\", \"SI\"]  # basal ganglia\n",
        "  cortical_sub = [\"BLA\", \"BMA\", \"EP\", \"EPd\", \"MEA\"]  # cortical subplate\n",
        "  total = visual + talamo + hipocampo + no_visual + midbrain + basal_g + cortical_sub\n",
        "  sarea = []\n",
        "  #0 visual cortex\n",
        "  #1 talamo\n",
        "  #2 hipocampo\n",
        "  #3 no visual cortex\n",
        "  #4 midbrain\n",
        "  #5 basal ganglia\n",
        "  #6 cortical subplates\n",
        "  for i in brain_areas:\n",
        "    if i in visual:\n",
        "      sarea.append('visual_cortex')\n",
        "    if i in talamo:\n",
        "      sarea.append('thalamus')\n",
        "    if i in hipocampo:\n",
        "      sarea.append('hippocampus')\n",
        "    if i in no_visual:\n",
        "      sarea.append('non visual cortex')\n",
        "    if i in midbrain:\n",
        "      sarea.append('midbrain')\n",
        "    if i in basal_g:\n",
        "      sarea.append('basal_ganglia')\n",
        "    if i in cortical_sub:\n",
        "      sarea.append('cortical_subplates')\n",
        "    if i not in total:\n",
        "      sarea.append('other')\n",
        "    \n",
        "  return sarea\n",
        "\n",
        "def topological_measures(graph,brain_areas):\n",
        "  '''\n",
        "  this function calculate some topological measures from a given graph\n",
        "  input:\n",
        "  graph: graph in the format provided for networkx\n",
        "  \n",
        "  output:\n",
        "  measures: dictionary with some topological measures, from nodal measures this contain mean,standar desviation and entropy of the nodal measure\n",
        "  '''\n",
        "  #relabel nodes\n",
        "  nodes_prev = np.array(list(graph.nodes()))\n",
        "  dict_labels = {}\n",
        "  for i in range(len(nodes_prev)):\n",
        "    dict_labels[str(nodes_prev[i])] = i\n",
        "  nx.relabel_nodes(graph,dict_labels)\n",
        "\n",
        "  #take the large connected component of the graph\n",
        "  nodes_prev = np.array(list(graph.nodes()))\n",
        "  Gcc = sorted(nx.connected_components(graph), key=len, reverse=True)\n",
        "  graph = graph.subgraph(Gcc[0])\n",
        "  nodes_post = np.array(list(graph.nodes()))\n",
        "  #find the index of the nodes in the big component\n",
        "  index = []\n",
        "  for i in range(len(nodes_post)):\n",
        "    c = np.where( nodes_prev == nodes_post[i] )\n",
        "    index.append(c[0][0])\n",
        "  index = np.array(index)\n",
        "\n",
        "  #filter brain areas\n",
        "  brain_areas = brain_areas[index]\n",
        "  sbrain_areas = super_areas(brain_areas)\n",
        "  sbrain_areas = np.array(sbrain_areas)\n",
        "  filter_midbrain = sbrain_areas == 'midbrain'\n",
        "  filter_basal_ganglia = sbrain_areas == 'basal_ganglia'\n",
        "  \n",
        "\n",
        "  #calculate clustering\n",
        "  clustering = nx.clustering(graph,weight = True)\n",
        "  clustering = np.array(list(clustering.values()))\n",
        "  #calculate closenes\n",
        "  g_distance_dict = {(e1, e2): 1 / weight for e1, e2, weight in graph.edges(data='weight')}\n",
        "  nx.set_edge_attributes(graph, g_distance_dict, 'distance')\n",
        "  closeness = nx.closeness_centrality(graph,distance = \"distance\")\n",
        "  closeness = np.array(list(closeness.values()))\n",
        "  #calculate degree\n",
        "  degree = node_degree(graph)\n",
        "  #calculate mean geodesic distance\n",
        "  geodd = nx.average_shortest_path_length(graph,weight = True)\n",
        "  #calculate strenght\n",
        "  FC = nx.to_numpy_array(graph)\n",
        "  strenght = np.sum(FC, axis = 1)\n",
        "  # calculate mean, standar desviation and entropy of degree, closeness, and clustering\n",
        "  mean_clustering = np.mean(clustering)\n",
        "  std_clustering = np.std(clustering)\n",
        "  mean_closeness = np.mean(closeness)\n",
        "  std_closeness = np.std(closeness)\n",
        "  mean_degree = np.mean(degree)\n",
        "  std_degree = np.std(degree)\n",
        "  mean_strenght = np.mean(strenght)\n",
        "  std_strenght= np.std(strenght)\n",
        "  entropy_closeness = entropy_dist(closeness,nbins = 25)\n",
        "  entropy_strenght = entropy_dist(strenght,nbins = 25)\n",
        "  entropy_clustering = entropy_dist(clustering,nbins = 25)\n",
        "  entropy_degree = entropy_dist(degree,nbins = 25)\n",
        "  #calculate small world coefficient\n",
        "  smallworld = mean_clustering/geodd\n",
        "\n",
        "  #calculate local measure\n",
        "  mean_clustering_midbrain = np.mean(clustering[filter_midbrain])\n",
        "  mean_clustering_basal_ganglia = np.mean(clustering[filter_basal_ganglia])\n",
        "  std_clustering_midbrain = np.std(clustering[filter_midbrain])\n",
        "  std_clustering_basal_ganglia = np.std(clustering[filter_basal_ganglia])\n",
        "\n",
        "  mean_degree_midbrain = np.mean(degree[filter_midbrain])\n",
        "  mean_degree_basal_ganglia = np.mean(degree[filter_basal_ganglia])\n",
        "  std_degree_midbrain = np.std(degree[filter_midbrain])\n",
        "  std_degree_basal_ganglia = np.std(degree[filter_basal_ganglia])\n",
        "\n",
        "  mean_strenght_midbrain = np.mean(strenght[filter_midbrain])\n",
        "  mean_strenght_basal_ganglia = np.mean(strenght[filter_basal_ganglia])\n",
        "  std_strenght_midbrain = np.std(strenght[filter_midbrain])\n",
        "  std_strenght_basal_ganglia = np.std(strenght[filter_basal_ganglia])\n",
        "\n",
        "  mean_closeness_midbrain = np.mean(closeness[filter_midbrain])\n",
        "  mean_closeness_basal_ganglia = np.mean(closeness[filter_basal_ganglia])\n",
        "  std_closeness_midbrain = np.std(closeness[filter_midbrain])\n",
        "  std_closeness_basal_ganglia = np.std(closeness[filter_basal_ganglia])\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "  #put all this in a dictionary\n",
        "  measures = {'degree':degree,'mean_degree':mean_degree, 'std_degree':std_degree,'entropy_degree':entropy_degree,\n",
        "            'closeness':closeness,'mean_closeness':mean_closeness, 'std_closeness':std_closeness,'entropy_closeness':entropy_closeness,\n",
        "            'strenght':strenght,'mean_strenght':mean_strenght, 'std_strenght':std_strenght,'entropy_strenght':entropy_strenght,\n",
        "            'clustering':clustering,'mean_clustering':mean_clustering, 'std_clustering':std_clustering,'entropy_clustering':entropy_clustering,\n",
        "            'geodd': geodd,\n",
        "            'smallworld': smallworld, \n",
        "            'mean_clustering_midbrain':mean_clustering_midbrain,'mean_clustering_basal_ganglia':mean_clustering_basal_ganglia,'std_clustering_midbrain':std_clustering_midbrain,'std_clustering_basal_ganglia':std_clustering_basal_ganglia,\n",
        "            'mean_degree_midbrain':mean_degree_midbrain,'mean_degree_basal_ganglia':mean_degree_basal_ganglia,'std_degree_midbrain':std_degree_midbrain,'std_degree_basal_ganglia':std_degree_basal_ganglia,\n",
        "            'mean_strenght_midbrain':mean_strenght_midbrain,'mean_strenght_basal_ganglia':mean_strenght_basal_ganglia,'std_strenght_midbrain':std_strenght_midbrain,'std_strenght_basal_ganglia':std_strenght_basal_ganglia,\n",
        "            'mean_closeness_midbrain':mean_closeness_midbrain,'mean_closeness_basal_ganglia':mean_closeness_basal_ganglia,'std_closeness_midbrain':std_closeness_midbrain,'std_closeness_basal_ganglia':std_closeness_basal_ganglia}\n",
        "  return measures\n",
        "\n",
        "def topological_measures_session(FCS,reward,session,trials,threshold,brain_areas):\n",
        "  ntrials = len(trials)\n",
        "  #global\n",
        "  mean_degree = np.ones(ntrials)\n",
        "  mean_closeness = np.ones(ntrials)\n",
        "  mean_clustering = np.ones(ntrials)\n",
        "  mean_strenght = np.ones(ntrials)\n",
        "\n",
        "  std_strenght = np.ones(ntrials)\n",
        "  std_degree = np.ones(ntrials)\n",
        "  std_closeness = np.ones(ntrials)\n",
        "  std_clustering = np.ones(ntrials)\n",
        "\n",
        "  entropy_degree = np.ones(ntrials)\n",
        "  entropy_closeness = np.ones(ntrials)\n",
        "  entropy_clustering = np.ones(ntrials)\n",
        "  entropy_strenght = np.ones(ntrials)\n",
        "\n",
        "  geodd = np.ones(ntrials)\n",
        "  smallworld = np.ones(ntrials)\n",
        "\n",
        "  #local\n",
        "  mean_degree_midbrain = np.ones(ntrials)\n",
        "  mean_closeness_midbrain = np.ones(ntrials)\n",
        "  mean_clustering_midbrain = np.ones(ntrials)\n",
        "  mean_strenght_midbrain = np.ones(ntrials)\n",
        "\n",
        "  std_strenght_midbrain = np.ones(ntrials)\n",
        "  std_degree_midbrain = np.ones(ntrials)\n",
        "  std_closeness_midbrain = np.ones(ntrials)\n",
        "  std_clustering_midbrain = np.ones(ntrials)\n",
        "\n",
        "  mean_degree_basal_ganglia = np.ones(ntrials)\n",
        "  mean_closeness_basal_ganglia = np.ones(ntrials)\n",
        "  mean_clustering_basal_ganglia = np.ones(ntrials)\n",
        "  mean_strenght_basal_ganglia = np.ones(ntrials)\n",
        "\n",
        "  std_strenght_basal_ganglia = np.ones(ntrials)\n",
        "  std_degree_basal_ganglia = np.ones(ntrials)\n",
        "  std_closeness_basal_ganglia = np.ones(ntrials)\n",
        "  std_clustering_basal_ganglia = np.ones(ntrials)\n",
        "\n",
        "\n",
        "  for trial in range(ntrials):\n",
        "    FC = FCS[trial]\n",
        "    FC = FC*(FC > threshold)\n",
        "    graph = nx.from_numpy_array(FC)\n",
        "    measures = topological_measures(graph,brain_areas)\n",
        "\n",
        "    #local\n",
        "\n",
        "    mean_degree[trial] = measures['mean_degree']\n",
        "    mean_closeness[trial] = measures['mean_closeness']\n",
        "    mean_clustering[trial] = measures['mean_clustering']\n",
        "    mean_strenght[trial] = measures['mean_strenght']\n",
        "\n",
        "    std_strenght[trial] = measures['std_strenght']\n",
        "    std_degree[trial] = measures['std_degree']\n",
        "    std_closeness[trial] = measures['std_closeness']\n",
        "    std_clustering[trial] = measures['std_clustering']\n",
        "\n",
        "    entropy_degree[trial] = measures['entropy_degree']\n",
        "    entropy_closeness[trial] = measures['entropy_closeness']\n",
        "    entropy_clustering[trial] = measures['entropy_clustering']\n",
        "    entropy_strenght[trial] = measures['entropy_strenght']\n",
        "\n",
        "    geodd[trial] = measures['geodd']\n",
        "    smallworld[trial] = measures['smallworld']\n",
        "\n",
        "    #global\n",
        "    mean_degree_midbrain[trial] = measures['mean_degree_midbrain']\n",
        "    mean_closeness_midbrain[trial] = measures['mean_closeness_midbrain']\n",
        "    mean_clustering_midbrain[trial] = measures['mean_clustering_midbrain']\n",
        "    mean_strenght_midbrain[trial] = measures['mean_strenght_midbrain']\n",
        "\n",
        "    std_strenght_midbrain[trial] = measures['std_strenght_midbrain']\n",
        "    std_degree_midbrain[trial] = measures['std_degree_midbrain']\n",
        "    std_closeness_midbrain[trial] = measures['std_closeness_midbrain']\n",
        "    std_clustering_midbrain[trial] = measures['std_clustering_midbrain']\n",
        "\n",
        "    mean_degree_basal_ganglia[trial] = measures['mean_degree_basal_ganglia']\n",
        "    mean_closeness_basal_ganglia[trial] = measures['mean_closeness_basal_ganglia']\n",
        "    mean_clustering_basal_ganglia[trial] = measures['mean_clustering_basal_ganglia']\n",
        "    mean_strenght_basal_ganglia[trial] = measures['mean_strenght_basal_ganglia']\n",
        "\n",
        "    std_strenght_basal_ganglia[trial] = measures['std_strenght_basal_ganglia']\n",
        "    std_degree_basal_ganglia[trial] = measures['std_degree_basal_ganglia']\n",
        "    std_closeness_basal_ganglia[trial] = measures['std_closeness_basal_ganglia']\n",
        "    std_clustering_basal_ganglia[trial] = measures['std_clustering_basal_ganglia']\n",
        "\n",
        "\n",
        "  measures_sesion = {'reward':reward,'session':np.array([session]*(ntrials)),'trial':trials,'mean_degree':mean_degree, 'std_degree':std_degree,'entropy_degree':entropy_degree,\n",
        "        'mean_strenght':mean_strenght, 'std_strenght':std_strenght,'entropy_strenght':entropy_strenght,\n",
        "        'mean_closeness':mean_closeness, 'std_closeness':std_closeness,'entropy_closeness':entropy_closeness,\n",
        "        'mean_clustering':mean_clustering, 'std_clustering':std_clustering,'entropy_clustering':entropy_clustering,\n",
        "        'geodd': geodd,\n",
        "        'smallworld': smallworld,\n",
        "        'mean_clustering_midbrain':mean_clustering_midbrain,'mean_clustering_basal_ganglia':mean_clustering_basal_ganglia,'std_clustering_midbrain':std_clustering_midbrain,'std_clustering_basal_ganglia':std_clustering_basal_ganglia,\n",
        "        'mean_degree_midbrain':mean_degree_midbrain,'mean_degree_basal_ganglia':mean_degree_basal_ganglia,'std_degree_midbrain':std_degree_midbrain,'std_degree_basal_ganglia':std_degree_basal_ganglia,\n",
        "        'mean_strenght_midbrain':mean_strenght_midbrain,'mean_strenght_basal_ganglia':mean_strenght_basal_ganglia,'std_strenght_midbrain':std_strenght_midbrain,'std_strenght_basal_ganglia':std_strenght_basal_ganglia,\n",
        "        'mean_closeness_midbrain':mean_closeness_midbrain,'mean_closeness_basal_ganglia':mean_closeness_basal_ganglia,'std_closeness_midbrain':std_closeness_midbrain,'std_closeness_basal_ganglia':std_closeness_basal_ganglia}\n",
        "  return measures_sesion"
      ],
      "metadata": {
        "id": "QKAAXm3VePkW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***`calculate topological measures and organize in a dictionary`***"
      ],
      "metadata": {
        "id": "aWSSjasXMNFp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(3,5):\n",
        "  measures = topological_measures_session(FCSS[i],f_types[i],sessions[i],trialss[i],0.02,areass[i])\n",
        "  data = pd.DataFrame(measures)\n",
        "  data.to_csv('/gdrive/Shareddrives/NoNameGroup - NMA/Results/Topological measures/all_measures_session_' + str(sessions[i])+'.csv' )\n",
        "  #save_dict(measures,'/gdrive/Shareddrives/NoNameGroup - NMA/Results/Topological measures/measures_session_' + str(sessions[i]) )"
      ],
      "metadata": {
        "id": "M136f4vHg9oC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "CCyR-wwXDV0-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "nB56RMC4-Mwt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "oinqjMGs-MzE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "l39GNJ2V-M1d"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "EdWG_EQwDV3_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# ***Check some networks***"
      ],
      "metadata": {
        "id": "FAyDfpp3xkBV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "pU8Ie2bOCpsG"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx \n",
        "grafo = nx.from_numpy_array(FC)\n",
        "Gcc = sorted(nx.connected_components(grafo), key=len, reverse=True)\n",
        "grafo = grafo.subgraph(Gcc[0])\n",
        "nx.draw(grafo)"
      ],
      "metadata": {
        "id": "MsuqOuE7xpQt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "nodos = list(grafo.nodes())\n",
        "for j in range(len(nodos)):\n",
        "  grafo.nodes[nodos[j]]['area'] = sarea[j]"
      ],
      "metadata": {
        "id": "kxaMZ137xpkK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "nx.write_graphml(grafo,'/gdrive/Shareddrives/NoNameGroup - NMA/Resultados/Redes funcionales/FC_reward.graphml')"
      ],
      "metadata": {
        "id": "r4J7Vu-1xrRU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array(['hola','adios'])\n",
        "b = a == 'hola'\n",
        "print(b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sGXzHrnrMO5M",
        "outputId": "216f6f22-be7a-46e9-ef2d-0a21588d3f28"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ True False]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "nx.draw(graph)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "hzFs6X8RMTCQ",
        "outputId": "f614f126-65fb-44c4-ed68-538b3065f765"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "FC = FCSS[0][10]\n",
        "graph = nx.from_numpy_array(FC)\n"
      ],
      "metadata": {
        "id": "q9c9EJdEeUvd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "nodes_prev = np.array(list(graph.nodes()))\n",
        "dict_labels = {}\n",
        "for i in range(len(nodes_prev)):\n",
        "  dict_labels[str(nodes_prev[i])] = i\n",
        "nx.relabel_nodes(graph,dict_labels)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1U095v4MlnKR",
        "outputId": "f44cb54b-96bf-4570-d889-d61c3c319e6a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<networkx.classes.graph.Graph at 0x7fa379330c90>"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(dict_labels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hN9uSf_MmN9y",
        "outputId": "c790f19d-d06a-499c-af8e-b0cdad5c3bf6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "{'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9, '10': 10, '11': 11, '12': 12, '13': 13, '14': 14, '15': 15, '16': 16, '17': 17, '18': 18, '19': 19, '20': 20, '21': 21, '22': 22, '23': 23, '24': 24, '25': 25, '26': 26, '27': 27, '28': 28, '29': 29, '30': 30, '31': 31, '32': 32, '33': 33, '34': 34, '35': 35, '36': 36, '37': 37, '38': 38, '39': 39, '40': 40, '41': 41, '42': 42, '43': 43, '44': 44, '45': 45, '46': 46, '47': 47, '48': 48, '49': 49, '50': 50, '51': 51, '52': 52, '53': 53, '54': 54, '55': 55, '56': 56, '57': 57, '58': 58, '59': 59, '60': 60, '61': 61, '62': 62, '63': 63, '64': 64, '65': 65, '66': 66, '67': 67, '68': 68, '69': 69, '70': 70, '71': 71, '72': 72, '73': 73, '74': 74, '75': 75, '76': 76, '77': 77, '78': 78, '79': 79, '80': 80, '81': 81, '82': 82, '83': 83, '84': 84, '85': 85, '86': 86, '87': 87, '88': 88, '89': 89, '90': 90, '91': 91, '92': 92, '93': 93, '94': 94, '95': 95, '96': 96, '97': 97, '98': 98, '99': 99, '100': 100, '101': 101, '102': 102, '103': 103, '104': 104, '105': 105, '106': 106, '107': 107, '108': 108, '109': 109, '110': 110, '111': 111, '112': 112, '113': 113, '114': 114, '115': 115, '116': 116, '117': 117, '118': 118, '119': 119, '120': 120, '121': 121, '122': 122, '123': 123, '124': 124, '125': 125, '126': 126, '127': 127, '128': 128, '129': 129, '130': 130, '131': 131, '132': 132, '133': 133, '134': 134, '135': 135, '136': 136, '137': 137, '138': 138, '139': 139, '140': 140, '141': 141, '142': 142, '143': 143, '144': 144, '145': 145, '146': 146, '147': 147, '148': 148, '149': 149, '150': 150, '151': 151, '152': 152, '153': 153, '154': 154, '155': 155, '156': 156, '157': 157, '158': 158, '159': 159, '160': 160, '161': 161, '162': 162, '163': 163, '164': 164, '165': 165, '166': 166, '167': 167, '168': 168, '169': 169, '170': 170, '171': 171, '172': 172, '173': 173, '174': 174, '175': 175, '176': 176, '177': 177, '178': 178, '179': 179, '180': 180, '181': 181, '182': 182, '183': 183, '184': 184, '185': 185, '186': 186, '187': 187, '188': 188, '189': 189, '190': 190, '191': 191, '192': 192, '193': 193, '194': 194, '195': 195, '196': 196, '197': 197, '198': 198, '199': 199, '200': 200, '201': 201, '202': 202, '203': 203, '204': 204, '205': 205, '206': 206, '207': 207, '208': 208, '209': 209, '210': 210, '211': 211, '212': 212, '213': 213, '214': 214, '215': 215, '216': 216, '217': 217, '218': 218, '219': 219, '220': 220, '221': 221, '222': 222, '223': 223, '224': 224, '225': 225, '226': 226, '227': 227, '228': 228, '229': 229, '230': 230, '231': 231, '232': 232, '233': 233, '234': 234, '235': 235, '236': 236, '237': 237, '238': 238, '239': 239, '240': 240, '241': 241, '242': 242, '243': 243, '244': 244, '245': 245, '246': 246, '247': 247, '248': 248, '249': 249, '250': 250, '251': 251, '252': 252, '253': 253, '254': 254, '255': 255, '256': 256, '257': 257, '258': 258, '259': 259, '260': 260, '261': 261, '262': 262, '263': 263, '264': 264, '265': 265, '266': 266, '267': 267, '268': 268, '269': 269, '270': 270, '271': 271, '272': 272, '273': 273, '274': 274, '275': 275, '276': 276, '277': 277, '278': 278, '279': 279, '280': 280, '281': 281, '282': 282, '283': 283, '284': 284, '285': 285, '286': 286, '287': 287, '288': 288, '289': 289, '290': 290, '291': 291, '292': 292, '293': 293, '294': 294, '295': 295, '296': 296, '297': 297, '298': 298, '299': 299, '300': 300, '301': 301, '302': 302, '303': 303, '304': 304, '305': 305, '306': 306, '307': 307, '308': 308, '309': 309, '310': 310, '311': 311, '312': 312, '313': 313, '314': 314, '315': 315, '316': 316, '317': 317, '318': 318, '319': 319, '320': 320, '321': 321, '322': 322, '323': 323, '324': 324, '325': 325, '326': 326, '327': 327, '328': 328, '329': 329, '330': 330, '331': 331, '332': 332, '333': 333, '334': 334, '335': 335, '336': 336, '337': 337, '338': 338, '339': 339, '340': 340, '341': 341, '342': 342, '343': 343, '344': 344, '345': 345, '346': 346, '347': 347, '348': 348, '349': 349, '350': 350, '351': 351, '352': 352, '353': 353, '354': 354, '355': 355, '356': 356, '357': 357, '358': 358, '359': 359, '360': 360, '361': 361, '362': 362, '363': 363, '364': 364, '365': 365, '366': 366, '367': 367, '368': 368, '369': 369, '370': 370, '371': 371, '372': 372, '373': 373, '374': 374, '375': 375, '376': 376, '377': 377, '378': 378, '379': 379, '380': 380, '381': 381, '382': 382, '383': 383, '384': 384, '385': 385, '386': 386, '387': 387, '388': 388, '389': 389, '390': 390, '391': 391, '392': 392, '393': 393, '394': 394, '395': 395, '396': 396, '397': 397, '398': 398, '399': 399, '400': 400, '401': 401, '402': 402, '403': 403, '404': 404, '405': 405, '406': 406, '407': 407, '408': 408, '409': 409, '410': 410, '411': 411, '412': 412, '413': 413, '414': 414, '415': 415, '416': 416, '417': 417, '418': 418, '419': 419, '420': 420, '421': 421, '422': 422, '423': 423, '424': 424, '425': 425, '426': 426, '427': 427, '428': 428, '429': 429, '430': 430, '431': 431, '432': 432, '433': 433, '434': 434, '435': 435, '436': 436, '437': 437, '438': 438, '439': 439, '440': 440, '441': 441, '442': 442, '443': 443, '444': 444, '445': 445, '446': 446, '447': 447, '448': 448, '449': 449, '450': 450, '451': 451, '452': 452, '453': 453, '454': 454, '455': 455, '456': 456, '457': 457, '458': 458, '459': 459, '460': 460, '461': 461, '462': 462, '463': 463, '464': 464, '465': 465, '466': 466, '467': 467, '468': 468, '469': 469, '470': 470, '471': 471, '472': 472, '473': 473, '474': 474, '475': 475, '476': 476, '477': 477, '478': 478, '479': 479, '480': 480, '481': 481, '482': 482, '483': 483, '484': 484, '485': 485, '486': 486, '487': 487, '488': 488, '489': 489, '490': 490, '491': 491, '492': 492, '493': 493, '494': 494, '495': 495, '496': 496, '497': 497, '498': 498, '499': 499, '500': 500, '501': 501, '502': 502, '503': 503, '504': 504, '505': 505, '506': 506, '507': 507, '508': 508, '509': 509, '510': 510, '511': 511, '512': 512, '513': 513, '514': 514, '515': 515, 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'599': 599, '600': 600, '601': 601, '602': 602, '603': 603, '604': 604, '605': 605, '606': 606, '607': 607, '608': 608, '609': 609, '610': 610, '611': 611, '612': 612, '613': 613, '614': 614, '615': 615, '616': 616, '617': 617, '618': 618, '619': 619, '620': 620, '621': 621, '622': 622, '623': 623, '624': 624, '625': 625, '626': 626, '627': 627, '628': 628, '629': 629, '630': 630, '631': 631, '632': 632, '633': 633, '634': 634, '635': 635, '636': 636, '637': 637, '638': 638, '639': 639, '640': 640, '641': 641, '642': 642, '643': 643, '644': 644, '645': 645}\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "za5SsCqsmN_2"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}