{
 "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",
    "# ignore warnings\n",
    "import warnings\n",
    "import sys\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Graph</th>\n",
       "      <th>Number of Nodes</th>\n",
       "      <th>Number of Edges</th>\n",
       "      <th>Average Degree</th>\n",
       "      <th>Average Clustering Coefficient</th>\n",
       "      <th>log N</th>\n",
       "      <th>Average Shortest Path Length</th>\n",
       "      <th>betweenness centrality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brightkite Checkins Graph</td>\n",
       "      <td>6493</td>\n",
       "      <td>292973</td>\n",
       "      <td>90.242723</td>\n",
       "      <td>0.713999</td>\n",
       "      <td>8.778480</td>\n",
       "      <td>3.013369</td>\n",
       "      <td>0.000534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Gowalla Checkins Graph</td>\n",
       "      <td>3073</td>\n",
       "      <td>62790</td>\n",
       "      <td>40.865604</td>\n",
       "      <td>0.548372</td>\n",
       "      <td>8.030410</td>\n",
       "      <td>3.508031</td>\n",
       "      <td>0.001277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Foursquare Checkins Graph</td>\n",
       "      <td>2324</td>\n",
       "      <td>246702</td>\n",
       "      <td>212.30809</td>\n",
       "      <td>0.65273</td>\n",
       "      <td>7.751045</td>\n",
       "      <td>2.186112</td>\n",
       "      <td>0.000938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Brightkite Friendship Graph</td>\n",
       "      <td>5420</td>\n",
       "      <td>14690</td>\n",
       "      <td>5.420664</td>\n",
       "      <td>0.218571</td>\n",
       "      <td>8.597851</td>\n",
       "      <td>5.231807</td>\n",
       "      <td>0.000664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Filtered) Gowalla Friendship Graph</td>\n",
       "      <td>2294</td>\n",
       "      <td>5548</td>\n",
       "      <td>4.836966</td>\n",
       "      <td>0.234293</td>\n",
       "      <td>7.738052</td>\n",
       "      <td>5.396488</td>\n",
       "      <td>0.001331</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Foursquare Friendship Graph</td>\n",
       "      <td>1397</td>\n",
       "      <td>5323</td>\n",
       "      <td>7.620616</td>\n",
       "      <td>0.183485</td>\n",
       "      <td>7.242082</td>\n",
       "      <td>6.45841</td>\n",
       "      <td>0.001531</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Graph Number of Nodes Number of Edges  \\\n",
       "0            Brightkite Checkins Graph            6493          292973   \n",
       "1               Gowalla Checkins Graph            3073           62790   \n",
       "2            Foursquare Checkins Graph            2324          246702   \n",
       "3          Brightkite Friendship Graph            5420           14690   \n",
       "4  (Filtered) Gowalla Friendship Graph            2294            5548   \n",
       "5          Foursquare Friendship Graph            1397            5323   \n",
       "\n",
       "  Average Degree Average Clustering Coefficient     log N  \\\n",
       "0      90.242723                       0.713999  8.778480   \n",
       "1      40.865604                       0.548372  8.030410   \n",
       "2      212.30809                        0.65273  7.751045   \n",
       "3       5.420664                       0.218571  8.597851   \n",
       "4       4.836966                       0.234293  7.738052   \n",
       "5       7.620616                       0.183485  7.242082   \n",
       "\n",
       "  Average Shortest Path Length betweenness centrality  \n",
       "0                     3.013369               0.000534  \n",
       "1                     3.508031               0.001277  \n",
       "2                     2.186112               0.000938  \n",
       "3                     5.231807               0.000664  \n",
       "4                     5.396488               0.001331  \n",
       "5                      6.45841               0.001531  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis_results = pd.read_pickle('analysis_results.pkl')\n",
    "analysis_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Graph</th>\n",
       "      <th>Number of Nodes</th>\n",
       "      <th>Number of Edges</th>\n",
       "      <th>Average Degree</th>\n",
       "      <th>Average Clustering Coefficient</th>\n",
       "      <th>log N</th>\n",
       "      <th>Average Shortest Path Length</th>\n",
       "      <th>betweenness centrality</th>\n",
       "      <th>omega-coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brightkite Checkins Graph</td>\n",
       "      <td>6493</td>\n",
       "      <td>292973</td>\n",
       "      <td>90.242723</td>\n",
       "      <td>0.713999</td>\n",
       "      <td>8.778480</td>\n",
       "      <td>3.013369</td>\n",
       "      <td>0.000534</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Gowalla Checkins Graph</td>\n",
       "      <td>3073</td>\n",
       "      <td>62790</td>\n",
       "      <td>40.865604</td>\n",
       "      <td>0.548372</td>\n",
       "      <td>8.030410</td>\n",
       "      <td>3.508031</td>\n",
       "      <td>0.001277</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Foursquare Checkins Graph</td>\n",
       "      <td>2324</td>\n",
       "      <td>246702</td>\n",
       "      <td>212.30809</td>\n",
       "      <td>0.65273</td>\n",
       "      <td>7.751045</td>\n",
       "      <td>2.186112</td>\n",
       "      <td>0.000938</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Brightkite Friendship Graph</td>\n",
       "      <td>5420</td>\n",
       "      <td>14690</td>\n",
       "      <td>5.420664</td>\n",
       "      <td>0.218571</td>\n",
       "      <td>8.597851</td>\n",
       "      <td>5.231807</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Filtered) Gowalla Friendship Graph</td>\n",
       "      <td>2294</td>\n",
       "      <td>5548</td>\n",
       "      <td>4.836966</td>\n",
       "      <td>0.234293</td>\n",
       "      <td>7.738052</td>\n",
       "      <td>5.396488</td>\n",
       "      <td>0.001331</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Foursquare Friendship Graph</td>\n",
       "      <td>1397</td>\n",
       "      <td>5323</td>\n",
       "      <td>7.620616</td>\n",
       "      <td>0.183485</td>\n",
       "      <td>7.242082</td>\n",
       "      <td>6.45841</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Graph Number of Nodes Number of Edges  \\\n",
       "0            Brightkite Checkins Graph            6493          292973   \n",
       "1               Gowalla Checkins Graph            3073           62790   \n",
       "2            Foursquare Checkins Graph            2324          246702   \n",
       "3          Brightkite Friendship Graph            5420           14690   \n",
       "4  (Filtered) Gowalla Friendship Graph            2294            5548   \n",
       "5          Foursquare Friendship Graph            1397            5323   \n",
       "\n",
       "  Average Degree Average Clustering Coefficient     log N  \\\n",
       "0      90.242723                       0.713999  8.778480   \n",
       "1      40.865604                       0.548372  8.030410   \n",
       "2      212.30809                        0.65273  7.751045   \n",
       "3       5.420664                       0.218571  8.597851   \n",
       "4       4.836966                       0.234293  7.738052   \n",
       "5       7.620616                       0.183485  7.242082   \n",
       "\n",
       "  Average Shortest Path Length betweenness centrality  omega-coefficient  \n",
       "0                     3.013369               0.000534                NaN  \n",
       "1                     3.508031               0.001277                NaN  \n",
       "2                     2.186112               0.000938                NaN  \n",
       "3                     5.231807               0.000664                NaN  \n",
       "4                     5.396488               0.001331                NaN  \n",
       "5                      6.45841               0.001531                NaN  "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis_results['omega-coefficient'] = np.nan\n",
    "analysis_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Graph</th>\n",
       "      <th>Number of Nodes</th>\n",
       "      <th>Number of Edges</th>\n",
       "      <th>Average Degree</th>\n",
       "      <th>Average Clustering Coefficient</th>\n",
       "      <th>log N</th>\n",
       "      <th>Average Shortest Path Length</th>\n",
       "      <th>betweenness centrality</th>\n",
       "      <th>omega-coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brightkite Checkins Graph</td>\n",
       "      <td>6493</td>\n",
       "      <td>292973</td>\n",
       "      <td>90.242723</td>\n",
       "      <td>0.713999</td>\n",
       "      <td>8.778480</td>\n",
       "      <td>3.013369</td>\n",
       "      <td>0.000534</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Gowalla Checkins Graph</td>\n",
       "      <td>3073</td>\n",
       "      <td>62790</td>\n",
       "      <td>40.865604</td>\n",
       "      <td>0.548372</td>\n",
       "      <td>8.030410</td>\n",
       "      <td>3.508031</td>\n",
       "      <td>0.001277</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Foursquare Checkins Graph</td>\n",
       "      <td>2324</td>\n",
       "      <td>246702</td>\n",
       "      <td>212.30809</td>\n",
       "      <td>0.65273</td>\n",
       "      <td>7.751045</td>\n",
       "      <td>2.186112</td>\n",
       "      <td>0.000938</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Brightkite Friendship Graph</td>\n",
       "      <td>5420</td>\n",
       "      <td>14690</td>\n",
       "      <td>5.420664</td>\n",
       "      <td>0.218571</td>\n",
       "      <td>8.597851</td>\n",
       "      <td>5.231807</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Filtered) Gowalla Friendship Graph</td>\n",
       "      <td>2294</td>\n",
       "      <td>5548</td>\n",
       "      <td>4.836966</td>\n",
       "      <td>0.234293</td>\n",
       "      <td>7.738052</td>\n",
       "      <td>5.396488</td>\n",
       "      <td>0.001331</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Foursquare Friendship Graph</td>\n",
       "      <td>1397</td>\n",
       "      <td>5323</td>\n",
       "      <td>7.620616</td>\n",
       "      <td>0.183485</td>\n",
       "      <td>7.242082</td>\n",
       "      <td>6.45841</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Graph Number of Nodes Number of Edges  \\\n",
       "0            Brightkite Checkins Graph            6493          292973   \n",
       "1               Gowalla Checkins Graph            3073           62790   \n",
       "2            Foursquare Checkins Graph            2324          246702   \n",
       "3          Brightkite Friendship Graph            5420           14690   \n",
       "4  (Filtered) Gowalla Friendship Graph            2294            5548   \n",
       "5          Foursquare Friendship Graph            1397            5323   \n",
       "\n",
       "  Average Degree Average Clustering Coefficient     log N  \\\n",
       "0      90.242723                       0.713999  8.778480   \n",
       "1      40.865604                       0.548372  8.030410   \n",
       "2      212.30809                        0.65273  7.751045   \n",
       "3       5.420664                       0.218571  8.597851   \n",
       "4       4.836966                       0.234293  7.738052   \n",
       "5       7.620616                       0.183485  7.242082   \n",
       "\n",
       "  Average Shortest Path Length betweenness centrality  omega-coefficient  \n",
       "0                     3.013369               0.000534                NaN  \n",
       "1                     3.508031               0.001277                NaN  \n",
       "2                     2.186112               0.000938                NaN  \n",
       "3                     5.231807               0.000664                NaN  \n",
       "4                     5.396488               0.001331                NaN  \n",
       "5                      6.45841               0.001531                NaN  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# rename (Filtered) Gowalla Friendship Graph in Gowalla Friendship Graph\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Filtered Gowalla Friendship Graph', 'Graph'] = 'Gowalla Friendship Graph'\n",
    "analysis_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Graph</th>\n",
       "      <th>Number of Nodes</th>\n",
       "      <th>Number of Edges</th>\n",
       "      <th>Average Degree</th>\n",
       "      <th>Average Clustering Coefficient</th>\n",
       "      <th>log N</th>\n",
       "      <th>Average Shortest Path Length</th>\n",
       "      <th>betweenness centrality</th>\n",
       "      <th>omega-coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brightkite Checkins Graph</td>\n",
       "      <td>6493</td>\n",
       "      <td>292973</td>\n",
       "      <td>90.242723</td>\n",
       "      <td>0.713999</td>\n",
       "      <td>8.778480</td>\n",
       "      <td>3.013369</td>\n",
       "      <td>0.000534</td>\n",
       "      <td>-0.180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Gowalla Checkins Graph</td>\n",
       "      <td>3073</td>\n",
       "      <td>62790</td>\n",
       "      <td>40.865604</td>\n",
       "      <td>0.548372</td>\n",
       "      <td>8.030410</td>\n",
       "      <td>3.508031</td>\n",
       "      <td>0.001277</td>\n",
       "      <td>-0.240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Foursquare Checkins Graph</td>\n",
       "      <td>2324</td>\n",
       "      <td>246702</td>\n",
       "      <td>212.30809</td>\n",
       "      <td>0.65273</td>\n",
       "      <td>7.751045</td>\n",
       "      <td>2.186112</td>\n",
       "      <td>0.000938</td>\n",
       "      <td>-0.056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Brightkite Friendship Graph</td>\n",
       "      <td>5420</td>\n",
       "      <td>14690</td>\n",
       "      <td>5.420664</td>\n",
       "      <td>0.218571</td>\n",
       "      <td>8.597851</td>\n",
       "      <td>5.231807</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(Filtered) Gowalla Friendship Graph</td>\n",
       "      <td>2294</td>\n",
       "      <td>5548</td>\n",
       "      <td>4.836966</td>\n",
       "      <td>0.234293</td>\n",
       "      <td>7.738052</td>\n",
       "      <td>5.396488</td>\n",
       "      <td>0.001331</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Foursquare Friendship Graph</td>\n",
       "      <td>1397</td>\n",
       "      <td>5323</td>\n",
       "      <td>7.620616</td>\n",
       "      <td>0.183485</td>\n",
       "      <td>7.242082</td>\n",
       "      <td>6.45841</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 Graph Number of Nodes Number of Edges  \\\n",
       "0            Brightkite Checkins Graph            6493          292973   \n",
       "1               Gowalla Checkins Graph            3073           62790   \n",
       "2            Foursquare Checkins Graph            2324          246702   \n",
       "3          Brightkite Friendship Graph            5420           14690   \n",
       "4  (Filtered) Gowalla Friendship Graph            2294            5548   \n",
       "5          Foursquare Friendship Graph            1397            5323   \n",
       "\n",
       "  Average Degree Average Clustering Coefficient     log N  \\\n",
       "0      90.242723                       0.713999  8.778480   \n",
       "1      40.865604                       0.548372  8.030410   \n",
       "2      212.30809                        0.65273  7.751045   \n",
       "3       5.420664                       0.218571  8.597851   \n",
       "4       4.836966                       0.234293  7.738052   \n",
       "5       7.620616                       0.183485  7.242082   \n",
       "\n",
       "  Average Shortest Path Length betweenness centrality  omega-coefficient  \n",
       "0                     3.013369               0.000534             -0.180  \n",
       "1                     3.508031               0.001277             -0.240  \n",
       "2                     2.186112               0.000938             -0.056  \n",
       "3                     5.231807               0.000664                NaN  \n",
       "4                     5.396488               0.001331                NaN  \n",
       "5                      6.45841               0.001531                NaN  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Foursquare Checkins Graph : -0.056\n",
    "# Gowalla Checkins Graph : -0.24\n",
    "# Brightkite Checkins Graph : -0.18\n",
    "\n",
    "# add omega-coefficient to the respective graphs\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Foursquare Checkins Graph', 'omega-coefficient'] = -0.056\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Gowalla Checkins Graph', 'omega-coefficient'] = -0.24\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Brightkite Checkins Graph', 'omega-coefficient'] = -0.18\n",
    "analysis_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rename (Filtered) Gowalla Friendship Graph in Gowalla Friendship Graph\n",
    "analysis_results.loc[analysis_results['Graph'] == '(Filtered) Gowalla Friendship Graph', 'Graph'] = 'Gowalla Friendship Graph'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# FourSquare Friendship Graph : -0.17\n",
    "# Gowalla Friendship Graph : -0.25\n",
    "# Brightkite Friendship Graph : -0.20\n",
    "\n",
    "# add omega-coefficient to the respective graphs\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Foursquare Friendship Graph', 'omega-coefficient'] = -0.17\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Gowalla Friendship Graph', 'omega-coefficient'] = -0.25\n",
    "analysis_results.loc[analysis_results['Graph'] == 'Brightkite Friendship Graph', 'omega-coefficient'] = -0.20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Graph</th>\n",
       "      <th>Number of Nodes</th>\n",
       "      <th>Number of Edges</th>\n",
       "      <th>Average Degree</th>\n",
       "      <th>Average Clustering Coefficient</th>\n",
       "      <th>log N</th>\n",
       "      <th>Average Shortest Path Length</th>\n",
       "      <th>betweenness centrality</th>\n",
       "      <th>omega-coefficient</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Brightkite Checkins Graph</td>\n",
       "      <td>6493</td>\n",
       "      <td>292973</td>\n",
       "      <td>90.242723</td>\n",
       "      <td>0.713999</td>\n",
       "      <td>8.778480</td>\n",
       "      <td>3.013369</td>\n",
       "      <td>0.000534</td>\n",
       "      <td>-0.180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Gowalla Checkins Graph</td>\n",
       "      <td>3073</td>\n",
       "      <td>62790</td>\n",
       "      <td>40.865604</td>\n",
       "      <td>0.548372</td>\n",
       "      <td>8.030410</td>\n",
       "      <td>3.508031</td>\n",
       "      <td>0.001277</td>\n",
       "      <td>-0.240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Foursquare Checkins Graph</td>\n",
       "      <td>2324</td>\n",
       "      <td>246702</td>\n",
       "      <td>212.30809</td>\n",
       "      <td>0.65273</td>\n",
       "      <td>7.751045</td>\n",
       "      <td>2.186112</td>\n",
       "      <td>0.000938</td>\n",
       "      <td>-0.056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Brightkite Friendship Graph</td>\n",
       "      <td>5420</td>\n",
       "      <td>14690</td>\n",
       "      <td>5.420664</td>\n",
       "      <td>0.218571</td>\n",
       "      <td>8.597851</td>\n",
       "      <td>5.231807</td>\n",
       "      <td>0.000664</td>\n",
       "      <td>-0.200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Gowalla Friendship Graph</td>\n",
       "      <td>2294</td>\n",
       "      <td>5548</td>\n",
       "      <td>4.836966</td>\n",
       "      <td>0.234293</td>\n",
       "      <td>7.738052</td>\n",
       "      <td>5.396488</td>\n",
       "      <td>0.001331</td>\n",
       "      <td>-0.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Foursquare Friendship Graph</td>\n",
       "      <td>1397</td>\n",
       "      <td>5323</td>\n",
       "      <td>7.620616</td>\n",
       "      <td>0.183485</td>\n",
       "      <td>7.242082</td>\n",
       "      <td>6.45841</td>\n",
       "      <td>0.001531</td>\n",
       "      <td>-0.170</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Graph Number of Nodes Number of Edges Average Degree  \\\n",
       "0    Brightkite Checkins Graph            6493          292973      90.242723   \n",
       "1       Gowalla Checkins Graph            3073           62790      40.865604   \n",
       "2    Foursquare Checkins Graph            2324          246702      212.30809   \n",
       "3  Brightkite Friendship Graph            5420           14690       5.420664   \n",
       "4     Gowalla Friendship Graph            2294            5548       4.836966   \n",
       "5  Foursquare Friendship Graph            1397            5323       7.620616   \n",
       "\n",
       "  Average Clustering Coefficient     log N Average Shortest Path Length  \\\n",
       "0                       0.713999  8.778480                     3.013369   \n",
       "1                       0.548372  8.030410                     3.508031   \n",
       "2                        0.65273  7.751045                     2.186112   \n",
       "3                       0.218571  8.597851                     5.231807   \n",
       "4                       0.234293  7.738052                     5.396488   \n",
       "5                       0.183485  7.242082                      6.45841   \n",
       "\n",
       "  betweenness centrality  omega-coefficient  \n",
       "0               0.000534             -0.180  \n",
       "1               0.001277             -0.240  \n",
       "2               0.000938             -0.056  \n",
       "3               0.000664             -0.200  \n",
       "4               0.001331             -0.250  \n",
       "5               0.001531             -0.170  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis_results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# save the results into a pickle file\n",
    "analysis_results.to_pickle('analysis_results.pkl')"
   ]
  }
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