mirror of
https://github.com/lukefleed/small-worlds.git
synced 2026-10-06 22:14:50 +00:00
almost final version, need to review the theory
This commit is contained in:
Luca Lombardo
@@ -147,3 +147,4 @@ data/
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backup/
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sources/
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extra/
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html_graphs/
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+4402
-4166
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+2
-11
@@ -31,20 +31,11 @@ if __name__ == "__main__":
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parser = argparse.ArgumentParser()
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parser.add_argument("graph", help="Name of the graph to be used. Options are 'checkins-foursquare', 'checkins-gowalla', 'checkins-brightkite', 'friends-foursquare', 'friends-gowalla', 'friends-brightkite'")
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parser.add_argument("k", help="Percentage of nodes to be sampled. Needs to be a float between 0 and 1")
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parser.add_argument("niter", help="Number of rewiring per edge. Needs to be an integer. Default is 5")
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parser.add_argument("nrand", help="Number of random graphs. Needs to be an integer. Default is 5")
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parser.add_argument("--niter", help="Number of rewiring per edge. Needs to be an integer. Default is 5", default=5)
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parser.add_argument("--nrand", help="Number of random graphs. Needs to be an integer. Default is 5", default=5)
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parser.add_help = True
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args = parser.parse_args()
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# if no input is given for niter and nrand, set them to default values
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if args.niter == None:
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print("No input for niter. Setting it to default value: 5")
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args.niter = 5
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if args.nrand == None:
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print("No input for nrand. Setting it to default value: 5")
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args.nrand = 5
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# the name of the graph is the first part of the input string
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name = args.graph.split('-')[1]
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if 'checkins' in args.graph:
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+122
-760
@@ -16,809 +16,171 @@
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"import pandas as pd\n",
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"import networkx as nx\n",
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"import plotly.graph_objects as go\n",
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"# from utils import *\n",
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"from utils import *\n",
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"from collections import Counter\n",
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"from tqdm import tqdm\n",
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"import time\n",
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"import geopandas as gpd\n",
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"import gdown # for downloading files from google drive\n",
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"import shutil\n",
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"# ignore warnings\n",
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"import warnings\n",
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"import sys\n",
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"from pyvis.network import Network\n",
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"warnings.filterwarnings(\"ignore\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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||||
"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>Graph</th>\n",
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" <th>Number of Nodes</th>\n",
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" <th>Number of Edges</th>\n",
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" <th>Average Degree</th>\n",
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" <th>Average Clustering Coefficient</th>\n",
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" <th>log N</th>\n",
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" <th>Average Shortest Path Length</th>\n",
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" <th>betweenness centrality</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>Brightkite Checkins Graph</td>\n",
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" <td>6493</td>\n",
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" <td>292973</td>\n",
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" <td>90.242723</td>\n",
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" <td>0.713999</td>\n",
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" <td>8.778480</td>\n",
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" <td>3.013369</td>\n",
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" <td>0.000534</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>Gowalla Checkins Graph</td>\n",
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" <td>3073</td>\n",
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" <td>62790</td>\n",
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" <td>40.865604</td>\n",
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||||
" <td>0.548372</td>\n",
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||||
" <td>8.030410</td>\n",
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" <td>3.508031</td>\n",
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" <td>0.001277</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2</th>\n",
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" <td>Foursquare Checkins Graph</td>\n",
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" <td>2324</td>\n",
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" <td>246702</td>\n",
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" <td>212.30809</td>\n",
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||||
" <td>0.65273</td>\n",
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" <td>7.751045</td>\n",
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" <td>2.186112</td>\n",
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" <td>0.000938</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>3</th>\n",
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" <td>Brightkite Friendship Graph</td>\n",
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" <td>5420</td>\n",
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" <td>14690</td>\n",
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" <td>5.420664</td>\n",
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||||
" <td>0.218571</td>\n",
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||||
" <td>8.597851</td>\n",
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||||
" <td>5.231807</td>\n",
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" <td>0.000664</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>4</th>\n",
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" <td>(Filtered) Gowalla Friendship Graph</td>\n",
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" <td>2294</td>\n",
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" <td>5548</td>\n",
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" <td>4.836966</td>\n",
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||||
" <td>0.234293</td>\n",
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||||
" <td>7.738052</td>\n",
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||||
" <td>5.396488</td>\n",
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" <td>0.001331</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>5</th>\n",
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" <td>Foursquare Friendship Graph</td>\n",
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" <td>1397</td>\n",
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" <td>5323</td>\n",
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||||
" <td>7.620616</td>\n",
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||||
" <td>0.183485</td>\n",
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||||
" <td>7.242082</td>\n",
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" <td>6.45841</td>\n",
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" <td>0.001531</td>\n",
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||||
" </tr>\n",
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||||
" </tbody>\n",
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"</table>\n",
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||||
"</div>"
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],
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"text/plain": [
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" Graph Number of Nodes Number of Edges \\\n",
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"0 Brightkite Checkins Graph 6493 292973 \n",
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"1 Gowalla Checkins Graph 3073 62790 \n",
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"2 Foursquare Checkins Graph 2324 246702 \n",
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"3 Brightkite Friendship Graph 5420 14690 \n",
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"4 (Filtered) Gowalla Friendship Graph 2294 5548 \n",
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"5 Foursquare Friendship Graph 1397 5323 \n",
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"\n",
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" Average Degree Average Clustering Coefficient log N \\\n",
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"0 90.242723 0.713999 8.778480 \n",
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"1 40.865604 0.548372 8.030410 \n",
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||||
"2 212.30809 0.65273 7.751045 \n",
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||||
"3 5.420664 0.218571 8.597851 \n",
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||||
"4 4.836966 0.234293 7.738052 \n",
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"5 7.620616 0.183485 7.242082 \n",
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"\n",
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||||
" Average Shortest Path Length betweenness centrality \n",
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"0 3.013369 0.000534 \n",
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"1 3.508031 0.001277 \n",
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"2 2.186112 0.000938 \n",
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"3 5.231807 0.000664 \n",
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||||
"4 5.396488 0.001331 \n",
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||||
"5 6.45841 0.001531 "
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||||
]
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||||
},
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||||
"execution_count": 14,
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||||
"metadata": {},
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||||
"output_type": "execute_result"
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||||
}
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||||
],
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"source": [
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"analysis_results = pd.read_pickle('analysis_results.pkl')\n",
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"analysis_results"
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]
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||||
},
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||||
{
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||||
"cell_type": "code",
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||||
"execution_count": 15,
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||||
"metadata": {},
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||||
"outputs": [
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||||
{
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||||
"data": {
|
||||
"text/html": [
|
||||
"<div>\n",
|
||||
"<style scoped>\n",
|
||||
" .dataframe tbody tr th:only-of-type {\n",
|
||||
" vertical-align: middle;\n",
|
||||
" }\n",
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||||
"\n",
|
||||
" .dataframe tbody tr th {\n",
|
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|
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|
||||
" 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",
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||||
" <th>Number of Nodes</th>\n",
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||||
" <th>Number of Edges</th>\n",
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||||
" <th>Average Degree</th>\n",
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||||
" <th>Average Clustering Coefficient</th>\n",
|
||||
" <th>log N</th>\n",
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||||
" <th>Average Shortest Path Length</th>\n",
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||||
" <th>betweenness centrality</th>\n",
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||||
" <th>omega-coefficient</th>\n",
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||||
" </tr>\n",
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||||
" </thead>\n",
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||||
" <tbody>\n",
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||||
" <tr>\n",
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||||
" <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",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" <tr>\n",
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||||
" <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",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" <tr>\n",
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||||
" <th>2</th>\n",
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||||
" <td>Foursquare Checkins Graph</td>\n",
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||||
" <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",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" <tr>\n",
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||||
" <th>3</th>\n",
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||||
" <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",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" <tr>\n",
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||||
" <th>4</th>\n",
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||||
" <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",
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||||
" <td>0.001331</td>\n",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" <tr>\n",
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" <th>5</th>\n",
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" <td>Foursquare Friendship Graph</td>\n",
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||||
" <td>1397</td>\n",
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||||
" <td>5323</td>\n",
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||||
" <td>7.620616</td>\n",
|
||||
" <td>0.183485</td>\n",
|
||||
" <td>7.242082</td>\n",
|
||||
" <td>6.45841</td>\n",
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||||
" <td>0.001531</td>\n",
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||||
" <td>NaN</td>\n",
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||||
" </tr>\n",
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||||
" </tbody>\n",
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||||
"</table>\n",
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||||
"</div>"
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||||
],
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||||
"text/plain": [
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||||
" 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",
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"\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 "
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||||
]
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||||
},
|
||||
"execution_count": 15,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
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||||
"source": [
|
||||
"analysis_results['omega-coefficient'] = np.nan\n",
|
||||
"analysis_results"
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||||
]
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||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
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|
||||
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|
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|
||||
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|
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|
||||
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|
||||
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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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",
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||||
" </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": {
|
||||
"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>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,
|
||||
"execution_count": 2,
|
||||
"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",
|
||||
"import multiprocessing\n",
|
||||
"import random\n",
|
||||
"import networkx as nx\n",
|
||||
"import numpy as np\n",
|
||||
"import math\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"
|
||||
"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": 27,
|
||||
"execution_count": 3,
|
||||
"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 "
|
||||
"'Graph with 200 nodes and 584 edges'"
|
||||
]
|
||||
},
|
||||
"execution_count": 27,
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"analysis_results\n"
|
||||
"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": null,
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"0.6776975801779451"
|
||||
]
|
||||
},
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# save the results into a pickle file\n",
|
||||
"analysis_results.to_pickle('analysis_results.pkl')"
|
||||
"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"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3.10.8 64-bit",
|
||||
"display_name": "Python 3 (ipykernel)",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
@@ -832,7 +194,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.10.9 (main, Dec 19 2022, 17:35:49) [GCC 12.2.0]"
|
||||
"version": "3.10.9"
|
||||
},
|
||||
"orig_nbformat": 4,
|
||||
"vscode": {
|
||||
|
||||
@@ -23,6 +23,7 @@ import numpy as np
|
||||
import gdown
|
||||
from networkx.utils import py_random_state
|
||||
import shutil
|
||||
from pyvis.network import Network
|
||||
|
||||
# ------------------------------------------------------------------------#
|
||||
|
||||
@@ -100,21 +101,15 @@ def download_datasets():
|
||||
|
||||
shutil.rmtree(os.path.join("data", "foursquare", "dataset_WWW2019"))
|
||||
shutil.rmtree(os.path.join("data", "foursquare", "__MACOSX"))
|
||||
|
||||
os.rename(os.path.join("data", "foursquare", "dataset_WWW_friendship_new.txt"), os.path.join("data", "foursquare", "foursquare_friends_edges.txt"))
|
||||
|
||||
os.rename(os.path.join("data", "foursquare", "dataset_WWW_Checkins_anonymized.txt"), os.path.join("data", "foursquare", "foursquare_checkins.txt"))
|
||||
os.rename(os.path.join("data", "foursquare", "dataset_WWW_Checkins_anonymized.txt"), os.path.join("data", "foursquare", "foursquare_checkins_full.txt"))
|
||||
|
||||
## BRIGHTKITE CLEANING ##
|
||||
|
||||
os.rename(os.path.join("data", "brightkite", "loc-brightkite_totalCheckins.txt"), os.path.join("data", "brightkite", "brightkite_checkins.txt"))
|
||||
|
||||
os.rename(os.path.join("data", "brightkite", "loc-brightkite_totalCheckins.txt"), os.path.join("data", "brightkite", "brightkite_checkins_full.txt"))
|
||||
os.rename(os.path.join("data", "brightkite", "loc-brightkite_edges.txt"), os.path.join("data", "brightkite", "brightkite_friends_edges.txt"))
|
||||
|
||||
## GOWALLA CLEANING ##
|
||||
|
||||
os.rename(os.path.join("data", "gowalla", "loc-gowalla_totalCheckins.txt"), os.path.join("data", "gowalla", "gowalla_checkins.txt"))
|
||||
|
||||
os.rename(os.path.join("data", "gowalla", "loc-gowalla_totalCheckins.txt"), os.path.join("data", "gowalla", "gowalla_checkins_full.txt"))
|
||||
os.rename(os.path.join("data", "gowalla", "loc-gowalla_edges.txt"), os.path.join("data", "gowalla", "gowalla_friends_edges.txt"))
|
||||
|
||||
# ------------------------------------------------------------------------#
|
||||
@@ -392,7 +387,7 @@ def average_shortest_path(G: nx.Graph, k=None) -> float:
|
||||
----------
|
||||
`G` : networkx graph
|
||||
The graph to compute the average shortest path length of.
|
||||
`k` : int
|
||||
`k` : float
|
||||
percentage of nodes to remove from the graph. If k is None, the average shortest path length of each connected component is computed using all the nodes of the connected component.
|
||||
|
||||
Returns
|
||||
@@ -548,3 +543,90 @@ def create_random_graphs(G: nx.Graph, model = None, save = True) -> nx.Graph:
|
||||
print("\tThe file graph has been saved in the folder data/random/watts_strogatz with the syntax watts_strogatz_n_nodes_n_edges.gpickle")
|
||||
|
||||
return G_random
|
||||
|
||||
|
||||
def visualize_graphs(G: nx.Graph, k: float, connected = True):
|
||||
|
||||
"""
|
||||
Function to visualize the graph in a HTML page using pyvis
|
||||
|
||||
Parameters
|
||||
----------
|
||||
G: nx.Graph
|
||||
The graph to visualize
|
||||
|
||||
k: float
|
||||
The percentage of nodes to remove from the graph. Default is None, in which case it will be chosen such that there are about 1000 nodes in the sampled graph. I strongly suggest to use the default value, other wise the visualization will be very slow.
|
||||
|
||||
connected: bool
|
||||
If True, we will consider only the largest connected component of the graph
|
||||
|
||||
Returns
|
||||
-------
|
||||
html file
|
||||
The html file containing the visualization of the graph
|
||||
|
||||
Notes:
|
||||
------
|
||||
This is of course an approximation, it's nice to have an idea of the graph, but it's not a good idea trying to understand the graph in details from this sampled visualization.
|
||||
"""
|
||||
|
||||
if k is None:
|
||||
if len(G.nodes) > 1500:
|
||||
k = 1 - 1500/len(G.nodes)
|
||||
else:
|
||||
k = 0
|
||||
|
||||
# remove a percentage of the nodes
|
||||
nodes_to_remove = np.random.choice(list(G.nodes), size=int(k*len(G.nodes)), replace=False)
|
||||
G.remove_nodes_from(nodes_to_remove)
|
||||
|
||||
if connected:
|
||||
# take only the largest connected component
|
||||
connected_components = list(nx.connected_components(G))
|
||||
largest_connected_component = max(connected_components, key=len)
|
||||
G = G.subgraph(largest_connected_component)
|
||||
|
||||
|
||||
# create a networkx graph
|
||||
net = net = Network(directed=False, bgcolor='#1e1f29', font_color='white')
|
||||
|
||||
# for some reasons, if I put % values, the graph is not displayed correctly. So I use pixels, sorry non FHD users
|
||||
net.width = '1920px'
|
||||
net.height = '1080px'
|
||||
|
||||
# add nodes and edges
|
||||
net.add_nodes(list(G.nodes))
|
||||
net.add_edges(list(G.edges))
|
||||
|
||||
# set the physics layout of the network
|
||||
net.set_options("""
|
||||
var options = {
|
||||
"edges": {
|
||||
"color": {
|
||||
"inherit": true
|
||||
},
|
||||
"smooth": false
|
||||
},
|
||||
"physics": {
|
||||
"repulsion": {
|
||||
"centralGravity": 0.25,
|
||||
"nodeDistance": 500,
|
||||
"damping": 0.67
|
||||
},
|
||||
"maxVelocity": 48,
|
||||
"minVelocity": 0.39,
|
||||
"solver": "repulsion"
|
||||
}
|
||||
}
|
||||
""")
|
||||
|
||||
name = G.name.replace(" ", "_").lower()
|
||||
|
||||
if not os.path.exists("html_graphs"):
|
||||
os.mkdir("html_graphs")
|
||||
|
||||
# save the graph in a html file
|
||||
net.show("html_graphs/{}.html".format(name))
|
||||
|
||||
print("The graph has been saved in the folder html_graphs with the name {}.html" .format(name))
|
||||
|
||||
Reference in New Issue
Block a user