694 lines
59 KiB
Text
694 lines
59 KiB
Text
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Network Analysis"
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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": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"import networkx as nx\n",
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"from networkx.drawing.nx_agraph import graphviz_layout\n",
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"import matplotlib.pyplot as plt\n",
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"import pandas as pd\n",
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"import numpy as np\n",
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"import dzcnapy_plotlib as dzcnapy\n",
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"import csv\n",
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"import math\n",
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"import collections as coll\n",
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"from networkx.algorithms import community as com\n",
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"import community as lou\n",
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"\n",
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"# Importazione dataset\n",
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"with open(\"dataset.csv\") as infile:\n",
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" csv_reader = csv.reader(infile)\n",
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" G = nx.Graph(csv_reader)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Nodes, Edges, Density"
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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": 8,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"#Nodes: 37702\n",
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"#Edges: 289004\n",
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"#Edges if graph was a full mesh: 710701551\n",
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"Density: 0.04%\n"
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]
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}
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],
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"source": [
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"# Nodi, Archi, Densità\n",
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"numNodes = G.number_of_nodes()\n",
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"numEdges = G.number_of_edges()\n",
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"allEdges = int(numNodes * (numNodes-1) / 2)\n",
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"density = nx.density(G) * 100\n",
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" \n",
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"# constants\n",
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"N = numNodes\n",
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"M = int(numEdges / numNodes)\n",
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"\n",
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"print(\"#Nodes:\", numNodes)\n",
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"print(\"#Edges:\", numEdges)\n",
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"print(\"#Edges if graph was a full mesh:\", allEdges)\n",
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"print(\"Density: %.2f%%\" % density)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Detecting and removing self-loops"
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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": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"#Self-loops: 0\n"
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]
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}
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],
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"source": [
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"ns = G.number_of_selfloops()\n",
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"print(\"#Self-loops:\", ns)\n",
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"\n",
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"if ns > 0:\n",
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" # removing self-loops\n",
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" G.remove_edges_from(G.selfloop_edges())\n",
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" print(\"#Edges without self-loops:\", G.number_of_edges())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Detecting and removing isolates"
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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": 4,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"#isolates: 0\n"
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]
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}
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],
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"source": [
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"ni = nx.number_of_isolates(G)\n",
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"print(\"#isolates:\", ni)\n",
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"\n",
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"if ni > 0:\n",
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" # remove isolates\n",
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" G.remove_nodes_from(nx.isolates(G))\n",
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" print(\"#Nodes without isolates\", G.number_of_nodes())\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Degree"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Average, variance and standard deviation"
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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": 5,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Average degree: 15.33\n",
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"Variance 6526.21\n",
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"Standard deviation 80.78\n"
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]
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}
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],
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"source": [
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"avgDeg = (2*G.number_of_edges())/(G.number_of_nodes())\n",
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"print(\"Average degree: %.2f\" % avgDeg)\n",
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"\n",
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"deg = [G.degree(n) for n in G.nodes]\n",
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"var = np.var(deg)\n",
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"devstd = math.sqrt(var)\n",
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"\n",
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"print(\"Variance {:.2f}\".format(var))\n",
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"print(\"Standard deviation {:.2f}\".format(devstd))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Linear scale distribution"
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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": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"findfont: Font family ['Arial'] not found. Falling back to DejaVu Sans.\n",
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"findfont: Font family ['Arial'] not found. Falling back to DejaVu Sans.\n"
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]
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},
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{
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"data": {
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"image/png": "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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"# Degree distribution\n",
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"degrees = sorted([d for n, d in G.degree()], reverse=True)\n",
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"degreeCount = coll.Counter(degrees)\n",
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"x, y = zip(*degreeCount.items())\n",
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"\n",
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"plt.figure() \n",
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"plt.plot(x, y, 'go-') \n",
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"plt.xlabel('Degree')\n",
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"plt.ylabel('Frequency')\n",
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"plt.title('Degree Distribution') \n",
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"plt.title('Degree Distribution with linear scale')\n",
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"plt.savefig('plots/LinScaleDegreeDistr.png')\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Logarithmic scale distribution"
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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": 7,
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"metadata": {},
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"outputs": [
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{
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"data": {
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|
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"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"plt.scatter(x, y, s=50, c=\"green\")\n",
|
||
|
|
"plt.xlim(0.9, max(x))\n",
|
||
|
|
"plt.ylim(0.9, max(y))\n",
|
||
|
|
"plt.xscale('log')\n",
|
||
|
|
"plt.yscale('log')\n",
|
||
|
|
"plt.xlabel(\"Degree\")\n",
|
||
|
|
"plt.ylabel(\"Frequency\")\n",
|
||
|
|
"plt.title('Degree Distribution with logarithmic scale') \n",
|
||
|
|
"plt.savefig('plots/LogScaleDegreeDistr.png')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Clustering coefficient"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 8,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Transitivity coefficient of the network: 1.24%\n",
|
||
|
|
"Average clustering coefficient 0.17\n"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# TODO eseguire\n",
|
||
|
|
"\n",
|
||
|
|
"if False:\n",
|
||
|
|
" trans= nx.transitivity(G)*100\n",
|
||
|
|
" # fraction of triadic closures (closed triangles) found in the network\n",
|
||
|
|
" print(\"Transitivity coefficient of the network: %.2f%%\" %trans)\n",
|
||
|
|
"\n",
|
||
|
|
" # Clustering coefficient\n",
|
||
|
|
" acc = nx.average_clustering(G)\n",
|
||
|
|
" print (\"Average clustering coefficient {:.2f}\".format(acc))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Greatest Connected Component "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": true
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"\n",
|
||
|
|
"numCC = nx.number_connected_components(G)\n",
|
||
|
|
"gcc = max(nx.connected_component_subgraphs(G), key=len)\n",
|
||
|
|
"\n",
|
||
|
|
"# TODO eseguire\n",
|
||
|
|
"\n",
|
||
|
|
"if False:\n",
|
||
|
|
" nodesGcc = Gcc.nodes()\n",
|
||
|
|
" edgesGcc = Gcc.edges()\n",
|
||
|
|
" nx.write_graphml(Gcc, \"graphs/GCC.graphml\");\n",
|
||
|
|
"\n",
|
||
|
|
" print(\"Numero di componenti connesse:\", numCC)\n",
|
||
|
|
" print(\"Numero nodi GCC:\", len(nodesGcc))\n",
|
||
|
|
" print(\"Numero archi GCC:\", len(edgesGcc))\n",
|
||
|
|
" print(\"Percentuale di nodi sul totale %.2f%%:\" %(len(nodesGcc)/len(G.nodes())*100))\n",
|
||
|
|
" print(\"Percentuale di archi sul totale %.2f%%:\" %(len(edgesGcc)/len(G.edges())*100))\n",
|
||
|
|
" print(\"Densità: {:.2f}\".format(nx.density(Gcc) * 100))\n",
|
||
|
|
" print(\"Distanza media: {:.2f}\".format(nx.average_shortest_path_length(Gcc)))\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Distanze GCC"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"ename": "KeyboardInterrupt",
|
||
|
|
"evalue": "",
|
||
|
|
"output_type": "error",
|
||
|
|
"traceback": [
|
||
|
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
|
||
|
|
"\u001b[0;32m<ipython-input-13-e177362aa0f9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mrow\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mgcc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnodes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mnodeDists\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msingle_source_shortest_path_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgcc\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0;31m#if i%1000 == 0:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;31m# print(i)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/shortest_paths/unweighted.py\u001b[0m in \u001b[0;36msingle_source_shortest_path_length\u001b[0;34m(G, source, cutoff)\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0mcutoff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 65\u001b[0m \u001b[0mnextlevel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0msource\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 66\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_single_shortest_path_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnextlevel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcutoff\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/shortest_paths/unweighted.py\u001b[0m in \u001b[0;36m_single_shortest_path_length\u001b[0;34m(adj, firstlevel, cutoff)\u001b[0m\n\u001b[1;32m 90\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mseen\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 91\u001b[0m \u001b[0mseen\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;31m# set the level of vertex v\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 92\u001b[0;31m \u001b[0mnextlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0madj\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# add neighbors of v\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 93\u001b[0m \u001b[0;32myield\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlevel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 94\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/classes/coreviews.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m 51\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_atlas\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 53\u001b[0;31m \u001b[0;32mdef\u001b[0m \u001b[0m__getitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 54\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_atlas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 55\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"# TODO eseguire\n",
|
||
|
|
"\n",
|
||
|
|
"distDict = {}\n",
|
||
|
|
"#i=1\n",
|
||
|
|
"row = []\n",
|
||
|
|
"for n in gcc.nodes():\n",
|
||
|
|
" nodeDists = nx.single_source_shortest_path_length(gcc,n)\n",
|
||
|
|
" #if i%1000 == 0:\n",
|
||
|
|
" # print(i)\n",
|
||
|
|
" \n",
|
||
|
|
" for d in nodeDists:\n",
|
||
|
|
" #if (int(d) in marked):\n",
|
||
|
|
" # continue\n",
|
||
|
|
" if nodeDists[d] in distDict:\n",
|
||
|
|
" distDict[nodeDists[d]] = distDict[nodeDists[d]] + 1\n",
|
||
|
|
" else:\n",
|
||
|
|
" distDict[nodeDists[d]] = 1\n",
|
||
|
|
" row.append(nodeDists[d])\n",
|
||
|
|
" #i += 1\n",
|
||
|
|
"\n",
|
||
|
|
"distDict.pop(0)\n",
|
||
|
|
"\n",
|
||
|
|
"avgDist, cnt = zip(*distDict.items()) \n",
|
||
|
|
"\n",
|
||
|
|
"plt.bar(avgDist, cnt, width=0.3, color='b')\n",
|
||
|
|
"plt.title(\"Distance Distribution for G\")\n",
|
||
|
|
"plt.ylabel(\"Frequency\")\n",
|
||
|
|
"plt.xlabel(\"Shortest Path Distance\")\n",
|
||
|
|
"#plt.savefig('plots/DistDistributionGlobal.png')\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### GCC Eccentricity - Diameter - Radius - Center - Periphery "
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"ename": "KeyboardInterrupt",
|
||
|
|
"evalue": "",
|
||
|
|
"output_type": "error",
|
||
|
|
"traceback": [
|
||
|
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
|
||
|
|
"\u001b[0;32m<ipython-input-15-edc2c6347a7b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m#Eccentricity\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mecc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meccentricity\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgcc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;31m# Adding eccentricity data to gcc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mecc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/distance_measures.py\u001b[0m in \u001b[0;36meccentricity\u001b[0;34m(G, v, sp)\u001b[0m\n\u001b[1;32m 224\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mG\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnbunch_iter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 225\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0msp\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 226\u001b[0;31m \u001b[0mlength\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnetworkx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msingle_source_shortest_path_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 227\u001b[0m \u001b[0mL\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlength\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 228\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/shortest_paths/unweighted.py\u001b[0m in \u001b[0;36msingle_source_shortest_path_length\u001b[0;34m(G, source, cutoff)\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[0mcutoff\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 65\u001b[0m \u001b[0mnextlevel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0msource\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 66\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_single_shortest_path_length\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnextlevel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcutoff\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/shortest_paths/unweighted.py\u001b[0m in \u001b[0;36m_single_shortest_path_length\u001b[0;34m(adj, firstlevel, cutoff)\u001b[0m\n\u001b[1;32m 90\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mseen\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 91\u001b[0m \u001b[0mseen\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;31m# set the level of vertex v\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 92\u001b[0;31m \u001b[0mnextlevel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0madj\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# add neighbors of v\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 93\u001b[0m \u001b[0;32myield\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlevel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 94\u001b[0m \u001b[0mlevel\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/classes/coreviews.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m 51\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0miter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_atlas\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 52\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 53\u001b[0;31m \u001b[0;32mdef\u001b[0m \u001b[0m__getitem__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 54\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_atlas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 55\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"#Eccentricity\n",
|
||
|
|
"ecc = nx.eccentricity(gcc)\n",
|
||
|
|
"\n",
|
||
|
|
"# Adding eccentricity data to gcc\n",
|
||
|
|
"for k in ecc.keys():\n",
|
||
|
|
" Gcc.node[k]['eccentricity'] = ecc.get(k)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"diameterGcc = nx.diameter(gcc, ecc)\n",
|
||
|
|
"radiusGcc = nx.radius(gcc, ecc)\n",
|
||
|
|
"centerGcc = nx.center(gcc, e=ecc)\n",
|
||
|
|
"peripheryGcc = nx.periphery(gcc, e=ecc)\n",
|
||
|
|
"\n",
|
||
|
|
"print (\"Diameter GCC:\", diameterGcc)\n",
|
||
|
|
"print (\"Radius GCC\", radiusGcc)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"#Adding data to gcc\n",
|
||
|
|
"nx.set_node_attributes(gcc, 0, 'center')\n",
|
||
|
|
"nx.set_node_attributes(gcc, 0, 'periphery')\n",
|
||
|
|
"\n",
|
||
|
|
"for v in range(len(centerGcc)):\n",
|
||
|
|
" gcc.node[centerGcc[v]][\"center\"] = 1\n",
|
||
|
|
"\n",
|
||
|
|
"for v in range(len(peripheryGcc)):\n",
|
||
|
|
" gcc.node[peripheryGcc[v]][\"periphery\"] = 1\n",
|
||
|
|
" \n",
|
||
|
|
"nx.write_graphml(gcc, \"graphs/GccEcc.graphml\");"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Distanze"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# Distanza media su tutta la rete\n",
|
||
|
|
"distDict = {}\n",
|
||
|
|
"#i=1\n",
|
||
|
|
"#marked = set()\n",
|
||
|
|
"row = []\n",
|
||
|
|
"for n in G.nodes():\n",
|
||
|
|
" nodeDists = nx.single_source_shortest_path_length(G,n)\n",
|
||
|
|
" #if i%1000 == 0:\n",
|
||
|
|
" # print(i)\n",
|
||
|
|
" \n",
|
||
|
|
" for d in nodeDists:\n",
|
||
|
|
" #if (int(d) in marked):\n",
|
||
|
|
" # continue\n",
|
||
|
|
" if nodeDists[d] in distDict:\n",
|
||
|
|
" distDict[nodeDists[d]] = distDict[nodeDists[d]] + 1\n",
|
||
|
|
" else:\n",
|
||
|
|
" distDict[nodeDists[d]] = 1\n",
|
||
|
|
" row.append(nodeDists[d])\n",
|
||
|
|
" #i += 1\n",
|
||
|
|
" #marked.add(int(n))\n",
|
||
|
|
"\n",
|
||
|
|
"avgShortPathG = np.average(row)\n",
|
||
|
|
"distDict.pop(0)\n",
|
||
|
|
"\n",
|
||
|
|
"avgDist, cnt = zip(*distDict.items()) \n",
|
||
|
|
"\n",
|
||
|
|
"print(\"Average Distance {:.2f}\".format(avgShortPathG))\n",
|
||
|
|
"\n",
|
||
|
|
"plt.bar(avgDist, cnt, width=0.3, color='b')\n",
|
||
|
|
"plt.title(\"Distance Distribution for G\")\n",
|
||
|
|
"plt.ylabel(\"Frequency\")\n",
|
||
|
|
"plt.xlabel(\"Shortest Path Distance\")\n",
|
||
|
|
"plt.savefig('plots/DistDistributionGlobal.png')\n",
|
||
|
|
"plt.show()\n",
|
||
|
|
"\n",
|
||
|
|
"\n",
|
||
|
|
"#print(\"Numero componenti connesse:\", nx.number_connected_components(G))\n",
|
||
|
|
"#print(\"Distanza media:\", nx.average_shortest_path_length(G))"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Degree correlation"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"# The following code fragment calculates the dictionary and separates the keys and values into \n",
|
||
|
|
"# two lists my_degree and their_degree:\n",
|
||
|
|
"\n",
|
||
|
|
"my_degree, their_degree = zip(*nx.average_degree_connectivity(G).items())\n",
|
||
|
|
"\n",
|
||
|
|
"plt.scatter(my_degree, their_degree, s=50, c=\"b\",)\n",
|
||
|
|
"plt.xscale('log')\n",
|
||
|
|
"plt.yscale('log')\n",
|
||
|
|
"plt.xlabel(\"k\")\n",
|
||
|
|
"plt.ylabel(\"$k_{nn}(k)$\")\n",
|
||
|
|
"plt.savefig('plots/Assortativity.png')"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Communities"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### 4-Clique Communities"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 5,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stdout",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"Clique computed\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"ename": "KeyboardInterrupt",
|
||
|
|
"evalue": "",
|
||
|
|
"output_type": "error",
|
||
|
|
"traceback": [
|
||
|
|
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
|
||
|
|
"\u001b[0;32m<ipython-input-5-42a7882a13fe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Clique computed\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mlClique\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mcl\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcommK\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mlClique\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcl\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;32m~/.local/lib64/python3.6/site-packages/networkx/algorithms/community/kclique.py\u001b[0m in \u001b[0;36mk_clique_communities\u001b[0;34m(G, k, cliques)\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0mperc_graph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_nodes_from\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcliques\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mclique\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mcliques\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m \u001b[0;32mfor\u001b[0m \u001b[0madj_clique\u001b[0m \u001b[0;32min\u001b[0m \u001b[0m_get_adjacent_cliques\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclique\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmembership_dict\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 70\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclique\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintersection\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0madj_clique\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mk\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 71\u001b[0m \u001b[0mperc_graph\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_edge\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mclique\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0madj_clique\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||
|
|
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"commK = com.k_clique_communities(G, 4)\n",
|
||
|
|
"\n",
|
||
|
|
"print(\"Clique computed\")\n",
|
||
|
|
"lClique = 0\n",
|
||
|
|
"for i,cl in enumerate(commK):\n",
|
||
|
|
" lClique += 1\n",
|
||
|
|
" for n in cl:\n",
|
||
|
|
" G.node[n][\"kClique\"] = i+1\n",
|
||
|
|
" \n",
|
||
|
|
"print(\"Numero 4-Clique communities: \", lClique)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"### Modularity based communities (Louvain)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"part = lou.best_partition(G)\n",
|
||
|
|
"mod = lou.modularity(part,G)\n",
|
||
|
|
"\n",
|
||
|
|
"part_as_seriesG = pd.Series(part)\n",
|
||
|
|
"part_as_seriesG.sort_values()\n",
|
||
|
|
"part_as_seriesG.value_counts() \n",
|
||
|
|
"\n",
|
||
|
|
"print(\"Numero Louvain communities: \", part_as_seriesG.value_counts().size)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"#Saving Communities Attribute\n",
|
||
|
|
"nx.set_node_attributes(G, 0, 'LvnG')\n",
|
||
|
|
"for k in part.keys():\n",
|
||
|
|
" part[k]+= 1\n",
|
||
|
|
"\n",
|
||
|
|
"for i in part.keys():\n",
|
||
|
|
" G.node[i][\"LvnG\"] = part.get(i)\n",
|
||
|
|
"\n",
|
||
|
|
"nx.write_graphml(G, \"graphs/GComm.graphml\");"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Centralities"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"dgr = nx.degree_centrality(G)\n",
|
||
|
|
"clo = nx.closeness_centrality(G)\n",
|
||
|
|
"har = nx.harmonic_centrality(G)\n",
|
||
|
|
"eig = nx.eigenvector_centrality(G)\n",
|
||
|
|
"bet = nx.betweenness_centrality(G)\n",
|
||
|
|
"pgr = nx.pagerank(G)\n",
|
||
|
|
"hits = nx.hits(G)\n",
|
||
|
|
"\n",
|
||
|
|
"centralities = pd.concat(\n",
|
||
|
|
" [pd.Series(c) for c in (hits[1], eig, pgr, har, clo, hits[0], dgr, bet)],\n",
|
||
|
|
" axis=1)\n",
|
||
|
|
"\n",
|
||
|
|
"centralities.columns = (\"Authorities\", \"Eigenvector\", \"PageRank\",\n",
|
||
|
|
" \"Harmonic Closeness\", \"Closeness\", \"Hubs\",\n",
|
||
|
|
" \"Degree\", \"Betweenness\")\n",
|
||
|
|
"centralities[\"Harmonic Closeness\"] /= centralities.shape[0]\n",
|
||
|
|
"\n",
|
||
|
|
"# Calculate the correlations for each pair of centralities\n",
|
||
|
|
"c_df = centralities.corr()\n",
|
||
|
|
"ll_triangle = np.tri(c_df.shape[0], k=-1)\n",
|
||
|
|
"c_df *= ll_triangle\n",
|
||
|
|
"c_series = c_df.stack().sort_values()\n",
|
||
|
|
"c_series.tail()"
|
||
|
|
]
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.6.9"
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 2
|
||
|
|
}
|