commit 90de410ec88f020f0ebd4a029ae7facb3ec9b315 parent ac097e05b5e016919ed85af4224cae5ea5328619 Author: miksa234 <milutin@popovic.xyz> Date: Sat, 11 Dec 2021 13:30:14 +0100 L07 done Diffstat:
| A | assingments/barabasi-2012.pdf | | | 0 | |
| A | assingments/exercise_5.pdf | | | 0 | |
| A | assingments/exercise_6.pdf | | | 0 | |
| A | assingments/exercise_7.pdf | | | 0 | |
| A | sesh5/src/.ipynb_checkpoints/main-checkpoint.ipynb | | | 6 | ++++++ |
| A | sesh5/src/main.ipynb | | | 220 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh5/tex/main.pdf | | | 0 | |
| A | sesh5/tex/main.tex | | | 149 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh5/tex/uni.bib | | | 16 | ++++++++++++++++ |
| A | sesh6/src/.ipynb_checkpoints/main-checkpoint.ipynb | | | 228 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh6/src/main.ipynb | | | 243 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh6/tex/main.pdf | | | 0 | |
| A | sesh6/tex/main.tex | | | 134 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh6/tex/uni.bib | | | 16 | ++++++++++++++++ |
| A | sesh7/src/.ipynb_checkpoints/main-checkpoint.ipynb | | | 294 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh7/src/.ipynb_checkpoints/main_paper-checkpoint.ipynb | | | 6 | ++++++ |
| A | sesh7/src/ex_71.png | | | 0 | |
| A | sesh7/src/main.ipynb | | | 294 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh7/src/main_paper.ipynb | | | 270 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh7/tex/ex_71.png | | | 0 | |
| A | sesh7/tex/main.pdf | | | 0 | |
| A | sesh7/tex/main.tex | | | 175 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | sesh7/tex/uni.bib | | | 16 | ++++++++++++++++ |
23 files changed, 2067 insertions(+), 0 deletions(-)
diff --git a/assingments/barabasi-2012.pdf b/assingments/barabasi-2012.pdf Binary files differ. diff --git a/assingments/exercise_5.pdf b/assingments/exercise_5.pdf Binary files differ. diff --git a/assingments/exercise_6.pdf b/assingments/exercise_6.pdf Binary files differ. diff --git a/assingments/exercise_7.pdf b/assingments/exercise_7.pdf Binary files differ. diff --git a/sesh5/src/.ipynb_checkpoints/main-checkpoint.ipynb b/sesh5/src/.ipynb_checkpoints/main-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh5/src/main.ipynb b/sesh5/src/main.ipynb @@ -0,0 +1,220 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 125, + "id": "177caec0", + "metadata": {}, + "outputs": [], + "source": [ + "import networkx as nx\n", + "import numpy as np\n", + "import itertools as it\n", + "import random\n", + "from matplotlib import pyplot as plt\n", + "from scipy.optimize import curve_fit\n", + "path = './../../../network_course/data/'" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "id": "6e681c9b", + "metadata": {}, + "outputs": [], + "source": [ + "G_protein = nx.read_edgelist(path + 'protein.edgelist.txt')\n", + "G_collab = nx.read_edgelist(path + 'collaboration.edgelist.txt')\n", + "G_powergrid = nx.read_edgelist(path + 'powergrid.edgelist.txt')" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "id": "3c808615", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_131746/874358227.py:4: RuntimeWarning: divide by zero encountered in power\n", + " return c*x**(gamma)\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 1080x360 with 3 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def exponential(x, gamma, c):\n", + " return c*np.exp(gamma)\n", + "def power_law(x, gamma, c):\n", + " return c*x**(gamma)\n", + " \n", + "Graphs = {'Protein': G_protein, 'Collaboration': G_collab, 'Powergrid': G_powergrid}\n", + "fig, ax = plt.subplots(1, 3,figsize=(15, 5))\n", + "\n", + "c = 0 \n", + "for name, G in Graphs.items():\n", + " freq = nx.degree_histogram(G)\n", + " degrees = range(len(freq))\n", + " if c == 2:\n", + " popt, pcov = curve_fit(exponential, degrees, freq)\n", + " ax[c].loglog(degrees, freq, 'go-', label=fr'$k/m = {round(popt[1], 2)}$') \n", + " else:\n", + " popt, pcov = curve_fit(power_law, degrees, freq)\n", + " ax[c].loglog(degrees, freq, 'go-', label=fr'$\\gamma = {round(popt[1], 2)}$') \n", + " \n", + " ax[c].set_title(name+'-Network', fontsize=15)\n", + " ax[c].legend(loc='best')\n", + " c += 1\n", + "\n", + "ax[0].annotate(\"power-law\", [20, 400], fontsize=13)\n", + "ax[1].annotate(\"power-law\", [50, 900], fontsize=13)\n", + "ax[2].annotate(\"exponential\", [7, 500], fontsize=13)\n", + "plt.suptitle('Cummulative Degree Distribution', fontsize=20)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 332, + "id": "b9e7a974", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "FRIENDSHIP PARADOX - Protein\n", + "In 74 out of 100 cases the average next neareset neighbor degree is bigger than the actual degree of the node\n", + "\n", + "FRIENDSHIP PARADOX - Collaboration\n", + "In 82 out of 100 cases the average next neareset neighbor degree is bigger than the actual degree of the node\n", + "\n", + "FRIENDSHIP PARADOX - Powergrid\n", + "In 67 out of 100 cases the average next neareset neighbor degree is bigger than the actual degree of the node\n", + "\n" + ] + } + ], + "source": [ + "def avg_nnd(G):\n", + " nn = {}\n", + " for n in G.nodes():\n", + " nnd = list(dict(G.degree(list(G.neighbors(n)))).items())\n", + " nnavgd = 1/len(nnd) * sum(d[1] for d in nnd)\n", + " nn[n] = nnavgd\n", + " return dict(sorted(list(nn.items()), key= lambda x: int(x[0])))\n", + "\n", + "# Friendship Paradox\n", + "for name, G in Graphs.items():\n", + " avgnn = list(avg_nnd(G).items())\n", + " avgd = sorted(list(dict(nx.degree(G)).items()), key = lambda x: int(x[0]))\n", + " paradox = []\n", + " for nnd, myd in zip(avgnn, avgd):\n", + " if nnd[1] > myd[1]:\n", + " paradox.append(True)\n", + " else:\n", + " paradox.append(False)\n", + " print(f\"FRIENDSHIP PARADOX - {name}\") \n", + " print(f\"In {int(np.average(paradox)*100)} out of 100 cases the average next neareset neighbor degree is bigger than the actual degree of the node\\n\")\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 356, + "id": "697396df", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Powergrid\n", + "k_nn numerical: k_nn = 10.74812990953724\n", + "k_nn analytical: k_nn = 11.111262798634812\n", + "\n", + "Powergrid\n", + "k_nn numerical: k_nn = 17.31863657392649\n", + "k_nn analytical: k_nn = 11.111262798634812\n", + "\n", + "Powergrid\n", + "k_nn numerical: k_nn = 3.966044118638146\n", + "k_nn analytical: k_nn = 11.111262798634812\n", + "\n" + ] + } + ], + "source": [ + "for n, G in Graphs.items():\n", + " nnd = list(nx.average_neighbor_degree(G).items())\n", + " f_nnavg = 1/len(nnd) * sum(s[1] for s in nnd)\n", + "\n", + " model_k2 = sum(s[1]**2 for s in list(G.degree()))\n", + " model_k1 = sum(s[1] for s in list(G.degree()))\n", + " model_knn = k2/k1\n", + "\n", + " print(f\"{name}\")\n", + " print(f\"k_nn numerical: k_nn = {f_nnavg}\")\n", + " print(f\"k_nn analytical: k_nn = {model_knn}\\n\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "874f5ac1", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "025b45ce", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2213f26d", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh5/tex/main.pdf b/sesh5/tex/main.pdf Binary files differ. diff --git a/sesh5/tex/main.tex b/sesh5/tex/main.tex @@ -0,0 +1,149 @@ +\documentclass[a4paper]{article} + + +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{mathptmx} + +%\usepackage{ngerman} % Sprachanpassung Deutsch + +\usepackage{graphicx} +\usepackage{geometry} +\geometry{a4paper, top=15mm} + +\usepackage{subcaption} +\usepackage[shortlabels]{enumitem} +\usepackage{amssymb} +\usepackage{amsthm} +\usepackage{mathtools} +\usepackage{braket} +\usepackage{bbm} +\usepackage{graphicx} +\usepackage{float} +\usepackage{yhmath} +\usepackage{tikz} +\usetikzlibrary{patterns,decorations.pathmorphing,positioning} +\usetikzlibrary{calc,decorations.markings} + +\usepackage[backend=biber, sorting=none]{biblatex} \addbibresource{uni.bib} + +\usepackage[framemethod=TikZ]{mdframed} + +\tikzstyle{titlered} = + [draw=black, thick, fill=white,% + text=black, rectangle, + right, minimum height=.7cm] + + +\usepackage[colorlinks=true,naturalnames=true,plainpages=false,pdfpagelabels=true]{hyperref} +\usepackage[parfill]{parskip} +\usepackage{lipsum} + + +\usepackage{tcolorbox} +\tcbuselibrary{skins,breakable} + +\pagestyle{myheadings} + +\markright{Popović\hfill 1st Exercise \hfill} + + +\title{University of Vienna\\ Faculty of Mathematics\\ + \vspace{1.25cm}Seminar: Introduction to complex network analysis \\ 5th +Exercise +} +\author{Milutin Popović} +\begin{document} +\maketitle + +Looking at a social graph with $N$ nodes, the expected degree of a random +node is $\langle k\rangle$. Each of $\langle k \rangle$ edges points to a +different node. The probability that a random edge is connected to a node +$i$ with degree $k_i$ is +\begin{align}\label{eq: annd} + p(k_i) = \frac{k_i}{\sum_{j}^N k_j} \;\;\;\; +\end{align} +for all $i = 1,\dots,N$. Thus the average degree is calculated by the +weighted average +\begin{align} + \langle k_{nn} \rangle = \sum_i^N k_i p(k_i) = \frac{\sum_i^N + k_i^2}{\sum_j^N k_j} = \frac{\langle k^2\rangle}{\langle k\rangle}. +\end{align} +For scale-free networks we have a power law distribution, meaning +\begin{align} + p(k) = c\cdot k^{-\gamma} +\end{align} +Thereby we can calculate the $n-th$ moment of the degree distribution +\begin{align} + \langle k^n \rangle = \int_{k_{\text{min}}}^{k_{\text{max}}} k^n p(k) dk + = c \frac{k_{\text{max}}^{n-\gamma+1} - + k_{\text{min}}^{n-\gamma+1}}{n-\gamma +1} +\end{align} +We can substitute the $1$-st and $2$-th moment of the degree distribution in +to the equation \ref{eq: annd}, giving us +\begin{align} + \langle k_{nn} \rangle \frac{}{} = \frac{\gamma-2}{\gamma-3}\; \cdot \; + \frac{k_{\text{max}}^{3-\gamma} - + k_{\text{min}}^{3-\gamma}}{k_{\text{max}}^{2-\gamma} - +k_{\text{min}}^{2-\gamma}} +\end{align} +In the cases of $\gamma \rightarrow 2$ and $\gamma \rightarrow 3$ we have the +friendship paradox. Let us compute both cases +\begin{align}\label{eq: scalefree} + \lim_{\gamma \rightarrow 2} = \frac{\gamma-2}{\gamma-3}\; \cdot \; + \frac{k_{\text{max}}^{3-\gamma} - + k_{\text{min}}^{3-\gamma}}{k_{\text{max}}^{2-\gamma} - +k_{\text{min}}^{2-\gamma}}, +\end{align} +we will need to use the L'Hopital rule once since we have the case +$\frac{0}{0}$. By applying differentiation in both the numerator and the +denominator we get +\begin{align} + \lim_{\gamma \rightarrow 2}& \frac{ + \frac{d}{d\gamma}}{\frac{d}{d\gamma}}\frac{(\gamma-2)}{(\gamma-3)} + \frac{(k_{\text{max}}^{3-\gamma} - + k_{\text{min}}^{3-\gamma})}{(k_{\text{max}}^{2-\gamma} - +k_{\text{min}}^{2-\gamma})}=\nonumber \\ + &= \frac{k_{\text{max}} - k_{\text{min}}}{\ln(k_{\text{max}}) - + \ln(k_{\text{min}})}. +\end{align} +Similarly for the $\gamma \rightarrow 3$ case we need to apply the rule of +l'Hopital, giving us +\begin{align} + \lim_{\gamma \rightarrow 3}& \frac{ + \frac{d}{d\gamma}}{\frac{d}{d\gamma}}\frac{(\gamma-2)}{(\gamma-3)} + \frac{(k_{\text{max}}^{3-\gamma} - + k_{\text{min}}^{3-\gamma})}{(k_{\text{max}}^{2-\gamma} - +k_{\text{min}}^{2-\gamma})}=\nonumber\\ + &= \frac{k_{\text{max}}k_{\text{min}}\left(\ln(k_{\text{max}}) - + \ln(k_{\text{min}})\right)}{k_{\text{max}} - k_{\text{min}}}. +\end{align} +We can compare this to a random network which follows a Poisson distribution, +where the 1st and 2nd moments are +\begin{align} + \langle k^2 \rangle = k^2 \\ + \langle k \rangle = k, +\end{align} +giving us +\begin{align} + \langle k_{nn}\rangle = \frac{k^2}{k} = k. +\end{align} + +We will now take \ref{eq: scalefree} and substitute $k_{\text{max}}$ with the +natural cutoff (largest expected hub) to get an approximate expression +depending on the number of nodes $N$. Explicitly we substitute +\begin{align} + k_{\text{max}} = k_{\text{min}} N^{\frac{1}{\gamma -1}}. +\end{align} +This will give us +\begin{align} + \langle k_{nn} \rangle = k_{\text{min}}\frac{2- \gamma}{3-\gamma} + \frac{N^{\frac{3-\gamma}{\gamma-1}} - 1}{N^{\frac{2-\gamma}{\gamma-1}} - + 1} \;\;\;\; \underset{N\rightarrow \infty}{{\longrightarrow}} \;\; \infty +\end{align} + +\nocite{code} +\nocite{barabasi2016network} +\printbibliography + +\end{document} diff --git a/sesh5/tex/uni.bib b/sesh5/tex/uni.bib @@ -0,0 +1,16 @@ +@online{code, + author = {Popovic Milutin}, + title = {Git Instance, Introduction to complex network analysis}, + urldate = {2021-10-10}, + url = {git://popovic.xyz/network_ana.git}, +} + +@book{barabasi2016network, + title={Network Science}, + author={Barab{\'a}si, A.L. and P{\~A}3sfai, M.{\~A}.}, + isbn={9781107076266}, + lccn={2016439537}, + url={https://books.google.at/books?id=iLtGDQAAQBAJ}, + year={2016}, + publisher={Cambridge University Press} +} diff --git a/sesh6/src/.ipynb_checkpoints/main-checkpoint.ipynb b/sesh6/src/.ipynb_checkpoints/main-checkpoint.ipynb @@ -0,0 +1,228 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 14, + "id": "608ff8af", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "import random" + ] + }, + { + "cell_type": "code", + "execution_count": 154, + "id": "058ac30e", + "metadata": {}, + "outputs": [], + "source": [ + "class Attack:\n", + " def __init__(self, G, steps=25):\n", + " self.G = G\n", + " self.steps = steps\n", + " self.N = G.number_of_nodes()\n", + " self.M = N // steps\n", + " self.num_nodes_removed = range(0, N, M)\n", + "\n", + " def betweenness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " betweenness = nx.centrality.betweenness_centrality(C)\n", + " nodes_sorted_by_betweenness= sorted(C.nodes, key=betweenness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_betweenness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def degree(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_sorted_by_degree = sorted(C.nodes, key=C.degree, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_degree[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def closeness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " closeness = nx.centrality.closeness_centrality(C)\n", + " nodes_sorted_by_closeness = sorted(C.nodes, key=closeness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_closeness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return num_nodes_removed, random_attack_core_proportions " + ] + }, + { + "cell_type": "code", + "execution_count": 155, + "id": "a08557c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 143 nodes and 623 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7f437ab70370>" + ] + }, + "execution_count": 155, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "path = './../../../network_course/data/'\n", + "G = nx.read_edgelist(path + 'ia-enron-only/ia-enron-only.edges', nodetype=int)\n", + "print(nx.info(G))\n", + "\n", + "attack = Attack(G)\n", + "\n", + "x_d, y_d = attack.degree()\n", + "x_b, y_b = attack.betweenness()\n", + "x_c, y_c = attack.closeness()\n", + "\n", + "plt.title('Degree-Betweenness-Closeness Attack')\n", + "plt.xlabel('Number of nodes removed')\n", + "plt.ylabel('Proportion of nodes in core')\n", + "plt.plot(x_d, y_d, marker='o', label='Degree-Attack')\n", + "plt.plot(x_b, y_b, marker='^', label='Betweenness-Atack')\n", + "plt.plot(x_c, y_c, marker='.', label='Closeness-Atack')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 156, + "id": "76f1387a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 4941 nodes and 6594 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7f4377b09460>" + ] + }, + "execution_count": 156, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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Bq5Z8xYoVuXE1bty4SPutJDyWCERkOtZ8onVEJAn4KxAIYIx5G2vS7KHATuACcJenYhnRMcLp6euTQ1tza9conp+TyL/mbmX6qgMMaF2P/X7PckXqBnZWjWNo4FBGdLPXzcqAQ79bSWHfCtg081KV0vLXoN/j0PthCKrqqbeilNfkTwKFLS8NCxYsYOPGjbm/9k+fPs2OHTv45ZdfuOmmm/Dz86NBgwa51TU5brnlFgBWrlxJQkICvXtbc9inp6fTs2dPtm3bxubNmxk4cCBgVSE1bNjw8veWns7cuXOZMmUK1atXp3v37syfP9+t+vwlS5bw73//mwsXLnDy5EliY2Pp378/ycnJjBw5ErA6f+VITEzk3nvvZcGCBWVeveTJq4ZGF/K8wZqM3aua163G+2O7snTbUR6f+TvvLdsDNGEBTeAMLPt6E2CfWfgHQmQX69b7Efj5ZVjyPJhs6/bTi/Drf6HNcGh/CzTtC346iofyDYX9cu/94mKSU1IvWx4RHsqM+3qWWhy7d+/G39+fevXqYYzhjTfeID4+Pk+ZuXPnFriNqlWtH2PGGAYOHJhbpZNj06ZNxMbG8uuvv+ZZfuDAAa6//noAxo8fT0REBCkpKbRr1w6ACxcuEBoaWmgiSEtL44EHHmDNmjVERUXxt7/9rdBr+xs2bEhaWhrr168v80SgRylb/5h6BPhfvjtSM7KYPH+b85Wa9QP/YBB/CAiFoa9A7EhImA0fD7OuSlr0dzjmYn2lfMiE+BhCA/M2vIYG+jMhPqbUXuPYsWOMHz+eBx98EBEhPj6et956i4yMDAC2b9/O+fPn6d27N1999RXZ2dkcOXKEpUuXOt1ejx49WL58OTt37gTg/PnzbN++nZiYGI4dO5abCDIyMtiyZQtRUVFs2LCBDRs2MH78eKZPn857773H3r172bt3L3v27GHhwoVcuHCB6tWrc/bs2dzXcnycc9CvU6cO586dyz2jqV69OpGRkcyaNQuAixcvcuHCBQDCw8OZM2cOkyZNcvl+PMUnrhoqK4dSnGfsg05+BQFWm8Cds2HvMuvXf04bwdDJsG0u/P45LP8P/DIFGnWExr0gqAq0HKTtCcrnXGpvK92rhlJTU4mLiyMjI4OAgABuv/12Hn30UQD++Mc/snfvXjp16oQxhrp16zJr1ixuuOEGfvzxR9q0aUNUVBSdOnUiLCzssm3XrVuXadOmMXr0aC5evAjAc889R3R0NDNnzuThhx/m9OnTZGZm8uc//5nY2EtnRRcuXGDevHm8/fbbucuqVq1Knz59+O6777j11lsZN24cr7/+OjNnzmTs2LGMHz+e0NBQfv31V8aNG0fbtm1p0KABXbt2zd3GJ598wn333cezzz5LYGAgX375Ze5z9evX5/vvv2fIkCF88MEHdO/evUT71l0+N2dxly5djKcmpnF16gvw8ICWPHjVFQQFFPEk6txRqy1h9Xtw0r4KwD8Yxn6vyUB5XWJiIq1bt/Z2GMVy7tw5qlWrxokTJ+jWrRvLly+nQYMG3g6rXHD2fxWRtcaYLs7Ka9WQA2enviGBfnRpEs7rP+5g2H9/YVPS6aJttFo96PkAdBwDYu/urIuw9EUoZ51mlPIl1113HXFxcfTt25dnnnlGk0AJaNWQg4JOfX9MPMKT32xixP+Wc1+/5jxyTUuCA4rQUaVpX+tMICsdMLDrR5h+K4x8G6rU8swbUqoCK+t69IpMq4aK4HRqBs99n8CXa5O4ol41rmvfkC/XJLlfX3pgldWe0KQPHN4I85+EqvXgpg+1mkh5hS9XDSnXtGrIg8JCA5l8Uwem3dWVY2fTeG3RjqL1sozqBn0fg8bdods4uGcB+PnDh0NgxRvgY0lZKVUxaCIohv4x9agSdHmtWoGXmjrTqCPc9zNED4YFT8Pnt1m9mJVSqgxpIiimw6eLeKmpK6HhcMunMPhF2LEQ3u4HSWtLHqBSSrlJE0ExNQoPdbq8SrA/6ZlFvBpIBHrcD3fPtx5/EA8/TISfdShsVTkcPnyYW2+9lRYtWtC5c2eGDh3K9u3badu2rbdDK5G4uDhuvfXWPMtee+213E5kRTVt2jQefPDB0ggtD00ExeTsUlN/P+H8xSxumfpr0c8MACI7w30/QURn+O0tWPxP+GiYJgNVoRljGDlyJP3792fXrl2sXbuWF154gSNHjng7tBJJTEwkKyuLZcuWcf78pWHuS5IIPEUTQTGN6BjBC6PaEREeimCNt/LKTR1487ZObD98luve+IVlO4o2iQ5gXUracpD9wFiXm+5dVpqhK1UyB1aV6sRNS5YsITAwkPHjx+cu69ChA1FRl0apT0tL46677qJdu3Z07NiRJUuWALBlyxa6detGXFwc7du3Z8eOHQB8+umnucvvu+8+srKyAKhWrRpPPfUUHTp0oEePHrnJ5tixY9xwww107dqVrl27snz5cgB++ukn4uLiiIuLo2PHjpw9e5ZDhw7Rr18/4uLiaNu2LcuWOf9+Tp8+ndtvv51Bgwbx7bffAvD6669z8OBBrrrqqtyB8u6//366dOlCbGwsf/3rX3PXX716Nb169aJDhw5069Ytz3AWAHPmzKFnz54cP368+Dvfpv0ISsDVqKatGlbn/k/XcscHq/jzgGgeuvoK/PyKMI9os75W5zOTDf5BVh8EpTzth4lweFPBZS6egSObrc+m+EH9thBcw3X5Bu1gyIsFbnLz5s107ty5wDJvvvkmIsKmTZvYunUrgwYNYvv27bz99ts88sgjjBkzhvT0dLKyskhMTGTGjBksX76cwMBAHnjgAT777DPuuOMOzp8/T48ePXj++ed5/PHHeffdd3n66ad55JFH+L//+z/69OnD/v37iY+PJzExkZdffpk333yT3r17c+7cOUJCQpg6dSrx8fE89dRTZGVlufx1P2PGDBYuXMjWrVt54403uO2223j44YeZMmUKS5YsoU6dOgA8//zz1KpVi6ysLAYMGMDGjRtp1aoVt9xyCzNmzKBr166cOXOG0NBL1dHffPMNU6ZMYe7cudSsWfJJszQReECLutWY9afePP3NZl5dtJ21+08xqE193lq6y70+B1HdrIP/4U1w2wztY6DKj7TTVhIA62/a6YITQSn55ZdfeOihhwBo1aoVTZo0Yfv27fTs2ZPnn3+epKQkRo0aRcuWLfnxxx9Zu3Zt7vg+qamp1KtXD4CgoKDckUM7d+7MwoULAVi0aFGeaSfPnDnDuXPn6N27N48++ihjxoxh1KhRREZG0rVrV+6++24yMjIYMWIEcXFxl8W7Zs0a6tSpQ+PGjYmIiODuu+/m5MmT1Kp1eefRL774gqlTp5KZmcmhQ4dISEhARGjYsGHue6hR49I+Xrx4MWvWrGHBggV5lpeEJgIPqRIUwCs3d6Bz05o8O2szy7YfI6eXQE6fA8B1MmjYAfavhMiuzp9XqrQV8ssdsKqDPhpmT9wUBDe8V+IfKrGxsbmjcxbVbbfdRvfu3ZkzZw5Dhw7lnXfewRjDnXfeyQsvvHBZ+cDAQESss3N/f38yMzMBa8azlStX5pkfAGDixIlce+21zJ07l969ezN//nz69evHzz//zJw5cxg7diyPPvoo1atXz51a87333mP69Ols3bqVpk2bAlZi+eqrrxg3blye7e/Zs4eXX36Z1atXU7NmTcaOHVvocNUtWrRg9+7dbN++PXcSnJLSNgIPEhHGdG9CrWrB5O8qVmifg7BIa0yi8yWv/1Oq1OSMuHv1U9bfUjhbvfrqq7l48SJTp07NXbZx48bcWbsA+vbty2effQZYQ1Hv37+fmJgYdu/eTfPmzXn44YcZPnw4GzduZMCAAcycOZOjR60pZU+ePMm+ffsKjGHQoEG88cYbuY9z5lDetWsX7dq144knnqBr165s3bqVffv2Ub9+fcaNG8cf//hH1q1bx8iRI3OHr+7UqRNffPEFmzZtyh2++ttvv82dE8FxuOozZ85QtWpVwsLCOHLkCD/88AMAMTExHDp0iNWrVwNw9uzZ3KTVpEkTvvrqK+644w62bNlS7P3uSBNBGTh+9qLT5QVeWRQWaf09fcB1GaW8IaeHfClVWYoI33zzDYsWLaJFixbExsYyadKkPIPIPfDAA2RnZ9OuXTtuueUWpk2bRnBwMF988QVt27YlLi6OzZs3c8cdd9CmTRuee+45Bg0aRPv27Rk4cKDL+YhzvP7666xZs4b27dvTpk2b3KGnX3vtNdq2bUv79u0JDAxkyJAhLF26lA4dOtCxY0dmzJjBI488kmdby5YtIyIiIs/kMv369SMhIYFDhw5x7733MnjwYK666qrc7bRq1Yrbbrstdya1oKAgZsyYwUMPPUSHDh0YOHBgnjOFVq1a8dlnn3HTTTeVytzGOtZQGXA1vHVwgB+z/tSb1g2d1PMd+h3e6Qc3fwJthpVBlKoy0rGGKiYda6gcctbnINBf8BO49vVlTPp6E8fP5TtrCLMvnTudVEZRKqUqK00EZcBZn4PJN3Zg5aRruLNXU75cc4CrJi9l6s+7uJiZxaz1yfT+z3oumGA+X7Si4IHslFKqhPSqoTLiqs/BX6+PZUz3JvxrbiL/mruVd37axdm0TNKzDAeDalMj/QiPFXaFkVIlYIzJvZJG+b7iVPfrGUE5cEW9anwwtisf3d2N06lWEgA4aGrTSI4XfVRTpdwUEhLCiRMninXwUOWPMYYTJ05cdhlsYfSMoBy5MrouWdmXvpDJpg6t/fYDxRjVVCk3REZGkpSUxLFjxRgORZVLISEhREZGFmkdTQTlTKPw0NwrjA6a2tSV0wSRQd1wz/feVJVPYGAgzZo183YYysu0aqiccbzC6KCxxiJpGniKCfEx3gxLKVWB6RlBOZPTIDx5/jYOnqkNwN1tA7WhWCnlMZoIyqGcK4wuHomCt57naNIuvbJDKeUxWjVUjgXXsjqVZZzcz9Lt2pinlPKMQhOBiFQRkWdE5F37cUsRuc7zoSkCQzBV69EyJIVXF27XS/yUUh7hzhnBh8BFoKf9OBl4zmMRqTwkLJJuNS+wMek0CxN8e+o+pVT55E4iaGGM+TeQAWCMuQBoZXVZCYukvjlO09pVeHXRDrKz9axAKVW63EkE6SISCtaQ+iLSAusMoVAiMlhEtonIThGZ6OT5xiKyRETWi8hGERlapOgrg7Ao5EwSjwy4gsRDZ5i35bC3I1JKVTDuJIK/AvOAKBH5DPgReLywlUTEH3gTGAK0AUaLSJt8xZ4GvjDGdARuBf5XhNgrh7BIyLjAsOgqXFGvGq8u3J6n97FSSpVUgYlARPyAmsAoYCwwHehijFnqxra7ATuNMbuNMenA58DwfGUMkNNlNgw46HbklYU9QY3/2ST+fE1Ldhw9x/cbdTcppUpPgYnAGJMNPG6MOWGMmWOM+d4Y4+7ciRGA4/RaSfYyR38D/iAiScBc4CFnGxKRe0VkjYisqXRjouTOVJbE0LYNadWgOq8t2kFmVrZ341JKVRjuVA0tEpG/iEiUiNTKuZXS648GphljIoGhwCf2WUgexpipxpguxpgudevWLaWX9hG5E9Qk4+cn/N/AaPYcP883OkeBUqqUuNOz+Bb7758clhmgeSHrJQNRDo8j7WWO7gEGAxhjfhWREKAOcNSNuCqHqnXAPzh37uJBberTLiKM1xfvYETHCAL9tU+gUqpkCj2KGGOaObkVlgQAVgMtRaSZiARhNQbPzldmPzAAQERaAyFAJav7KYQIhEXkTlkpIjw6MJoDJ1OZuVansVRKlZw7PYsDReRhEZlp3x4UkcDC1jPGZAIPAvOBRKyrg7aIyD9EJGc29seAcSLyO1ZD9Fij3WcvFxaZZ+7i/jF1iYsK540fd3AxM8uLgSmlKgJ36hXeAjpjXdr5P/v+W+5s3Bgz1xgTbYxpYYx53l72rDFmtn0/wRjT2xjTwRgTZ4xZULy3UcGFReVJBCLCY4OiOXg6jRmrDxSwolJKFc6dNoKuxpgODo8X27/gVVkJi4SzhyArA/ytk7E+V9ShW9Na/HfxTm7uEkWIPYeBUkoVlTtnBFl2b2IARKQ5oPURZSksEjBw5lL/ARHh0UHRHD17ke7/WkSziXPo/eJiZunVREqpInLnjGACsEREdmONMdQEuMujUam8HPoSULNJ7uLDp9PwEzidmglAckoqk77eBKAT2Sil3FZoIjDG/CgiLYGcuRK3GWPcGmtIlZLcvgR5rxKaPH8b+UebSM3IYvL8bZoIlFJuc+eqoT8BocaYjcaYjUAVEXnA86GpXDXsg/rpvA3DB+1J7vNztVwppZxxp41gnDEmJeeBMeYUMM5jEanLBVWBKrUvOyNoFB7qtLir5Uop5Yw7icBfHCbLtUcVDfJcSMqpfH0JACbExxDq5Gqhzk3CyygopVRF4E4imAfMEJEBIjIAq+PXPM+GpS4TFgVn8l4RNKJjBC+MakdEeCgCNAoPIS4qjNm/H2L6qv3eiVMp5XPcuWroCeBe4H778ULgPY9FpJyrEQF7fr5s8YiOEXkahtMzs7nvkzU8+c0mqgYHMKxDo7KMUinlg9wZayjbGPO2MeZG+/aOMUb7EZS1sEi4eAbSThdYLCjAj7f+0JmuTWvx6IwNLN6q8xwrpQqmQ1f6Cse+BIUICfTn/Tu70KZRDe7/dB2/7jrh4eCUUr5ME4GvcNGXwJXqIYF8dFc3Gteqwh8/Ws3vB1I8F5tSyqe500agyoPcMwL3B5mrWTWIT//YnRvfXsGdH67ivn7N+XTlfg6mpNIoPJQJ8THa8Uwp5VaHsmgReVdEFojI4pxbWQSnHFSrD36Bbp8R5KhfI4TP7ulBdnY2L83bRnJKKoZLw1Ho2ERKKXfOCL4E3gbeRQeb8x4/P6jRqMiJAKBx7SqEBAZwJi3vv0+Ho1BKgXuJINMY49b8A8rD8s1LUBTHzjofHkqHo1BKudNY/J2IPCAiDT0web0qCie9i92lw1EopVxxJxHciTUU9QpgrX1b48mglAthkdacBNlFr6FzNhxFaKA/E+JjXKyhlKos3BmGullZBKLcEBYJJgvOHrYmtC+CnHaAyfOtBmN/P+H5EW21fUAp5ToRiMjVxpjFIjLK2fPGmK89F5ZyyrFTWRETAVwajmLe5kOM/3QdIUE6vaVSquAzgiuBxcD1Tp4zgCaCspanL0H3Ym9mYJsGNK1dhXd+3s2Qtg1wGFxWKVUJuUwExpi/2n91WsryIneCmuI1GOfw9xPu6ducZ2ZtZs2+U3Rtqm3/SlVmOsSELwmpASFhJU4EADd2iqRmlUCm/ry7FAJTSvkyTQS+pgR9CRyFBvlze8+mLEo8wq5j50ohMKWUr9JE4GtK0Jcgvzt6NiHQ34/3f9lTKttTSvkmd8YauklEqtv3nxaRr0Wkk+dDU06FRRZp4LmC1KkWzA2dIvlqbRLHzznveayUqvjcOSN4xhhzVkT6ANcA7wM65IS3hEVCWgpcPFsqm/tj32ZczMzmk1/3lcr2lFK+x51EkNON9VpgqjFmDjp5vffkzktQOqOGtqhbjWta1+eTlftITdcxBZWqjNxJBMki8g5wCzBXRILdXE95QhFmKnPXvf2ac/J8OjPXld42lVK+w50D+s3AfCDeGJMC1MIae0h5Q04iOFN6B+2uTWvSISqc95ftJivblNp2lVK+wZ3J6y8AR4E+9qJMYIcng1IFqNYAxK9UzwhEhHv7NmfviQssTNDJ7pWqbNy5auivwBPAJHtRIPCpOxsXkcEisk1EdorIRBdlbhaRBBHZIiL/z93AKy3/AKhevAlqChIfW5+oWqG8u0w7mClV2bhTNTQSGAacBzDGHASqF7aSiPgDbwJDgDbAaBFpk69MS6wE09sYEwv8uSjBV1ql2JcgR4C/H/f0bsbafadYu+9kqW5bKVW+uZMI0o0xBmugOUSkqpvb7gbsNMbsNsakA58Dw/OVGQe8aYw5BWCMOermtiu3UuxL4OimLlGEhQby7s/awUypysSdRPCFfdVQuIiMAxZhzV9cmAjA8WiVZC9zFA1Ei8hyEVkpIoOdbUhE7hWRNSKy5tixY268dAUXFmldPpqdXaqbrRocwB96NGZ+wmH2Hj9fqttWSpVf7jQWvwzMBL4CYoBnjTFvlNLrBwAtgf7AaOBdEQl3EsNUY0wXY0yXunXrltJL+7CwSMjOgPOlfwJ1Z8+mBPrpsBNKVSbuTF6PMWYhsLCI204GohweR9rLHCUBvxljMoA9IrIdKzGsLuJrVS65ncqSoHqDUt10vRohdGwcxicr9/Hpyn00Cg9lQnyMzmSmVAXm8oxARM6KyBlXNze2vRpoKSLNRCQIuBWYna/MLKyzAUSkDlZVkV62Upg8E9SUrlnrk9lw4DRgNQolp6Qy6etNzFpfOj2ZlVLlj8tEYIypboypAfwHmIhVvx+JdSnpa4Vt2BiTCTyI1RktEfjCGLNFRP4hIsPsYvOBEyKSACwBJhhjTpTg/VQOHuhdnGPy/G1czMzb9pCakcXk+dtK/bWUUuWDO1VDw4wxHRwevyUivwPPFraiMWYuMDffsmcd7hvgUfum3BUSBkHVPZIIDqakOl2enJLKvM2H6R9Tl5BAnetYqYrEnURwXkTGYF3+abAadfWSEm8S8UhfAoBG4aEkO0kGfgLjP11LteAABrapz3XtG9K3ZV3mbjrE5PnbOJiSqu0JSvkodxLBbVjVQ/+xH/9iL1PeFBbhkUQwIT6GSV9vIjXj0kikoYH+PD8iljrVQ/h+40HmbT7MN+uTCQkQMrIgy1jjE+W0JwCaDJTyIYUmAmPMXi7vCKa8LSwSDm4o9c3mHMBd/crvF12X50a045edx/jTZ+vJMnmHrs5pT9BEoJTvKDQRiEgk8AbQ2160DHjEGKNjFntTWCRcOA4ZqRAYWqqbHtExosADeVCAH1e3qk9ahvP5C1y1Myilyid3ehZ/iHXZZyP79p29THlTKU9QUxyNwp0noAB/YY/2TFbKZ7iTCOoaYz40xmTat2mAdu/1Ng/2JXDXhPgYQvNdQRTkLwT4Cde+voyZa5MwRuc3UKq8cycRnBCRP4iIv337A6DX+nubB/sSuGtExwheGNWOiPBQBIgID+XfN3bgx8f60y4ijL98+TsPf76B06kZXotRKVU4d64auhurjeBVrMtHVwB3eTIo5YbqjQDxaiIA1+0J/29cD97+aRdTFm5n3b5TvD46js5NankhQqVUYdy5amgf1nwEqjwJCLLGGfJyInDF30/401VX0LNFbR75fD03v7OSga3rszE5hUMpadrnQKlyxJ2rhupizRvQ1LG8MeZuz4Wl3OKheQlKU6fGNZn7cF/GfrCKeVsO5y7XPgdKlR/utBF8C4RhzUMwx+GmvM1DvYtLW/WQQA6fuXjZch3DSKnywZ02girGmCc8HokqurBI2PYDGGMNO1GOuepboH0OlPI+d84IvheRoR6PRBVdjUjITIML5f8iLld9DurXCCnjSJRS+bmTCB7BSgap9lwEZ92cj0B5WjnoS+AuZ30OALJNNsfPXV5tpJQqO+5MVVndGONnjAk1xtRwmKdAeVs56EvgLmd9Dh68qgVn0jK5/f1VnL6gfQ2U8ha3pqpU5ZTjlJU+wFmfg67NajPuozXc+eEqPv1jd6oF60dSqbLmTtWQKq+q1IKAUJ9JBM5cGV2XN27ryKbk09wzbTWp6c4HslNKeU5BcxY3K8tAVDHkTlBT/tsIChIf24ApN3dg1d6TjP90LRczNRkoVZYKOiOYCSAiP5ZRLKo4fKQvQWGGx0Xwwsh2/LT9GI9M30BmVnbhKymlSkVBFbJ+IvIkEC0il80pbIyZ4rmwlNvCImHHAm9HUSpu7daY8+lZ/PP7BG6d+isHT6fpcBRKlYGCEsGtwAi7TPUyiUYVXVgUnDsCmRchINjb0ZTYPX2asXbvSeZu1uEolCorLhOBMWYb8JKIbDTG/FCGMamiyLmE9Ewy1Gru3VhKye9JKZct0ykwlfIcd64aWiEiU0RkjX17RUTCPB6Zck+YfWD85VU4sKrw8gdWwbJX3CvrJQdT0lws1+EolPIEdy7a/gDYDNxsP74da6rKUZ4KShXBhZPW33UfWzd3iB/4B8OdsyGqm+diK6ZG4aEkOznouxqmQilVMu4kghbGmBscHv9dRDZ4KB5VVCf3AII1Z5BAs37QuKfzsvtXwJ6fwWRDVjrsXVYuE8GE+Bgmfb2J1IxLl5GGBPoxIT7Gi1EpVXG5kwhSRaSPMeYXABHpDeg5ennRrC8EhFgHdv8guPpp1wf3A6vgg3grEfgHQdO+ZRurm3LaASbP38bBlFQMcH2HRto+oJSHuJMIxgMfO7QLnALu9FxIqkiiullVPHuXWQf2gn7hR3WDruNg1Tswamq5PBvIkTMchTGG4W8uZ83eU2RnG/z8yvdw20r5IncGnfvdGNMBaA+0N8Z0NMZs9Hxoym1R3aDvY+4d2LvfZ/09e7jgcuWEiDCub3P2HD/PosQj3g5HqQrJ7bGGjDFnjDE6/LSvq90CareE7b5zRfCQtg2IrBnK1J93ezsUpSokHXSuMooZDHt/gYtnvR2JWwL8/binTzPW7DvF2n2nvB2OUhWOJoLKKHqI1bi8a7G3I3HbzV2iqBESwHvL9KxAqdLmViIQkV4icpuI3JFzc3O9wSKyTUR2isjEAsrdICJGRLq4G7gqgajuEBIO2+Z5OxK3VQ0O4A89mjBvy2H2Hj/v7XCUqlAKTQQi8gnwMtAH6GrfCj1gi4g/8CYwBGgDjBaRNk7KVceaDvO3IkWuis8/AFoOgh3zIdt3hnwe26spgX5+vP/LHm+HolSF4s4ZQRegtzHmAWPMQ/btYTfW6wbsNMbsNsakA58Dw52U+yfwEuB8XAHlGTGDrUnvk9Z4OxK31asRwoiOjfhy7QFOnk/3djhKVRjuJILNQINibDsCcJwxJclelktEOgFRxpg5xdi+KokrrgG/AJ+6eghgXN/mpGVk8+nKfd4ORakKw51EUAdIEJH5IjI751bSFxYRP2AK8JgbZe/NGfTu2LFjJX1pBRASBk16+VQ7AUDL+tW5ulU9Plqxl7QM36nWUqo8cycR/A1rXoJ/Aa843AqTDEQ5PI60l+WoDrQFlorIXqAHMNtZg7ExZqoxposxpkvdunXdeGnllughcCwRTu31diRFMq5vc06cT+frdcmFF1ZKFcqdnsU/AVuxDtzVgUR7WWFWAy1FpJmIBGFNdJN7JmGMOW2MqWOMaWqMaQqsBIYZY3yn0trXRcdbf33srKBH81q0iwjjvWW7yc423g5HKZ/nzlVDNwOrgJuwhqL+TURuLGw9Y0wm8CAwH0gEvjDGbBGRf4jIsJKFrUpF7RZQJ9rn2glEhHH9mrP7+Hl+3HrU2+Eo5fPcGXTuKaCrMeYogIjUBRZhT25fEGPMXGBuvmXPuijb341YVGmLHgwr34K0MxBSw9vRuG1o2wa8FB7K1J93MbBNfW+Ho5RPc6eNwC8nCdhOuLme8gUxQyA7A3b96O1IiiRn2InVe0+xbr8OO6FUSbhzQJ9nXzE0VkTGAnPI9ytf+bDIbhBa0+faCQBu7qrDTihVGtxpLJ4ATMUehhqYaox5wtOBqTKS28t4gU/1MgaoFhzAmB5NmLf5MPtO6LATShWXO20EGGO+Ar7ycCzKW6IHw8YZ1gxmTVxMc1lO3dWrKe/8tIuh/1nGhfQsGoWHMiE+RmczU6oIXJ4RiEjO1JRnReSMw+2siOi8BBXJFQN8spcxwIpdJxCE8+lZGCA5JZVJX29i1nrtY6CUu1wmAmNMH/tvdWNMDYdbdWOM71xeogoXEgZNevtkO8Hk+dvIMnn7EqRmZDF5/jYvRaSU73F39NFClykfFzMEjm+Dk77V8HowJbVIy5VSl3PnqqFYxwciEgB09kw4ymuiB1t/feysoFF4aJGWK6UuV1AbwSQROQu0d2wfAI4A35ZZhKps1GoGdVv5XDvBhPgYQgP98ywLDfRnQnyMlyJSyvcU1EbwAhAGfJyvfaC2MWZS2YWoykz0YNi3AtJOezsSt43oGMELo9oRYZ8BBPoLL4xqp1cNKVUEBVYNGWOysWYkU5VBzBDIzoSdi7wdSZGM6BjB8olX88TgVmRkGbo2q+XtkJTyKe60EawTEU0GlUFkV6hS2+faCXLEx1pjDi3YctjLkSjlW9xJBN2BX0Vkl4hsFJFNIrLR04EpL/Dzv9TLOCvT29EUWfO61YiuX435mgiUKhJ3EkE80AK4GrgeuM7+qyqi6MGQlgIHfvN2JMUyOLYBq/ac5MS5i94ORSmf4c5YQ/uAcKyD//VAuL1MVUQtrga/QJ+7eihHfNsGZBtYlHjE26Eo5TPc6VD2CPAZUM++fSoiD3k6MOUlITWgaR+fbSdo07AGUbVCmbdZq4eUcpc7VUP3AN2NMc/ak8r0AMZ5NizlVTFD4MQOOLHL25EUmYgwOLYBy3ee4ExahrfDUconuJMIBHAcnzjLXqYqqtxexr5ZPTS4bQPSs7JZotNYKuUWdxLBh1jzFP9NRP6ONcn8+54NS3lVzSZQsymsetcamtrHdIyqSd3qwXr1kFJuKnQ+AmPMFBFZCvQBDHCXMWa9pwNTXnRgFZxOsjqXfRBvjUxatxVUqwdV69p/60G1utbfI5th7zJo2heiunk7evz8hPjY+ny1Npm0jCxC8g1BoZTKy62JaWyClQi0Wqii27sMTLZ132TD0QQ4vLHwoSf8AmDIv6HTndbMZ140OLYhn67cz8/bjzEotoFXY1GqvCv02yoizwI3Yc1QJsCHIvKlMeY5TwenvKRpX/APhqx08A+C0Z9bv/QzL8L5Y3Du6KW/W76GXUsAY51BzHkUFv8TrhgI0fHWpDehNcv8LXRvXouw0EDmbTmsiUCpQrjzs20M0MEYkwYgIi8CGwBNBBVVVDe4c/bl1T0BwRAWad1y1I2Bfb/aSSMQ+k2AEzut3smbvgDxhya9rKQQPQRST5ZJNVKgvx/XtK7PwoTDZGRlE+jvTnOYUpWTO4ngIBACpNmPgwGdB7Cii+rm3oHaVdLIzoKkNbB9nnVb8LR1y6lZ9A+CO7716BzJg9s24Kt1SazcfYK+Let67HWU8nVi8k3zd1kBkVlYI5AuxGojGAisApIAjDEPezbEvLp06WLWrFlTli+pSsOpffDDE3l7LAdWgbY3QKvroHl/CAwp1ZdMy8ii0z8XMrJjBM+PbFeq21bK14jIWmNMF2fPuXNG8I19y7G0NIJSlUzNJtD3Udi91KpG8vOzzh62zIL1n0BgVWh5jZUUWg4slXaFkEB/roqpx/wtR/jH8Lb4++l1Dko5487lox+JSBAQbS/aZozRLpuq6JxVI2VehD3LYOv3sG0uJHxrXX3UtA/Ubwvp56FhHNRvU/C2jyTAucPWWEkOVVqDYuszZ9Mh1u8/RZemOk+BUs64UzXUH/gI2ItVwRsF3GmM+dnDsTmlVUMVWHY2JK+Frd/BxplwthhNUQEhcOd3ucngbFoGnf+5iDt6NuHp6wpJJkpVYCWtGnoFGGSM2WZvLBqYjk5gr0qbnx9EdbVuwWGw5DmrH4P4QYfR0HaU8/U2fw0b/h9gIDMNEmbnJoLqIYH0vqI28xMO89S1rRHR6iGl8nMnEQTmJAEAY8x2EQn0YExKQbO+8LNDX4bOY11fxRRcw0oGWRetxLHhM4i7Lbc6aXDbBjzx1SYSDp0htlFY2b0HpXyEOxdXrxWR90Skv317F9C6GeVZOe0JVz9l/S3oUtbcsk/DqHetxDFtKCStBeCa1vXxE5ivQ1Mr5ZQ7iWA8kAA8bN8SgPvd2biIDBaRbSKyU0QmOnn+URFJsKfA/FFEmhQleFXBRXWDvo+535+h72PQ/ma4e551lvDxMNjzM7WrBdOtWS3m6SB0SjlVYCIQEX/gd2PMFGPMKPv2qjGm0HkA7XXfBIYAbYDRIpK/tW490MUY0x6YCfy7WO9CKUe1msHd8yEsCj69Ebb9wODYBmw/co5dx855Ozqlyp0CE4ExJgvYJiKNi7HtbsBOY8xuY0w68DkwPN/2lxhjLtgPVwKRKFUaajSEu+ZC/Vj4fAzD/ZcD6NDUSjnhTtVQTWCLXXUzO+fmxnoRwAGHx0n2MlfuAXxzJhRVPlWpZbUdNOlFzXkPMrHOL9pOoJQT7lw19IyngxCRPwBdgCtdPH8vcC9A48bFOTlRlVZwdRjzJXx5F+O3/48zp06QnNKZiPBQb0emVLnhMhGISAhWQ/EVwCbgfWNMZhG2nYzV+SxHJE4GqxORa4CngCtdtT0YY6YCU8HqUFaEGJSCwFC45RPOzriXx7fPYNfnZ6FVB2vCnUin/WsuSV4HB1aWm0l3lPKEgs4IPgIygGVcavB9pAjbXg20FJFmWAngVuA2xwIi0hF4BxhsjNEJZpXn+AdS/db3WfLPZK46PBcOz3VrNQNkGyFDAvmt7zSuHHCtZ+NUygsKSgRtjDHtAETkfawRR91mjMkUkQeB+YA/8IExZouI/ANYY4yZDUwGqgFf2j0+9xtjhhXjfShVqFm/H2JnRlP6+a/CXwxZRlhh2lOr7QBiG9XIU3bLwTOc3PwjfeR3/MWAyWDtT7M5VSuOER0LaupSyvcUlAhyB5azD+pF3rgxZi4wN9+yZx3uX1PkjSpVTJPnb6N+Vmv+5B9IoMkkgwBezRjJ5t9b0f1sLYL8/QgK8CPQ349FiUdolVGDLkEJhJgM/DDsz6zJV/O3aSJQFU5BiaCDiJyx7wsQaj8WwBhjarheVany52BKKslEMyb9SXr4JbIyuzXrTDRkZXPuYibpmdmkZ2aTkZXNhfQs1hHNmPSnuMZvLbcELGVC4BeMTGnr7behVKlzmQiMMf5lGYhSntYoPJTklFTWmWjWZUXnLo8ID+WbB3rnKdv7xcV5ys7J7sEXQf/gw5ApkD4SgqqWdfhKeYxO5KoqjQnxMYQG5v19Exroz4T4mELLbjHNeCTjQVqZ3ax77WYOnNAeyqri0ESgKo0RHSN4YVQ7IsJDEawzgRdGtXNa5++s7JAb7uK36MfodOEXFvznPt5cspP0zOwyfx9KlbZCJ6Ypb3RiGuVVxnB+1v9R9fcPeTLjHlbVHk58bH1mrT/IwZRUGoWHMiE+RhuUVblT0olplFI5RKg67GW4kMxzO6fx0LkGvLkkNvfp5JRUJn29CUCTgfIZWjWkVFH5B8CNH+BXrw3/zp5CtBzI83RqRhaT529zsbJS5Y8mAqWKI7g63DaDcyaYD4ImU5eUPE8fTEn1TlxKFYMmAqWKKyyCScFPU4uzfBb0HA/7f0Un2Q5ASKA/aRlZztc7sAqWvWL9LYynyirlQBuLlSqBWeuT2fH1c/zF7/9hgEwC+G/WSHZlN6Rx7Src17c54VUcpvg+sRN+ngxZGeAfCP0mQO0rnG+8OGWzM8E/uPDpPVWlU1BjsSYCpUpoy4y/0jrxP/hRjr5LcWNg+JtQjKFhVMWkVw0p5UGxva6FHe9AVrrVkDzsTWjQjj3Hz/Ps7M0cP5fOYwNbck3rBnB4E8z+E2Rl5inrVHHKZqYDBjZ8Bkc2Q59HofX14KcDBSjX9IxAqdJwYBXsXXbZvAWnzqfzwGfr+HX3Ce7r15zHB7fCP3m107JF2W6BZaO6w8nd8Mur1t/aLaHPn6HdzRAQVPL3qnySVg0p5UUZWdn88/sEPv51H60bVCclNYPDp9MK7Xw2a30yk+dvK35HtewsSPgWfplinTHUiIReD0GnOyCoSim9O+UrNBEoVQ5MmPk7X65JyrMsNNDf6TAXs9YnM+nrTaQ6XHnkqmyhjIGdi2DZFNi/AqrUhlbXW2cHjTpBg0JGVD28BU7vh+b9tQHah2kiUKocyBnR1JkAv7yNupnZzr+XEeGhLJ94dfGD2L8SFjwLSb8Vfd2AYLjze00GPkobi5UqBwrqZHbflc3zPH5zyS6n5ZJTUkk4eIY2jYo5HUjjHhATD8mrwWSD+EHbG6GNi4kBE2bDpi8BA5kXYdVUTQQVkCYCpcpIznwI+UWEhzIhvlWeZbPWH3RaVoChry+jZ/Pa3N2nGVe3qoe/XxEvEW3a1+prkJUO/kHQbZzrg3u1+pD4nVWWbCspVKsP1/zN6tugKgStGlKqjBSl3t9V2Weua83ZtEw+WrGXg6fTaFyrCmN7NaVKkB9vLN7lfsNyca9G2vINrH4PGveCmz6E6g2KtS9U2dM2AqXKiaJcCVRQ2cysbOZvOcIHy/ewdt+py9YtdsOyOzZ+Ad89AkHV4KZp0LR3oaso79NEoFQF1vW5RRw7d/Gy5RHhISyfOMAzL3okAb64HU7usaqJej2kvZjLuYISgQ46p5SPO+4kCQAkp6QxfdV+14PflUT9NjBuCbS6FhY+AzP+AGmnS/91VJnQMwKlfJyry1ID/ITMbEN4lUBGd2vMHT2b0DAstOQd1RwZAyv/BwuegZpNoN8TcDa5dHtNF6c9w52ylYxWDSlVgblqWP7XyLY0DA/lw+V7WJhwBBGhXUQNEg+d5aLDXMul0p6wbwV8PgZST1qPRaB2NARXc17+4jk4sd1KJAWVdbfcZWX9rR7Uza+EWi2gdgsIqlr891cBaD8CpSqwnAO4q1/5PZrX5sDJC3yych/v/rz7sjFSc2ZUK1EiaNILOo+1hrMA62CcnQmhNZ2XT02xyhRW1t1yl5XNgrUfWrcc1RvaSaG5NZx3djacToJGcVA/1tkWLzmyBU7ugpihFfJMQ88IlKpEmk2c43Kw7K/u70VcVHiefglFqkY6sAo+Gnapf0JBcyK4W7Yk2xz9OVSpZR3AT+yEE7vt+7vgwnHXO6lAAp3uhO73Qb3WPtVArlVDSimg4GEuAGpVDaJ/dF2ubl2PM2kZ/PO7xKKNd+SJ+nxPbHPx87Ds5Uu9q9vdDLEjnZfd8o11ySzZeZfXbAox11oN5lHdraHCyzGtGlJKATAhPsZlR7VqIYEs2XqUxduO8vX6ZKfrF1SNZJ09nONgSisahZ9jQnxyIX0kCi/riW0C/GTi6G4CCDCZZBLAb2HDuDJmsPOySVl052urrASwodur9KiXDlvnwup3YeWbEFoLogdbSSG4hjWEh6eGGfdAQ7ieEShVyRRW3ZOVbdhw4BQ3vPWry22M7dWUlvWr0bJedVrWq8ZP24+VuNd0/rKl0RO7oLKtMxPp4ZfIyuzWJAa0Ll7Zi2dh54+wdQ7smJ/vElqBsCgIDHW+EzNS4fQBwBShLBAQUqypSLVqSClVZK6qkQL9hUB/Py6kXzro+gk4GzC1WnAAY7o3zrPss9/2c+5iZqFl3S3njbINagSzYuIA/BzHecrKYO9H99F4/1f4YVUkna3ekrAo5w3Rpw9sofrZHUUum4kf21o/TOwtf3da1hVNBEqpIivoV/awDo04dCaNHUfOsvPoOZ6bk+hyOyGBefutpmVkuyiZt6y75bxVNsjfj0bhIUTVqkJkzVDOpGZwNHEZH/s/TyCZZBDA2KynuXrgtQxoXT/Puj8mHmHxwjlM838ut+xd2U8z4vqRjOoUSaC/IHZD9Kz1ycz4+is+8Ptnbtm7s5/hllE3FOlKL00ESqlicfeqIVdnD87mT3C3rCe2WVplw0KtTnoHTl0g6VQqSScvcOJ8OgCdZHtuNdI6E33Zuo5clRWB4AA/gvz9OHcxk2xzedmizk3htcZiERkM/AfwB94zxryY7/lg4GOgM3ACuMUYs9eTMSml3DeiY4RbvzpdNUJPiI8pdllPbLO0yv59WOxl+yXn0tx1Jpp1WXkTwBujO+Z5/ND09eCi7F8GRXMxM5v0zGwuZmYzbcVep2ULmt+iqDyWCETEH3gTGAgkAatFZLYxJsGh2D3AKWPMFSJyK/AScIunYlJKeUZhndqKU9YT2/Rk2YLmm7i+Q6M8y178YavLsg9e3TLPsoUJR5yWbRTuomG5GDxWNSQiPYG/GWPi7ceTAIwxLziUmW+X+VVEAoDDQF1TQFBaNaSUKo88fZVTSeev9lbVUARwwOFxEtDdVRljTKaInAZqA3m6/YnIvcC9AI0bN0Yppcqb8nBWUlyePCO4ERhsjPmj/fh2oLsx5kGHMpvtMkn24112GZf9v/WMQCmlis5b8xEkA1EOjyPtZU7L2FVDYViNxkoppcqIJxPBaqCliDQTkSDgVmB2vjKzgTvt+zcCiwtqH1BKKVX6PNZGYNf5PwjMx7p89ANjzBYR+QewxhgzG3gf+EREdgInsZKFUkqpMuTRfgTGmLnA3HzLnnW4nwbc5MkYlFJKFUznLFZKqUrO54aYEJFjwL5irl6HfJemlnO+FK8vxQq+Fa8vxQq+Fa8vxQoli7eJMaausyd8LhGUhIiscXX5VHnkS/H6UqzgW/H6UqzgW/H6UqzguXi1akgppSo5TQRKKVXJVbZEMNXbARSRL8XrS7GCb8XrS7GCb8XrS7GCh+KtVG0ESimlLlfZzgiUUkrlo4lAKaUquUqTCERksIhsE5GdIjLR2/E4EpEoEVkiIgkiskVEHrGX1xKRhSKyw/5b09ux5hARfxFZLyLf24+bichv9v6dYY8vVS6ISLiIzBSRrSKSKCI9y/m+/T/7c7BZRKaLSEh52b8i8oGIHLVHDs5Z5nRfiuV1O+aNItKpnMQ72f4sbBSRb0Qk3OG5SXa820Qk3tuxOjz3mIgYEaljPy7VfVspEoHDbGlDgDbAaBFp492o8sgEHjPGtAF6AH+y45sI/GiMaQn8aD8uLx4BHGcsfwl41RhzBXAKa/a58uI/wDxjTCugA1bc5XLfikgE8DDQxRjTFmucrpzZ+8rD/p0GDM63zNW+HAK0tG/3Am+VUYyOpnF5vAuBtsaY9sB2YBKA/Z27FYi11/mffewoK9O4PFZEJAoYBOx3WFyq+7ZSJAKgG7DTGLPbGJMOfA4M93JMuYwxh4wx6+z7Z7EOVBFYMX5kF/sIGOGVAPMRkUjgWuA9+7EAVwMz7SLlKdYwoB/WAIcYY9KNMSmU031rCwBC7aHZqwCHKCf71xjzM9YAkY5c7cvhwMfGshIIF5GGZRKozVm8xpgFxphM++FKrCHywYr3c2PMRWPMHmAn1rHDa7HaXgUeBxyv7CnVfVtZEoGz2dJKb3qfUiQiTYGOwG9AfWPMIfupw0B9b8WVz2tYH8xs+3FtIMXhy1We9m8z4BjwoV2V9Z6IVKWc7ltjTDLwMtavv0PAaWAt5Xf/gut96Qvfu7uBH+z75S5eERkOJBtjfs/3VKnGWlkSgU8QkWrAV8CfjTFnHJ+z52nw+rW+InIdcNQYs9bbsbgpAOgEvGWM6QicJ181UHnZtwB2/fpwrATWCKiKk+qC8qo87cvCiMhTWNWyn3k7FmdEpArwJPBsYWVLqrIkAndmS/MqEQnESgKfGWO+thcfyTnds/8e9VZ8DnoDw0RkL1YV29VYdfDhdlUGlK/9mwQkGWN+sx/PxEoM5XHfAlwD7DHGHDPGZABfY+3z8rp/wfW+LLffOxEZC1wHjHGYDKu8xdsC6wfB7/b3LRJYJyINKOVYK0sicGe2NK+x69jfBxKNMVMcnnKcwe1O4Nuyji0/Y8wkY0ykMaYp1n5cbIwZAyzBmmUOykmsAMaYw8ABEYmxFw0AEiiH+9a2H+ghIlXsz0VOvOVy/9pc7cvZwB32FS49gNMOVUheIyKDsao2hxljLjg8NRu4VUSCRaQZVkPsKm/ECGCM2WSMqWeMaWp/35KATvZnunT3rTGmUtyAoVhXCOwCnvJ2PPli64N1Or0R2GDfhmLVvf8I7AAWAbW8HWu+uPsD39v3m2N9aXYCXwLB3o7PIc44YI29f2cBNcvzvgX+DmwFNgOfAMHlZf8C07HaLjLsA9M9rvYlIFhX6+0CNmFdCVUe4t2JVb+e811726H8U3a824Ah3o413/N7gTqe2Lc6xIRSSlVylaVqSCmllAuaCJRSqpLTRKCUUpWcJgKllKrkNBEopVQlp4lAlQp7ZMRXHB7/RUT+VkrbniYiNxZessSvc5M9OumSUt5uf7FHaa3oRGSpiPjMZPDKoolAlZaLwKicYXLLC4feuO64BxhnjLnKU/GUljIeFVNVcJoIVGnJxJpP9f/yP5H/F72InLP/9heRn0TkWxHZLSIvisgYEVklIptEpIXDZq4RkTUist0e7yhnToTJIrLaHpP9PoftLhOR2Vi9cvPHM9re/mYRecle9ixWx773RWRyvvL97V+6OXMafGb3+kVEBtiD2W0Sazz5YHv5YLvsOmCUw7aq2uVW2esNt5fH2ss22O+lpZO4z4nIKyLyO9BTRP7gsM47OcnBLjdZrDkNFolINzv+3SIyzC4TIiIf2nGvF5Gr7OUrRSTW4TWXikiXAuIOFZHP7TOpb4BQp58OVb55o3ei3ireDTgH1MDq/RgG/AX4m/3cNOBGx7L23/5ACtAQq/dsMvB3+7lHgNcc1p+H9cOlJVavyxCscdiftssEY/UebmZv9zzQzEmcjbCGcaiLNSDdYmCE/dxSnPTQtLd3Gms8Fz/gV6ykEYLVQzXaLvcx8GeH5S2xeoB+waUe2P8C/mDfD8fq7V4VeANr3BuAICDUSRwGuNm+3xr4Dgi0H/8PuMOh3BD7/jfAAiAQay6GDfbyx4AP7Put7H0SgpXIc/4HDYFthcT9qMN22mP9ICjzHsR6K9lNzwhUqTHWiKkfY02s4q7VxpqP4SJWd/kF9vJNQFOHcl8YY7KNMTuA3VgHr0FY461swBq2uzbWwRdglbHGlM+vK7DUWIO65Yw82c+NOFcZY5KMMdlYwxI0BWKwBojbbpf5yN5WK3v5DmMdIT912M4gYKId81Ksg29jrOTypIg8ATQxxqQ6iSELa2BCsMYg6gystrc1AGsYCoB0rMQJ1n78yVgD2Dnu0z45cRljtgL7gGispJVz9nYzl+ZAcBV3P4ftbMQaxkP5mKLUnyrljteAdcCHDssysashRcQP6xdvjosO97MdHmeT9/OZfywUg/Vr+yFjzHzHJ0SkP9YZQWlyjDOL4n93BLjBGLMt3/JEEfkNa8KfuSJynzFmcb4yacaYLIftfGSMmeTkNTLsBAQO+9QYk11Ym4kxJllETohIe+AWYHxBcds1ZMrH6RmBKlXGmJNYvyodp1Lci/XrFWAYVjVFUd0kIn52u0FzrEHB5gP3izWENyISLdakMwVZBVwpInXsOvXRwE/FiAc7hqYicoX9+HZ7W1vt5TltHKMd1pkPPOTQxtDR/tsc2G2MeR1r9M72hbz2j8CNIlLPXr+WiDQpQuzLgDH2utFYv+5zDvIzsEbnDLN/5buMG/gZuM1e1taNuFU5pIlAecIrgOPVQ+9iHXx/B3pSvF/r+7EO4j8A440xaVhTZSZgjdG+GXiHQn6pG2uo3olYwzr/Dqw1xhRrSGc7hruAL0VkE9av77ft5fcCc+zGYse5Dv6JlQg3isgW+zFY1TCb7aqXtlhVbAW9dgLwNLBARDZizcNblKkK/wf42XHPAMba1XNgVQfdipXQC4v7LaCaiCQC/8CaTU35GB19VCmlKjk9I1BKqUpOE4FSSlVymgiUUqqS00SglFKVnCYCpZSq5DQRKKVUJaeJQCmlKrn/DyPZOWe41AxhAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "G_america = nx.read_edgelist(path + 'powergrid.edgelist.txt')\n", + "print(nx.info(G_america))\n", + "\n", + "attack_usa = Attack(G_america, steps=5)\n", + "\n", + "x_d, y_d = attack_usa.degree()\n", + "x_c, y_c = attack_usa.closeness()\n", + "\n", + "plt.title('Degree-Closeness Attack of America')\n", + "plt.xlabel('Number of nodes removed')\n", + "plt.ylabel('Proportion of nodes in core')\n", + "plt.plot(x_d, y_d, marker='o', label='Degree-Attack')\n", + "plt.plot(x_c, y_c, marker='.', label='Closeness-Atack')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94cb242d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0fde2578", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh6/src/main.ipynb b/sesh6/src/main.ipynb @@ -0,0 +1,243 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 14, + "id": "608ff8af", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "import random" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "058ac30e", + "metadata": {}, + "outputs": [], + "source": [ + "class Attack:\n", + " def __init__(self, G, steps=25):\n", + " self.G = G\n", + " self.steps = steps\n", + " self.N = G.number_of_nodes()\n", + " self.M = self.N // self.steps\n", + " self.num_nodes_removed = range(0, self.N, self.M)\n", + " \n", + " def random(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_to_remove = random.sample(list(C.nodes), self.M)\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions\n", + "\n", + " def betweenness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " betweenness = nx.centrality.betweenness_centrality(C)\n", + " nodes_sorted_by_betweenness= sorted(C.nodes, key=betweenness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_betweenness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def degree(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_sorted_by_degree = sorted(C.nodes, key=C.degree, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_degree[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def closeness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " closeness = nx.centrality.closeness_centrality(C)\n", + " nodes_sorted_by_closeness = sorted(C.nodes, key=closeness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_closeness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions " + ] + }, + { + "cell_type": "code", + "execution_count": 155, + "id": "a08557c5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 143 nodes and 623 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7f437ab70370>" + ] + }, + "execution_count": 155, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "path = './../../../network_course/data/'\n", + "G = nx.read_edgelist(path + 'ia-enron-only/ia-enron-only.edges', nodetype=int)\n", + "print(nx.info(G))\n", + "\n", + "attack = Attack(G)\n", + "\n", + "x_d, y_d = attack.degree()\n", + "x_b, y_b = attack.betweenness()\n", + "x_c, y_c = attack.closeness()\n", + "\n", + "plt.title('Degree-Betweenness-Closeness Attack')\n", + "plt.xlabel('Number of nodes removed')\n", + "plt.ylabel('Proportion of nodes in core')\n", + "plt.plot(x_d, y_d, marker='o', label='Degree-Attack')\n", + "plt.plot(x_b, y_b, marker='^', label='Betweenness-Atack')\n", + "plt.plot(x_c, y_c, marker='.', label='Closeness-Atack')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": 156, + "id": "76f1387a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 4941 nodes and 6594 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "<matplotlib.legend.Legend at 0x7f4377b09460>" + ] + }, + "execution_count": 156, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "G_america = nx.read_edgelist(path + 'powergrid.edgelist.txt')\n", + "print(nx.info(G_america))\n", + "\n", + "attack_usa = Attack(G_america, steps=5)\n", + "\n", + "x_d, y_d = attack_usa.degree()\n", + "x_c, y_c = attack_usa.closeness()\n", + "\n", + "plt.title('Degree-Closeness Attack of America')\n", + "plt.xlabel('Number of nodes removed')\n", + "plt.ylabel('Proportion of nodes in core')\n", + "plt.plot(x_d, y_d, marker='o', label='Degree-Attack')\n", + "plt.plot(x_c, y_c, marker='.', label='Closeness-Atack')\n", + "plt.legend()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "94cb242d", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0fde2578", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh6/tex/main.pdf b/sesh6/tex/main.pdf Binary files differ. diff --git a/sesh6/tex/main.tex b/sesh6/tex/main.tex @@ -0,0 +1,134 @@ +\documentclass[a4paper]{article} + + +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{mathptmx} + +%\usepackage{ngerman} % Sprachanpassung Deutsch + +\usepackage{graphicx} +\usepackage{geometry} +\geometry{a4paper, top=15mm} + +\usepackage{subcaption} +\usepackage[shortlabels]{enumitem} +\usepackage{amssymb} +\usepackage{amsthm} +\usepackage{mathtools} +\usepackage{braket} +\usepackage{bbm} +\usepackage{graphicx} +\usepackage{float} +\usepackage{yhmath} +\usepackage{tikz} +\usetikzlibrary{patterns,decorations.pathmorphing,positioning} +\usetikzlibrary{calc,decorations.markings} + +\usepackage[backend=biber, sorting=none]{biblatex} \addbibresource{uni.bib} + +\usepackage[framemethod=TikZ]{mdframed} + +\tikzstyle{titlered} = + [draw=black, thick, fill=white,% + text=black, rectangle, + right, minimum height=.7cm] + + +\usepackage[colorlinks=true,naturalnames=true,plainpages=false,pdfpagelabels=true]{hyperref} +\usepackage[parfill]{parskip} +\usepackage{lipsum} +\newtheorem{definition}[section]{Definition} + + +\usepackage{tcolorbox} +\tcbuselibrary{skins,breakable} + +\pagestyle{myheadings} + +\markright{Popović\hfill 6-th Exercise \hfill} + + +\title{University of Vienna\\ Faculty of Mathematics\\ + \vspace{1.25cm}Seminar: Introduction to complex network analysis \\ 6-th +Exercise +} +\author{Milutin Popović} +\begin{document} +\maketitle + +\section{Exercise 6} +\subsection{Consider a Barabasi-Albert} +We consider a Barabasi-Albert model with a preferential attachment given by +\begin{align} + \Pi(k_i) = \frac{1}{m_0 + t - 1}. +\end{align} +With the following differential equation +\begin{align} + \frac{\partial k_i}{\partial t} = m \Pi(k_i) \;\;\;\; k_i(t_i) = m +\end{align} +we can solve for the degree dynamics. By simply integrating we get +\begin{align} + k_i(t) &= \int \frac{m}{m_0 +t -1}dt \nonumber\\ + &=m\ln(m_0 + t - 1) + c. +\end{align} +With the initial condition $k_i(t_i) = m$ we get the degree dynamics +\begin{align} + k_i(t) = m \ln(e\cdot\frac{m_0 + t - 1}{m_0 + t_i - 1}). +\end{align} +To calculate the degree distribution, we look at nodes with degree $k_i < k$, +which by substitution is essentially +\begin{align} + t_i > e^{-\frac{k}{m}}e\cdot (m+t-1) -m_0 + 1. +\end{align} +Meaning that every node that entered after time $t_i$ has degree smaller than +$k$. There are exactly $t_i - t$ such nodes, thus the probability to find +such node is +\begin{align} + P(k) = 1 - e^{-\frac{k}{m}}e\cdot (m+t-1) +m_0 - 1. +\end{align} +By differentiating with respect to $k$ we get the degree distribution +\begin{align} + p(k) = \frac{\partial P(k_i<k)}{\partial k} = + \frac{e}{m}e^{-\frac{m}{k}}(m_0 + t -1) +\end{align} +For $t \gg m_0$ we get +\begin{align} + p(k) = \frac{e}{m} e^{-\frac{e}{m}}. +\end{align} +\subsection{Betweeness- and Closeness Centrality} +\begin{definition} + The betweenness centrality of a node $k$ is given by + \begin{align} + g(k) = \sum_{i \neq j \neq k} + \frac{\sigma_{k_ik_j}(k)}{\sigma_{k_ik_j}}, + \end{align} + where $\sigma_{k_ik_j}$ is the number of shortest paths from node $k_i$ to + node $k_j$, and $\sigma_{k_i k_j}(k)$ is the number of shortest paths + from node $k_i$ to node $k_j$ that pass through node $k$. +\end{definition} +Betweenness centrality of a node $k$, basically describes how good the node +is connected in term of shortest paths. The maximum of this function would +give us a node that is especially well connected by shortest paths to most of +the nodes in the network. + +\begin{definition} + The closeness centrality $C(k)$ of a node $k$ in a connected graph with + $N$ number of nodes is given by + \begin{align} + C(k) = \frac{N - 1}{\sum_{i} d(k_i, k)}, + \end{align} + where $d(k_i, k)$ is the shortest distance from node $k_i$ to node $k$. +\end{definition} +Closeness centrality of a node $k$, resembles how well closed up with respect +to a node $k$ a network is. With this function we can find nodes that are +close to other nodes, i.e. how efficient a given node is. + + + + +\nocite{code} +\nocite{barabasi2016network} +\printbibliography + +\end{document} diff --git a/sesh6/tex/uni.bib b/sesh6/tex/uni.bib @@ -0,0 +1,16 @@ +@online{code, + author = {Popovic Milutin}, + title = {Git Instance, Introduction to complex network analysis}, + urldate = {2021-10-10}, + url = {git://popovic.xyz/network_ana.git}, +} + +@book{barabasi2016network, + title={Network Science}, + author={Barab{\'a}si, A.L. and P{\~A}3sfai, M.{\~A}.}, + isbn={9781107076266}, + lccn={2016439537}, + url={https://books.google.at/books?id=iLtGDQAAQBAJ}, + year={2016}, + publisher={Cambridge University Press} +} diff --git a/sesh7/src/.ipynb_checkpoints/main-checkpoint.ipynb b/sesh7/src/.ipynb_checkpoints/main-checkpoint.ipynb @@ -0,0 +1,294 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "e1d43e31", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import networkx as nx\n", + "import itertools\n", + "import random\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "974f553a", + "metadata": {}, + "outputs": [], + "source": [ + "class Attack:\n", + " def __init__(self, G, steps=25):\n", + " self.G = G\n", + " self.steps = steps\n", + " self.N = G.number_of_nodes()\n", + " self.M = self.N // self.steps\n", + " self.num_nodes_removed = range(0, self.N, self.M)\n", + " \n", + " def random(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_to_remove = random.sample(list(C.nodes), self.M)\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions\n", + "\n", + " def betweenness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " betweenness = nx.centrality.betweenness_centrality(C)\n", + " nodes_sorted_by_betweenness= sorted(C.nodes, key=betweenness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_betweenness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def degree(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_sorted_by_degree = sorted(C.nodes, key=C.degree, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_degree[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def closeness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " closeness = nx.centrality.closeness_centrality(C)\n", + " nodes_sorted_by_closeness = sorted(C.nodes, key=closeness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_closeness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions " + ] + }, + { + "cell_type": "markdown", + "id": "dc8fce39", + "metadata": {}, + "source": [ + "# Exercise 7a) Barabasi-Albert-Model" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "5d87dc35", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0.98, 'Random Attack on Barabasi Albert Model (n, m)')" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x576 with 4 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ns = [100, 1000]\n", + "ms = [2, 5]\n", + "fig, ax = plt.subplots(2, 2, figsize=(10, 8))\n", + "for i, n in enumerate(ns):\n", + " for j, m in enumerate(ms):\n", + " marker = '.'\n", + " if j == 1:\n", + " marker='o'\n", + " G = nx.generators.random_graphs.barabasi_albert_graph(n, m)\n", + " attack = Attack(G)\n", + " ax[i][j].plot(*attack.random(), marker=marker, label=f\"(n, m) = ({n}, {m})\")\n", + " ax[i][j].set_xlabel(\"Number of Nodes removed\")\n", + " ax[i][j].set_ylabel(\"Porportion of nodes in Core\")\n", + " ax[i][j].legend(loc=\"best\")\n", + "fig.suptitle(\"Random Attack on Barabasi Albert Model (n, m)\", fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "id": "d434d77e", + "metadata": {}, + "source": [ + "# Exercise 7b)" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "id": "553a7f9a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 2018 nodes and 2930 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Random Attack on protein.elist')" + ] + }, + "execution_count": 83, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "path = './../../../network_course/data/'\n", + "G = nx.read_edgelist(path + 'protein.edgelist.txt', nodetype=int)\n", + "print(nx.info(G))\n", + "attack = Attack(G)\n", + "\n", + "x_r, y_r = attack.random()\n", + "plt.plot(x_r, y_r, marker='o', label=\"protein.elist\")\n", + "plt.xlabel(\"Number of nodes removed\")\n", + "plt.ylabel(\"Porportion of nodes in core\")\n", + "plt.legend(loc='best')\n", + "plt.title(\"Random Attack on protein.elist\", fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "id": "af3a7c1d", + "metadata": {}, + "source": [ + "# Exercise 7c)" + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "id": "e7c3e3c7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0.98, 'Random Attack on Erdos-Renyi Network (n, p)')" + ] + }, + "execution_count": 104, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x576 with 4 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ns = [100, 1000]\n", + "ps = [0.1, 0.5]\n", + "\n", + "fig, ax = plt.subplots(2, 2, figsize=(10, 8))\n", + "for i, n in enumerate(ns):\n", + " for j, p in enumerate(ps):\n", + " G = nx.generators.random_graphs.binomial_graph(n, p)\n", + " attack = Attack(G)\n", + " avrg_y = np.zeros(len(attack.num_nodes_removed))\n", + " for _ in range(100):\n", + " x_r, y_r = attack.random()\n", + " avrg_y += np.array(y_r)\n", + " \n", + " marker = '.'\n", + " if j == 1:\n", + " marker='o'\n", + " ax[i][j].plot(x_r, avrg_y/100, marker=marker, label=f\"(n, p) = ({n}, {p})\")\n", + " ax[i][j].set_xlabel(\"Number of Nodes removed\")\n", + " ax[i][j].set_ylabel(\"Porportion of nodes in Core\")\n", + " ax[i][j].legend(loc=\"best\")\n", + "fig.suptitle(\"Random Attack on Erdos-Renyi Network (n, p)\", fontsize=16)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.9.9" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh7/src/.ipynb_checkpoints/main_paper-checkpoint.ipynb b/sesh7/src/.ipynb_checkpoints/main_paper-checkpoint.ipynb @@ -0,0 +1,6 @@ +{ + "cells": [], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh7/src/ex_71.png b/sesh7/src/ex_71.png Binary files differ. diff --git a/sesh7/src/main.ipynb b/sesh7/src/main.ipynb @@ -0,0 +1,294 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "e1d43e31", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import networkx as nx\n", + "import itertools\n", + "import random\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "974f553a", + "metadata": {}, + "outputs": [], + "source": [ + "class Attack:\n", + " def __init__(self, G, steps=25):\n", + " self.G = G\n", + " self.steps = steps\n", + " self.N = G.number_of_nodes()\n", + " self.M = self.N // self.steps\n", + " self.num_nodes_removed = range(0, self.N, self.M)\n", + " \n", + " def random(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_to_remove = random.sample(list(C.nodes), self.M)\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions\n", + "\n", + " def betweenness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " betweenness = nx.centrality.betweenness_centrality(C)\n", + " nodes_sorted_by_betweenness= sorted(C.nodes, key=betweenness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_betweenness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def degree(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " nodes_sorted_by_degree = sorted(C.nodes, key=C.degree, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_degree[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions \n", + "\n", + " def closeness(self):\n", + " C = self.G.copy()\n", + " random_attack_core_proportions = []\n", + " for nodes_removed in self.num_nodes_removed:\n", + " # Measure the relative size of the network core\n", + " core = sorted(nx.connected_components(C), key = len, reverse=True)[0] # mistake in notebook 6\n", + " core_proportion = len(core) / self.N\n", + " random_attack_core_proportions.append(core_proportion)\n", + "\n", + " # If there are more than M nodes, select M nodes at random and remove them\n", + " if C.number_of_nodes() > self.M:\n", + " closeness = nx.centrality.closeness_centrality(C)\n", + " nodes_sorted_by_closeness = sorted(C.nodes, key=closeness.get, reverse=True)\n", + " nodes_to_remove = nodes_sorted_by_closeness[:self.M]\n", + " C.remove_nodes_from(nodes_to_remove)\n", + " return self.num_nodes_removed, random_attack_core_proportions " + ] + }, + { + "cell_type": "markdown", + "id": "dc8fce39", + "metadata": {}, + "source": [ + "# Exercise 7a) Barabasi-Albert-Model" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "id": "5d87dc35", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0.98, 'Random Attack on Barabasi Albert Model (n, m)')" + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 720x576 with 4 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ns = [100, 1000]\n", + "ms = [2, 5]\n", + "fig, ax = plt.subplots(2, 2, figsize=(10, 8))\n", + "for i, n in enumerate(ns):\n", + " for j, m in enumerate(ms):\n", + " marker = '.'\n", + " if j == 1:\n", + " marker='o'\n", + " G = nx.generators.random_graphs.barabasi_albert_graph(n, m)\n", + " attack = Attack(G)\n", + " ax[i][j].plot(*attack.random(), marker=marker, label=f\"(n, m) = ({n}, {m})\")\n", + " ax[i][j].set_xlabel(\"Number of Nodes removed\")\n", + " ax[i][j].set_ylabel(\"Porportion of nodes in Core\")\n", + " ax[i][j].legend(loc=\"best\")\n", + "fig.suptitle(\"Random Attack on Barabasi Albert Model (n, m)\", fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "id": "d434d77e", + "metadata": {}, + "source": [ + "# Exercise 7b)" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "id": "553a7f9a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Graph with 2018 nodes and 2930 edges\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'Random Attack on protein.elist')" + ] + }, + "execution_count": 83, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "path = './../../../network_course/data/'\n", + "G = nx.read_edgelist(path + 'protein.edgelist.txt', nodetype=int)\n", + "print(nx.info(G))\n", + "attack = Attack(G)\n", + "\n", + "x_r, y_r = attack.random()\n", + "plt.plot(x_r, y_r, marker='o', label=\"protein.elist\")\n", + "plt.xlabel(\"Number of nodes removed\")\n", + "plt.ylabel(\"Porportion of nodes in core\")\n", + "plt.legend(loc='best')\n", + "plt.title(\"Random Attack on protein.elist\", fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "id": "af3a7c1d", + "metadata": {}, + "source": [ + "# Exercise 7c)" + ] + }, + { + "cell_type": "code", + "execution_count": 104, + "id": "e7c3e3c7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 0.98, 'Random Attack on Erdos-Renyi Network (n, p)')" + ] + }, + "execution_count": 104, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 720x576 with 4 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "ns = [100, 1000]\n", + "ps = [0.1, 0.5]\n", + "\n", + "fig, ax = plt.subplots(2, 2, figsize=(10, 8))\n", + "for i, n in enumerate(ns):\n", + " for j, p in enumerate(ps):\n", + " G = nx.generators.random_graphs.binomial_graph(n, p)\n", + " attack = Attack(G)\n", + " avrg_y = np.zeros(len(attack.num_nodes_removed))\n", + " for _ in range(100):\n", + " x_r, y_r = attack.random()\n", + " avrg_y += np.array(y_r)\n", + " \n", + " marker = '.'\n", + " if j == 1:\n", + " marker='o'\n", + " ax[i][j].plot(x_r, avrg_y/100, marker=marker, label=f\"(n, p) = ({n}, {p})\")\n", + " ax[i][j].set_xlabel(\"Number of Nodes removed\")\n", + " ax[i][j].set_ylabel(\"Porportion of nodes in Core\")\n", + " ax[i][j].legend(loc=\"best\")\n", + "fig.suptitle(\"Random Attack on Erdos-Renyi Network (n, p)\", fontsize=16)" + ] + } + ], + 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\"ex_71.png\")\n", + "plot(p)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8f32cf49", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 1.6.3", + "language": "julia", + "name": "julia-1.6" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/sesh7/tex/ex_71.png b/sesh7/tex/ex_71.png Binary files differ. diff --git a/sesh7/tex/main.pdf b/sesh7/tex/main.pdf Binary files differ. diff --git a/sesh7/tex/main.tex b/sesh7/tex/main.tex @@ -0,0 +1,175 @@ +\documentclass[a4paper]{article} + + +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{mathptmx} + +%\usepackage{ngerman} % Sprachanpassung Deutsch + +\usepackage{graphicx} +\usepackage{geometry} +\geometry{a4paper, top=15mm} + +\usepackage{subcaption} +\usepackage[shortlabels]{enumitem} +\usepackage{amssymb} +\usepackage{amsthm} +\usepackage{mathtools} +\usepackage{braket} +\usepackage{bbm} +\usepackage{graphicx} +\usepackage{float} +\usepackage{yhmath} +\usepackage{tikz} +\usetikzlibrary{patterns,decorations.pathmorphing,positioning} +\usetikzlibrary{calc,decorations.markings} + +\usepackage[backend=biber, sorting=none]{biblatex} \addbibresource{uni.bib} + +\usepackage[framemethod=TikZ]{mdframed} + +\tikzstyle{titlered} = + [draw=black, thick, fill=white,% + text=black, rectangle, + right, minimum height=.7cm] + + +\usepackage[colorlinks=true,naturalnames=true,plainpages=false,pdfpagelabels=true]{hyperref} +\usepackage[parfill]{parskip} +\usepackage{lipsum} +\newtheorem{definition}[section]{Definition} + + +\usepackage{tcolorbox} +\tcbuselibrary{skins,breakable} + +\pagestyle{myheadings} + +\markright{Popović\hfill 6-th Exercise \hfill} + + +\title{University of Vienna\\ Faculty of Mathematics\\ + \vspace{1.25cm}Seminar: Introduction to complex network analysis \\ 6-th +Exercise +} +\author{Milutin Popović} +\begin{document} +\maketitle + +\section{Exercise 7} +\subsection{Bianconi-Barabasi model and network failure} +Consider a Bianconi-Barabasi model with two fitness values $\eta = 1$ and +$\eta = a$ where $0 \leq a \leq 1$, with a fitness distribution +\begin{align} + \varrho(\eta) = \frac{1}{2} \delta (\eta - 1) + \frac{1}{2} \delta (\eta + - a), +\end{align} +where $\delta(\eta)$ is the Dirac delta distribution. + +We know that the dynamic epxonent $\beta(\eta)$ satisfies +\begin{align} + \beta(\eta) = \frac{\eta}{C}, +\end{align} +where +\begin{align}\label{eq: c} + C = \in \varrho(\eta) \frac{\eta}{1-\beta(\eta)} d\eta. +\end{align} +To calculate $C$ we plug $\varrho(\eta)$ into equation \ref{eq: c} +\begin{align} + C &= \frac{1}{2}\left( + \int \delta(\eta - 1) \frac{\eta}{1-\beta(\eta)}+ + \int \delta(\eta - a) \frac{\eta}{a-\beta(\eta)} + \right) =\\ + &= \frac{1}{2} \left(\frac{1}{1-\beta(1)} + \frac{1}{1-\beta(a)}\right). +\end{align} +Into the calculation we substitute $\beta(\eta)$, thereby getting +\begin{align} + C = \frac{1}{2} \left(\frac{C}{C-1} + \frac{Ca}{C-a}\right), +\end{align} +this expression has two solutions +\begin{align} + C_1 &= \frac{1}{4} \left(\sqrt{9a^2 - 14a + 9} +3a +3 \right), \\ + C_2 &= \frac{1}{4} \left(-\sqrt{9a^2 - 14a + 9} +3a +3 \right). +\end{align} +We choose $C = C_1$ because +\begin{align} + C = C_1 = \frac{1}{4} \left(\sqrt{9a^2 - 14a + 9} +3a +3 \right) = + \begin{cases} + \frac{3}{2} \;\;\;\;\; \text{for} \;\;\; a=0 \\ + 2 \;\;\;\;\; \text{for} \;\;\; a=1 + \end{cases} +\end{align} +satisfies to the calculation of the reduced model for $a = 0$, which is the +Barabasi-Albert model. Thus the stationary $p_k$ degree distribution can be +calculated +\begin{align} + p_k &~ C\int d\eta \frac{\varrho(\eta)}{\eta} \left(\frac{m}{k} + \right)^{\frac{C}{\eta} +1} =\\ + &= \frac{C}{2} \left(\frac{m}{k}\right) \left(\left(\frac{m}{k}\right)^C + \frac{1}{4} + \left(\frac{m}{k}\right)^{\frac{C}{a}} \right) +\end{align} +Thereby the degree exponent $\gamma$ is estimated to be around +\begin{align} + \gamma \simeq C + 1 +\end{align} +Which agrees with the boundaries $a=0$ and $a=1$. The figure below shows the +relations +\begin{figure}[H] + \centering + \includegraphics[width=\textwidth]{./ex_71.png} + \caption{Constant $C$ and degree exponent $\gamma$ against $0\leq a \leq$} +\end{figure} +\subsection{The Breakdown Threshold} +The breakdown threshold $f_c$ of networks with a given degree distribution +$p_k$ can be written as +\begin{align} + f_c = 1- \frac{1}{\kappa - 1} \;\;\;\;\; \kappa = \frac{\langle k^2 + \rangle}{\langle k \rangle}, +\end{align} +For Scale Erdős Rényi networks the distribution is +\begin{align} + p_k = \begin{bmatrix}N \\ k\end{bmatrix} p^k (1-p)^{N-k}, +\end{align} +with $N$ number of nodes for a node with degree $k$ and probability of +connectivity $p$. Thereby we can calculate the first and second moment of the +degree $\langle k^m \rangle$ for $m = 1, 2$ just by extending the summation +to the continuum +\begin{align} + \langle k \rangle &= \int_0^N k p_k dk = Np\\ + \langle k^2 \rangle &= \int_0^N k^2 p_k dk = p(1-p)N + p^2N^2.\\ +\end{align} +Thereby the degree dynamics is +\begin{align} + \kappa = 1+(N-1)p, +\end{align} +and the for the breakdown threshold +\begin{align} + f_c = 1 - \frac{1}{(N-1)p} \underset{N\rightarrow + \infty}{{\longrightarrow}} 1 +\end{align} + +For the scale free network we have a exponential distribution +\begin{align} + p(k) = c \cdot k^{-\gamma}. +\end{align} +We calculated the degree dynamics $\kappa$ in exercise 5, with +$k_{\text{max}} = k_{\text{min}} N^{\frac{1}{N-\gamma}}$ we have the +following +\begin{align} + \kappa = k_{\text{min}}\frac{2- \gamma}{3-\gamma} + \frac{N^{\frac{3-\gamma}{\gamma-1}} - 1}{N^{\frac{2-\gamma}{\gamma-1}} - + 1} \;\;\;\; \underset{N\rightarrow \infty}{{\longrightarrow}} \;\; \infty +\end{align} +thereby the breakdown threshold is +\begin{align} + f_c = 1 - \frac{1}{k_{\text{min}}\frac{2- \gamma}{3-\gamma} + \frac{N^{\frac{3-\gamma}{\gamma-1}} - 1}{N^{\frac{2-\gamma}{\gamma-1}} - + 1} - 1} \;\;\;\; \underset{N\rightarrow \infty}{{\longrightarrow}} \;\; 1 +\end{align} + +\nocite{code} +\nocite{barabasi2016network} +\printbibliography + +\end{document} diff --git a/sesh7/tex/uni.bib b/sesh7/tex/uni.bib @@ -0,0 +1,16 @@ +@online{code, + author = {Popovic Milutin}, + title = {Git Instance, Introduction to complex network analysis}, + urldate = {2021-10-10}, + url = {git://popovic.xyz/network_ana.git}, +} + +@book{barabasi2016network, + title={Network Science}, + author={Barab{\'a}si, A.L. and P{\~A}3sfai, M.{\~A}.}, + isbn={9781107076266}, + lccn={2016439537}, + url={https://books.google.at/books?id=iLtGDQAAQBAJ}, + year={2016}, + publisher={Cambridge University Press} +}
