{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# CS579: Lecture 04 \n",
"\n",
"**Small Worlds** \n",
"*[Dr. Aron Culotta](http://cs.iit.edu/~culotta)* \n",
"*[Illinois Institute of Technology](http://iit.edu)*"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"**Milgram's experiment:**\n",
"\n",
"\n",
"\n",
"[Source](http://en.wikipedia.org/wiki/Small-world_experiment)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"** 6-degrees of Kevin Bacon**\n",
"\n",
"[Source](http://readingeagle.com/life/article/six-degress-of-kevin-bacon-a-game-changer#.VA35Z7ywKcI)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"\n",
"\n",
"[Source](https://github.com/iit-cs579/main/blob/master/read/ek-20.pdf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** What does it mean for a world to be small? **\n",
"\n",
"- Sparsely connected (i.e., few edges)\n",
"- Despite the above, the path between two nodes is usually short\n",
"\n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"More concretely:\n",
"\n",
"$$ L \\propto \\log N $$\n",
"\n",
"- $L$: average shortest path between any two nodes\n",
"- $N$: number of nodes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"
\n",
"- Milgram's [original paper](http://www.jstor.org/stable/2786545) on small worlds\n",
"- Is the global friendship network really a small world? See [rebuttal paper](kleinfeld02.pdf)\n",
"\n",
"\n",
"
\n",
"\n",
"- Only a small fraction of Milgram's letters actually made it to their destination\n",
"- Experiments to reproduce with email also have low success rates\n",
"- Success rates vary by demographics of person (e.g., income, ethnicity, ...)\n",
"- **Search** is an imporant problem\n",
" - Given that we only have local information, how do we decide whom \n",
" to send the letter to?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Generative models of graphs**\n",
"\n",
"To understand what makes some graphs \"small worlds\" and some not, \n",
"we will consider alternative ways graphs could form.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Option 1: Random Graphs**\n",
"\n",
"- Create $N$ nodes\n",
"- For each pair of nodes, draw an edge with probability $p$."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"created random graph with p=0.5 N=20 E=102\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create a random graph with $n$ nodes, where each pair of nodes is linked at random with probability $p$.\n",
"%matplotlib inline\n",
"from itertools import combinations # combinations([1,2,3], 2) -> [(1, 2), (1, 3), (2, 3)]\n",
"import matplotlib.pyplot as plt\n",
"import networkx as nx\n",
"import random\n",
"\n",
"def random_graph(n, p, seed=1234):\n",
" G = nx.Graph()\n",
" random.seed(seed)\n",
" G.add_nodes_from(range(n))\n",
" for edge in combinations(range(n), 2):\n",
" if random.random() < p:\n",
" G.add_edge(edge[0], edge[1])\n",
" print('created random graph with p=%g N=%d E=%d' \n",
" % (p, len(G.nodes()), len(G.edges())))\n",
" return G\n",
"\n",
"G = random_graph(20, .5)\n",
"nx.draw(G)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Graph density=0.537\n"
]
}
],
"source": [
"def total_edges(N):\n",
" return N * (N - 1) / 2\n",
"\n",
"print('Graph density=%.3f' % \n",
" (1. * len(G.edges()) / total_edges(len(G.nodes()))))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"created random graph with p=0.1 N=20 E=22\n",
"created random graph with p=0.3 N=20 E=59\n",
"created random graph with p=0.5 N=20 E=102\n",
"created random graph with p=0.9 N=20 E=175\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot graphs with different $p$ values:\n",
"for p in [.1, .3, .5, .9]:\n",
" plt.figure()\n",
" plt.axis('off')\n",
" nx.draw(random_graph(20, p))\n",
" plt.title('random graph, p=%.1f' % p)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Is this a realistic model of actual networks?\n",
"\n",
"Compare with the important properties of graphs:\n",
"- Degree distribution: $P(k)$\n",
"- Clustering coefficient: $C$\n",
"- Node distance: $D$"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# Let's plot the degree distribution again.\n",
"from collections import Counter\n",
"import numpy as np\n",
"\n",
"def plot_degree_dist(G, title):\n",
" degrees = list(dict(nx.degree(G)).values())\n",
" degree_counts = Counter(degrees)\n",
" \n",
" p_k = [(degree, count / len(G.nodes()))\n",
" for degree, count in degree_counts.items()]\n",
" p_k = sorted(p_k)\n",
" ks = [x[0] for x in p_k]\n",
" x_pos = range(len(ks))\n",
" plt.xlabel('$k$')\n",
" plt.ylabel('$P(k)$')\n",
" plt.bar(x_pos, [x[1] for x in p_k], align='center', alpha=0.4)\n",
" plt.locator_params(nbins=10) \n",
" plt.title('Degree Distribution for %s (mean=%.2f, N=%d)' \n",
" % (title, np.mean(degrees), len(G.nodes())))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"created random graph with p=0.1 N=100 E=467\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"G = random_graph(100, .1)\n",
"plot_degree_dist(G, 'random graph')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"import urllib\n",
"# Fetch co-author network from http://snap.stanford.edu/data/ca-GrQc.html\n",
"urllib.request.urlretrieve(\"http://snap.stanford.edu/data/ca-GrQc.txt.gz\", \"ca-GrQc.txt.gz\")\n",
"coauthor = nx.read_edgelist('ca-GrQc.txt.gz')"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot the citation degree distribution.\n",
"plot_degree_dist(coauthor, 'coauthor network')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"created random graph with p=0.01 N=5242 E=137210\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"random_g = random_graph(len(coauthor.nodes()), .01)\n",
"plot_degree_dist(random_g, 'random graph (p=%.1f)' % .01)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Random degree distribution is normal, but real degree distribution is skewed. **\n",
"\n",
"**Average degree roughly 10x higher in random graph! (5.53 vs. 52.35)**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# Now let's compare the distribution of clustering coefficients.\n",
"def plot_clustering_dist(G, title):\n",
" clustering_coef = list(nx.clustering(G).values())\n",
" plt.hist(list(clustering_coef), alpha=0.4, bins=20)\n",
" plt.xlabel('$C$')\n",
" plt.ylabel('count')\n",
" plt.title('Clustering Coefficient for %s (mean=%.2f)' % \n",
" (title, np.mean(clustering_coef)))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_clustering_dist(coauthor, 'coauthor')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_clustering_dist(random_g, 'random')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Real network: bi-modal distribution; random network: unimodal normal distribution **\n",
"\n",
"**Real network has 50x more clustering, on average. (.53 vs .01)**"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Finally, let's compare the average shortest path (distance)\n",
"# This takes a while since all-pairs-shortest-paths is =~ $O(|V|^3)$\n",
"# See http://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm\n",
"# and https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm\n",
"def get_shortest_paths(G):\n",
" lengths = nx.all_pairs_shortest_path_length(G)\n",
" return [np.mean(list(paths.values()))\n",
" for paths in dict(lengths).values()]\n",
"\n",
"def plot_shortest_paths_dist(G, title):\n",
" means = get_shortest_paths(G)\n",
" plt.hist(means, alpha=0.4)\n",
" plt.xlabel('avg. shortest path')\n",
" plt.ylabel('count')\n",
" plt.title('Shortest Paths for %s (mean=%.2f)' \n",
" % (title, np.mean(means)))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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mVprDw8zMSmtaeEiaKmmlpPmFtu9IelDSPEnXSBqc21skvSxpbu5+WJjm3ZLuk7RQ0vckqVk1m5lZY5q55zENOLiu7WZgr4jYG/gT8LXCsEciYnTuTii0XwAcB4zKXf08zcyshzUtPCLiduDpurbfRMSa/HImMLyzeUjaERgUETMjIoBLgMObUa+ZmTWuynMenwVuLLzeRdI9km6TtH9uGwYsKYyzJLe1S9JkSbMlzW5ra+v+is3MDKgoPCR9HVgDXJqblgEjI2If4F+AyyQNKjvfiJgSEa0R0Tp06NDuK9jMzNYxsKcXKGkS8FHgwHwoiohYDazO/XMkPQLsBixl3UNbw3ObmZlVqEf3PCQdDHwFOCwiXiq0D5U0IPe/jXRi/NGIWAY8J2m/fJXV0cC1PVmzmZm9UdP2PCRNBw4AhkhaApxGurpqM+DmfMXtzHxl1fuBMyT9BfgrcEJE1E62f5505dYWpHMkxfMkZmZWgaaFR0RMaKf5og7GvRq4uoNhs4G9urE0MzPbQP6GuZmZlebwMDOz0hweZmZWmsPDzMxKc3iYmVlpDg8zMyvN4WFmZqU5PMzMrDSHh5mZlebwMDOz0hweZmZWmsPDzMxKc3iYmVlpDYWHpFsaaTMzs41Dp7dkl7Q5sCXpmRzbAsqDBtHJs8TNzKx/6+p5HscDXwR2Aubweng8B/ygiXWZmVkv1ml4RMS5wLmS/ikivt9DNZmZWS/X0JMEI+L7kv4OaClOExGXNKkuMzPrxRoKD0k/BXYF5gKv5eYAHB5mZhuhRp9h3grsGRFRZuaSpgIfBVZGxF65bTvgCtJezCJgXESskiTgXOBQ4CVgUkTcnaeZCPxrnu03I+LiMnWYmVn3avR7HvOBt67H/KcBB9e1nQLcEhGjgFvya4BDgFG5mwxcAGvD5jRgDLAvcFq+8svMzCrS6J7HEOB+SXcCq2uNEXFYZxNFxO2SWuqaxwIH5P6LgRnAV3P7JXnvZqakwZJ2zOPeHBFPA0i6mRRI0xus3czMulmj4XF6Ny5zh4hYlvuXAzvk/mHA4sJ4S3JbR+1vIGkyaa+FkSNHdmPJZmZW1OjVVrc1Y+EREZJKnUfpYn5TgCkAra2t3TZfMzNbV6O3J3le0nO5e0XSa5KeW89lrsiHo8g/V+b2pcCIwnjDc1tH7WZmVpGGwiMitomIQRExCNgC+Afg/PVc5nXAxNw/Ebi20H60kv2AZ/PhrV8DH5a0bT5R/uHcZmZmFSl9V91Ifgl8pKtxJU0H7gB2l7RE0rHAt4EPSXoYOCi/BrgBeBRYCFwIfD4v72ng34G7cndG7eS5mZlVo9EvCX6i8HIT0vc+XulquoiY0MGgA9sZN4ATO5jPVGBq15WamVlPaPRqq48V+teQvtw3tturMTOzPqHRq62OaXYhZmbWdzR6tdVwSddIWpm7qyUNb3ZxZmbWOzV6wvwnpKuhdsrdr3KbmZlthBoNj6ER8ZOIWJO7acDQJtZlZma9WKPh8ZSkz0gakLvPAE81szAzM+u9Gg2PzwLjSPeiWgZ8EpjUpJrMzKyXa/RS3TOAiRGxCtbeJv0sUqiYmdlGptE9j71rwQFrv/W9T3NKMjOz3q7R8Nik+ACmvOfR6F6LmZn1M40GwNnAHZJ+nl9/CjizOSWZmVlv1+g3zC+RNBv4YG76RETc37yyqnXZrCcqWe4RY/wAKzPrGxo+9JTDot8GhpmZNa70LdnNzMwcHmZmVprDw8zMSnN4mJlZaQ4PMzMrzeFhZmal9Xh4SNpd0txC95ykL0o6XdLSQvuhhWm+JmmhpIckfaSnazYzs3X1+C1GIuIhYDSApAHAUuAa4BjguxFxVnF8SXsC44F3kh5E9VtJu0XEaz1auJmZrVX1YasDgUci4vFOxhkLXB4RqyPiMWAhsG+PVGdmZu2qOjzGA9MLr0+SNE/S1MKNGIcBiwvjLMltbyBpsqTZkma3tbU1p2IzM6suPCS9CTgMqN1s8QJgV9IhrWWkmzGWEhFTIqI1IlqHDvVTcs3MmqXKPY9DgLsjYgVARKyIiNci4q/Ahbx+aGopMKIw3fDcZmZmFakyPCZQOGQlacfCsI8D83P/dcB4SZtJ2gUYBdzZY1WamdkbVPJAJ0lbAR8Cji80/6ek0UAAi2rDImKBpCtJd/RdA5zoK63MzKpVSXhExIvA9nVtR3Uy/pn44VNmZr1G1VdbmZlZH+TwMDOz0hweZmZWmsPDzMxKc3iYmVlpDg8zMyvN4WFmZqU5PMzMrDSHh5mZlebwMDOz0hweZmZWmsPDzMxKc3iYmVlpDg8zMyvN4WFmZqU5PMzMrDSHh5mZlebwMDOz0ip5DC2ApEXA88BrwJqIaJW0HXAF0EJ6jvm4iFglScC5wKHAS8CkiLi7irrN+qrLZj1R2bKPGDOysmVbc1S95/G/I2J0RLTm16cAt0TEKOCW/BrgEGBU7iYDF/R4pWZmtlbV4VFvLHBx7r8YOLzQfkkkM4HBknasokAzM6s2PAL4jaQ5kibnth0iYlnuXw7skPuHAYsL0y7JbeuQNFnSbEmz29ramlW3mdlGr7JzHsD7ImKppLcAN0t6sDgwIkJSlJlhREwBpgC0traWmtbMzBpX2Z5HRCzNP1cC1wD7Aitqh6Pyz5V59KXAiMLkw3ObmZlVoJLwkLSVpG1q/cCHgfnAdcDEPNpE4Nrcfx1wtJL9gGcLh7fMzKyHVXXYagfgmnQFLgOByyLiJkl3AVdKOhZ4HBiXx7+BdJnuQtKlusf0fMlmZlZTSXhExKPAu9ppfwo4sJ32AE7sgdLMzKwBve1SXTMz6wMcHmZmVprDw8zMSnN4mJlZaQ4PMzMrzeFhZmalOTzMzKw0h4eZmZXm8DAzs9IcHmZmVprDw8zMSnN4mJlZaQ4PMzMrzeFhZmalOTzMzKw0h4eZmZXm8DAzs9IcHmZmVprDw8zMSuvx8JA0QtKtku6XtEDSybn9dElLJc3N3aGFab4maaGkhyR9pKdrNjOzdQ2sYJlrgC9FxN2StgHmSLo5D/tuRJxVHFnSnsB44J3ATsBvJe0WEa/1aNVmZrZWj+95RMSyiLg79z8PPAAM62SSscDlEbE6Ih4DFgL7Nr9SMzPrSKXnPCS1APsAs3LTSZLmSZoqadvcNgxYXJhsCR2EjaTJkmZLmt3W1takqs3MrLLwkLQ1cDXwxYh4DrgA2BUYDSwDzi47z4iYEhGtEdE6dOjQbq3XzMxeV8U5DyRtSgqOSyPiFwARsaIw/ELg+vxyKTCiMPnw3NbvXDbricqWfcSYkZUt28z6niquthJwEfBARPxXoX3HwmgfB+bn/uuA8ZI2k7QLMAq4s6fqNTOzN6piz+O9wFHAfZLm5rZTgQmSRgMBLAKOB4iIBZKuBO4nXal1oq+0MjOrVo+HR0T8HlA7g27oZJozgTObVpSZmZXib5ibmVlpDg8zMyvN4WFmZqU5PMzMrDSHh5mZlebwMDOz0hweZmZWmsPDzMxKc3iYmVlpDg8zMyvN4WFmZqVVckt2M9u4VPW4AT9qoHm852FmZqV5z8MqVeUDsMxs/XnPw8zMSnN4mJlZaQ4PMzMrzeFhZmal+YS5mfVbVV6Q0d8vE+4zex6SDpb0kKSFkk6puh4zs41ZnwgPSQOA84BDgD2BCZL2rLYqM7ONV185bLUvsDAiHgWQdDkwFri/0qr6EX/fwqx79fdv1feV8BgGLC68XgKMqR9J0mRgcn75gqSH1nN5Q4A/r+e0vVV/XCfon+vVH9cJ+ud69bp1OnLDJt+50RH7Sng0JCKmAFM2dD6SZkdEazeU1Gv0x3WC/rle/XGdoH+uV39cp0b1iXMewFJgROH18NxmZmYV6CvhcRcwStIukt4EjAeuq7gmM7ONVp84bBURaySdBPwaGABMjYgFTVzkBh/66oX64zpB/1yv/rhO0D/Xqz+uU0MUEVXXYGZmfUxfOWxlZma9iMPDzMxKc3gU9MdboEgaIelWSfdLWiDp5Kpr6i6SBki6R9L1VdfSXSQNlnSVpAclPSDpb6uuaUNJ+uf8tzdf0nRJm1dd0/qQNFXSSknzC23bSbpZ0sP557ZV1tiTHB5ZP74FyhrgSxGxJ7AfcGI/WS+Ak4EHqi6im50L3BQRewDvoo+vn6RhwBeA1ojYi3TBy/hqq1pv04CD69pOAW6JiFHALfn1RsHh8bq1t0CJiFeB2i1Q+rSIWBYRd+f+50kfRsOqrWrDSRoO/D3w46pr6S6S3gy8H7gIICJejYhnqq2qWwwEtpA0ENgSeLLietZLRNwOPF3XPBa4OPdfDBzeo0VVyOHxuvZugdLnP2SLJLUA+wCzqq2kW5wDfAX4a9WFdKNdgDbgJ/lw3I8lbVV1URsiIpYCZwFPAMuAZyPiN9VW1a12iIhluX85sEOVxfQkh8dGQtLWwNXAFyPiuarr2RCSPgqsjIg5VdfSzQYCfwNcEBH7AC/Sxw+D5HMAY0nBuBOwlaTPVFtVc0T63sNG890Hh8fr+u0tUCRtSgqOSyPiF1XX0w3eCxwmaRHp8OIHJf2s2pK6xRJgSUTU9gyvIoVJX3YQ8FhEtEXEX4BfAH9XcU3daYWkHQHyz5UV19NjHB6v65e3QJEk0jH0ByLiv6qupztExNciYnhEtJB+T/8/Ivr81mxELAcWS9o9Nx1I33/swBPAfpK2zH+LB9LHLwKocx0wMfdPBK6tsJYe1SduT9ITKrgFSk95L3AUcJ+kubnt1Ii4ocKarGP/BFyaN2AeBY6puJ4NEhGzJF0F3E268u8e+ugtPSRNBw4AhkhaApwGfBu4UtKxwOPAuOoq7Fm+PYmZmZXmw1ZmZlaaw8PMzEpzeJiZWWkODzMzK83hYWZmpTk8zEqS1FK8s+p6zuPw9b1BpaTRkg7dkOXXze/UQv8Gr5ttHBweZj0s3yDwcNLdm9fHaKDbwgM4tetRzNbl8LA+TdIvJc3Jz4uYnNtOkPSdwjiTJP0g9/9bfmbL7/OzJb7cxfzfKelOSXMlzZM0Kg8aIOnCvNzfSNoijz9a0sw87jW15ztImiHpHEmzga8ChwHfyfPdNXc35XX5naQ98nSfys/BuFfS7fnLg2cAn87Tfrqu3kmSrs3Le1jSaV28V98m3fF2rqRLO1s3s3VEhDt3fbYDtss/twDmA9sDQ0m316+NcyPwPuA9wFxgc2Ab4GHgy13M//vAkbn/TXk5LaRvS4/O7VcCn8n984AP5P4zgHNy/wzg/MJ8pwGfLLy+BRiV+8eQbrkCcB8wLPcPzj8nAT/ooN5JpLvXbl94T1o7eq/y6xcK03e4bu7cFTvveVhf9wVJ9wIzSTe2HBURbcCjkvaTtD2wB/AH0q1aro2IVyI92+RXDcz/DuBUSV8Fdo6Il3P7YxFRu93LHKAlP49jcETcltsvJj2fo+aK9haQ73j8d8DP8y1kfgTsmAf/AZgm6TjSbXMacXNEPJVr/QUpOKGd96qD6d+wbg0u1zYivreV9VmSDiDdtfVvI+IlSTNIexWQ7rY7DngQuCYiIt2Xr5yIuEzSLNKDp26QdDzpnlOrC6O9Rtqa78qLHbRvAjwTEaPbWf4Jksbk5c+R9O5Gyq5/3cV7VW991s02Mt7zsL7szcCq/GG4B+kxuzXXkJ4jMYEUJJC24j8mafO8tf/RrhYg6W3AoxHxPdIdU/fuaNyIeBZYJWn/3HQUcFsHoz9POnRGpOerPCbpU3mZkvSu3L9rRMyKiG+QHhQ1ojhtBz6k9GztLUgn5v9A5+/VX/Jt+80a5vCwvuwmYKCkB0h3N51ZGxARq0i3/t45Iu7MbXeRbqE9j3Qe5D7gWVh7kv2EdpYxDpifDyftBVzSRU0TSSfC55Guijqjg/EuB/6P0hMDdwWOBI7Nh5UW8PojkL8j6b58+ewfgXuBW4E92zthnt1Jen7LPODqiJjd2XtFusvtvMIJc7Mu+a66tlGRtHVEvCBpS+B2YHLkZ7z3B5ImkU6Qn1R1Lda/+ZyHbWym5C/nbQ5c3J+Cw6wnec/DzMxK8zkPMzMrzeFhZmalOTzMzKw0h4eZmZXm8DAzs9L+B/Uv8gvDDCaAAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# slow!\n",
"plot_shortest_paths_dist(coauthor, 'coauthor')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_shortest_paths_dist(random_g, 'random')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our definition of small world was:\n",
" \n",
"$$ L \\propto \\log N $$\n",
"\n",
"- $L$: average shortest path between any two nodes\n",
"- $N$: number of nodes\n",
"\n",
"We can empirically check this relationship by generating random graphs of increasingly large $N$ and plotting the growth of $L$.\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"created random graph with p=0.01 N=50 E=9\n",
"created random graph with p=0.01 N=100 E=43\n",
"created random graph with p=0.01 N=150 E=94\n",
"created random graph with p=0.01 N=200 E=182\n",
"created random graph with p=0.01 N=250 E=290\n",
"created random graph with p=0.01 N=300 E=431\n",
"created random graph with p=0.01 N=350 E=578\n",
"created random graph with p=0.01 N=400 E=786\n",
"created random graph with p=0.01 N=450 E=998\n",
"created random graph with p=0.01 N=500 E=1244\n",
"created random graph with p=0.01 N=550 E=1492\n",
"created random graph with p=0.01 N=600 E=1794\n",
"created random graph with p=0.01 N=650 E=2091\n",
"created random graph with p=0.01 N=700 E=2433\n",
"created random graph with p=0.01 N=750 E=2788\n",
"created random graph with p=0.01 N=800 E=3145\n",
"created random graph with p=0.01 N=850 E=3558\n",
"created random graph with p=0.01 N=900 E=3980\n",
"created random graph with p=0.01 N=950 E=4460\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import math\n",
"Ls = [] # mean shortest paths.\n",
"ns = [] # number of nodes.\n",
"for n in range(50,1000)[::50]:\n",
" Ls.append(np.mean(get_shortest_paths(random_graph(n, .01))))\n",
" ns.append(n)\n",
"\n",
"plt.plot(ns, Ls, 'bo', label='random graph')\n",
"plt.plot(ns, [math.log(n) for n in ns], label='log(N)')\n",
"plt.legend(loc='lower right')\n",
"plt.xlabel('N (number of nodes)')\n",
"plt.ylabel('L (mean shortest path)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Summary:** Random graphs are a poor match for degree distribution and clustering; close for distances.\n",
"\n",
"
\n",
"\n",
"**Option 2: $k$-Regular Graph**\n",
"\n",
"- Every node has degree $k$"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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kXnpEZBc8VJZ5GfdQSWd7NMkU34q0XOiN9Vv1VGWogXuPYUjb/H/cO4+I7EpQKw+4Ki406HSnSiFHUOsmFkxl3yQxthRXVGFv9uXb3tR5MzK5HPlVjVFW1bDz6ERElja8q1eDj2EGMLxLw4/jKCRRfKlHCht8jGurnoiI7Mm97q4ID/BEfZcbyGRAv0BPydzKAEik+LjqiYic2UsRaqgULvX6XJXCBVERagsnsm+SKD6ueiIiZ9apbTNoIoPgpqzbS7qbUg5NZBA6eknrKQ2SWNzCVU9E5Oyu3W98q/uUr5HJaie9P9+nLBWSKD6ueiIiKRjbyxsdvZphZVouvs66DBl+35QDqN2aTK/X4wHfuzH9sTDJTXrXSGKvzuKKKjzw1p4GFZ/U9rIjIsdWUlGF1KOF0BWVo0xvgIdKiaDWTVCw7xOczz6N9evXi44ojCQmvmurnnZmXqzXLQ1SXPVERI7tHnfXv9178+dOL0KtViM3NxdqtbQWtVwjicUtAFc9EREBQNOmTfHyyy9Dq9WKjiKMJE51XlOXvTqvqV31FCzJC8BE5JxKS0uhVqtx+PBh+Pr6io5jc5KZ+IDaC7+ayGC4KV0A863LTyYD3JQuLD0icjrNmjVDVFQU3nzzTdFRhJDUxHfNjh90GJewCY39e0Auk92w6kmlkMOM2mt6URFqya56IiLnduXKFfj7++PIkSPw9vYWHcemJFl8U6dOhUwmQ8zc+X+76ml4lzt/AjsRkaPSaDQoKSlBUlKS6Cg2JbniKy0tha+vLzIyMtC2bVvRcYiIhCkuLkZgYCDS09Ml9XooqWt8AJCUlIQhQ4ZI6h+ZiOjv3HvvvRg/fjwWLFggOopNSWriq6qqgo+PD7766it06tRJdBwiIuEuXbqEoKAgnDhxAm3atBEdxyYkNfFt3LgRoaGhLD0iot+0aNECL7zwAhYuXCg6is1IZuKrqalBhw4dsHz5cgwYMEB0HCIiu3HhwgWEhITg1KlTaN26teg4VieZie/LL7+ESqVC//79RUchIrIrrVq1wnPPPYeEhATRUWxCMhNf37598eKLL2L06NGioxAR2Z2ffvoJHTp0QGZmJlq2bCk6jlVJYuL77rvvcP78eYwYMUJ0FCIiu3TfffdhzJgxSExMFB3F6iQx8Q0fPhwPPfQQJk+eLDoKEZHdKiwsRMeOHZGVlQVPT0/RcazG6YsvNzcXvXr1Qn5+Ptzd3UXHISKya1FRUfDw8HDqe/ucvviioqLQvHlzxMfHi45CRGT3zp8/j86dOyMrKwv33nuv6DhW4dTFd+nSJQQGBkKn0zn9xVoiIkuZOHEiPD09nXZgcOrimzNnDoqKirBmzRrRUYiIHEZ+fj66du2KnJwcNG/eXHQci3Pa4vv111/h7e2Nb775BoGBgaLjEBE5lPHjx6NNmzaYO3eu6CgW57TFt2LFCuzcuRNbt24VHYWIyOHk5eWhZ8+eyM3NRbNmzvVcUqcsPpPJhICAACQnJ6NPnz6i4xAROaTnn38evr6+iI2NFR3Fopyy+D755BMsXboUBw4cEB2FiMhh5eTkoE+fPsjLy4OHh4foOBbjdDu3mM1mLFy4ENOmTRMdhYjIofn7++ORRx7B8uXLRUexKKeb+NLS0jBx4kRkZmZCLne6XicisimdToe+ffsiLy8PTZo0ER3HIpyuGRISEvDqq6+y9IiILCAoKAgDBw7EypUrRUexGKea+E6dOoUBAwYgPz8fKpVKdBwiIqdw6tQp9O/fH3l5eU6x9aNTjUWJiYmIjo5m6RERWVD79u0RHh6OpKQk0VEswmkmvh9//BGhoaHIzc11yp0GiIhEOnHiBAYNGoS8vDw0atRIdJwGcZqJb9myZXjmmWdYekREVhAaGoo+ffpg9erVoqM0mFNMfGVlZfDx8cGRI0fg7e0tOg4RkVNKT09HZGQk8vLy4ObmJjpOvTnFxLdmzRoMGjSIpUdEZEVhYWHo0aMH3n33XdFRGsThJ77q6mr4+flh27Zt6NKli+g4RERO7ciRI3jiiSeQm5vrsAsJHX7i27RpEwIDA1l6REQ20LVrV4SFheH9998XHaXeHHriM5vN6NixIxITEzF48GDRcYiIJOHw4cMYPnw4cnJy4OrqKjpOnTn0xPff//4XcrkcgwYNEh2FiEgyevTogfbt22PdunWio9SLQ098/fv3x7hx4/DMM8+IjkJEJCkHDx7E6NGjkZ2djbvuukt0nDpx2InvyJEjyMnJwahRo0RHISKSnN69eyMgIADr168XHaXOHHbiGzVqFLp3745XX31VdBQiIknav38/nn32WWRlZUGpVIqOc8cccuI7e/Ysdu3ahX//+9+ioxARSdaDDz4IHx8fbNy4UXSUOnHIiS86OhqNGzfGggULREchIpK0vXv34l//+hd0Oh0UCoXoOHfE4YqvpKQEarUap06dwn333Sc6DhGR5IWHh2P8+PEOs9DQ4U51rly5EkOHDmXpERHZiTlz5iA+Ph4mk0l0lDviUMVXWVmJFStW4LXXXhMdhYiIftOvXz94enoiJSVFdJQ74lDFt379enTv3h0hISGioxAR0W9kMhliY2MdZupzmOIzmUxITEzEtGnTREchIqI/efjhh9G0aVOkpqaKjnJbDlN827ZtQ/PmzfHQQw+JjkJERH9ybeqbN28eampqRMe5JYcoPrPZjISEBEybNg0ymUx0HCIi+huPPPII3NzcsGXLFtFRbskhiu/AgQO4fPkyhg4dKjoKERHdhEwmw5w5cxAXF2fXU59DFF9CQgKmTp0KFxcX0VGIiOgWhgwZAhcXF3z22Weio9yU3d/ArtPpEB4ejrNnz6JRo0ai4xAR0W1s3boVcXFxOHLkiF1enrL7iS8xMRFRUVEsPSIiB/HEE0+gpqYGX3zxhegof8uuJ76ioiKEhIQgJycH9957r+g4RER0hzZv3owFCxbg8OHDdjf12fXEt3z5cvzzn/9k6REROZihQ4dCr9fjv//9r+gof2G3E195eTl8fHzw3Xffwc/PT3QcIiKqo48//hiLFy/GwYMH7Wrqs9uJ77333kO/fv1YekREDuqpp55CWVkZdu7cKTrKDexy4jMYDFCr1UhNTUX37t1FxyEionr66KOP8M4772D//v12M/XZ5cT38ccfw8fHh6VHROTgnn76aRQXF2PPnj2io1xnd8X3x+3JiIjIsbm4uGDWrFmIi4sTHeU6uzvVuXPnTrzyyis4ceIE5HK762UiIqojo9GI4OBgrF27Fh269UbqkULoLpShTG+Eh0qBoFYeGNHVC/e4u9okj90V36BBgzB69GiMGzdOdBQiIrIQ7aoN2JheDFOLQABAlfH3vTxVCjnMACICPREVrkants2smsWuii89PR1DhgzBmTNn4Opqm+YnIiLr2nAoH/HbM6GvMgK3OJMnkwEqhQs0kUEY28vbanns6lxiYmIiJk+ezNIjInISGw7lQ7s9E3pDzS1LDwDMZqDSYIJ2eyY2HMq3Wia7mfjOnTuHLl264MyZM2jatKnoOERE1EAZBaUYtfYQKg2mOn+um9IFKRN6oaOX5U972s3Et3TpUowbN46lR0TkJFak5UJvrHvpAYDeaMLKtFwLJ6qlsMpRb6G4ouovK3raNVVifcqnSP9uv63jEBGRFRRXVGFv9mXU95yi2Qx8nXUZJRVVFl/tabPiyygoxYq0XOzNvgzgxhU9LqiBx7PLEb/3IqLCm1h9RQ8REVlX6pHCBh9DBiD1aCEm9rXs1pU2Kb7ai5s66I2mv21/E+SADNhx+iL2ZRdbfUUPERFZl+5C2Q0DTn3ojTXQFZVbKNHvrF5811b0VBpu/xfwxxU9AFh+REQOqkxvtNBxDBY5zh9ZdXFLRkEptNt1d1R6f1RpqIF2uw7HC0utlIyIiKzJQ2WZucpDpbTIcf7IqsVnryt6iIjIuoJaecBV0bCKUSnkCGrdxEKJfme14rPkih4iInIsw7t6NfgYZgDDuzT8OH9mteKz5IoeIiJyLPe6uyI8wBP1fQSfTAb0C/S0ysbVVis+e17RQ0RE1vdShBoqhUu9PlelcEFUhNrCiWpZrfjseUUPERFZX6e2zaCJDIKbsm5V46aUQxMZZJXtygArFp89r+ghIiLbGNvLG5rIYChQA5hvfRZQJqvdo1MTGeyYT2ew5xU9RERkO093uQ9V2xegp5cbXBVyqP7UDSqFHK4KOQaHtETKhF5Wv4fbajewD+/qhSW7sht0DGut6CEiItvZtGkTAj3dkPLyQJRUVCH1aCF0ReUo0xvgoVIiqHUTDO9iuyewW634rq3o2Zl5sV63NFhzRQ8REdmG2WxGYmIiEhISAAD3uLtafO/NurLqDez2uqKHiIhs43//+x9kMhkGDRokOsp1Vi0+e13RQ0REtpGQkIDXXnsNsvre0GcFNnkC++2eznA9DACV0oVPZyAicgJHjhzBk08+iTNnzkCptJ8V+jYpPgA4XliKlWm5+DrrMmSovTn9GpVCjiqDAe0U5Xj7P0M46REROYFRo0ahe/fuePXVV0VHuYHNiu+am63oCWtahUcHhuPMmTNo0oS3MBARObKzZ8+iW7duOHv2LDw8PETHuYHNi+9WxowZg9DQUMyYMUN0FCIiaoBJkyahUaNGWLBggegof2FXxXf69Gn069cPeXl5cHd3Fx2HiIjqoaSkBP7+/jh58iTuu+8+0XH+wqqrOusqJCQE4eHhSEpKEh2FiIjqadWqVXjyySftsvQAO5v4AOD48eMYNGgQzpw5g0aNGomOQ0REdVBZWQkfHx/s2bMHISEhouP8Lbua+ACgY8eO6NOnD9asWSM6ChER1dH69evRrVs3uy09wA4nPgA4duwYhgwZgry8PLi5uYmOQ0REd8BkMiE4OBhr165FeHi46Dg3ZXcTHwB07twZ3bp1w3vvvSc6ChER3aHPPvsMzZo1Q9++fUVHuSW7nPgA4Pvvv8ewYcOQm5sLV1duVE1EZO/69OmDKVOmYMSIEaKj3JJdTnwA0L17d4SGhmLdunWioxAR0W0cOHAAFy9exLBhw0RHuS27nfgA4ODBgxg9ejSys7Nx1113iY5DREQ38eSTT2LQoEGIiooSHeW27HbiA4DevXsjICAAycnJoqMQEdFN6HQ6HDx4EM8//7zoKHfEric+ANi/fz+effZZZGVl2dXu3kREVOvf//432rRpgzfeeEN0lDti98UHAP3798dzzz2H5557TnQUIiL6gwsXLiA4OBjZ2dnw9PQUHeeOOETxpaWlYcKECTh9+jQUCoXoOERE9BuNRoOrV69i5cqVoqPcMYcoPrPZjPDwcEycOBFjxowRHYeIiABUVFTA29sbhw4dglqtFh3njtn14pZrZDIZYmNjER8fD5PJJDoOEREBeO+999CvXz+HKj3AQYoPAAYMGIC7774bqampoqMQEUme0WjEkiVLMG3aNNFR6sxhik8mk2H27NmYN28eampqRMchIpK0Tz75BO3atUOPHj1ER6kzhyk+AHjkkUfg5uaGLVu2iI5CRCRZZrMZCxcudMhpD3Cw4rt2rS8uLo5THxGRILt370ZVVRUiIyNFR6kXhyo+AHj00Uchl8vx+eefi45CRCRJCQkJeO211yCXO1yFAHCQ2xn+bMuWLdBqtfj+++8hk8lExyEikoyMjAz84x//wNmzZx32yTkOWddPPPEEqqur8dVXX4mOQkQkKYmJiZg8ebLDlh7goBMfULuiaNGiRTh48CCnPiIiGygoKEBYWBjy8vLQrFkz0XHqzSEnPgB46qmnUF5ejp07d4qOQkQkCUuXLsXzzz/v0KUHOPDEBwAfffQR3nnnHezfv59THxGRFZWWlsLX1xcZGRlo27at6DgN4rATHwA8/fTTKC4uxtdffy06ChGRU0tKSsKQIUMcvvQAB5/4ACA5ORnvvfce0tLSREchInJKVVVV8PHxwVdffYVOnTqJjtNgDj3xAcDo0aNRWFiIvXv3io5CROSUNm7ciNDQUKcoPcAJJj4A+OCDD7Bx40bs2rVLdBQiIqdSU1ODDh064O2338bAgQNFx7EIh5/4AGDs2LHIy8vDgQMHREchInIq27dvh0qlwoABA0RHsRinKD6lUol/Q4LAAAAS3ElEQVSYmBjMmzdPdBQiIqeSkJCAadOmOdXKeacoPgB47rnnkJmZie+++050FCIip/Ddd9/h3LlzGDFihOgoFuU0xXfXXXdhxowZnPqIiCwkISEBU6ZMgUKhEB3Fopxiccs1er0earUa27ZtQ9euXUXHISJyWLm5uejVqxfy8/Ph7u4uOo5FOc3EBwAqlQqvv/464uPjRUchInJoixcvxsSJE52u9AAnm/gAoLKyEn5+fk5zoyURka1dvnwZAQEByMzMRKtWrUTHsTinmvgAwM3NDa+99hqnPiKielqxYgVGjBjhlKUHOOHEBwC//PIL/Pz8sGvXLnTo0EF0HCIih/Hrr7/C29sb33zzDQIDA0XHsQqnm/gAoHHjxpg6dSq0Wq3oKEREDuWDDz5Anz59nLb0ACed+ACgoqICvr6+2LdvH4KCgkTHISKyeyaTCQEBAVi/fj0eeOAB0XGsxiknPgBwd3fHK6+8wqmPiOgOffrpp2jZsqVTlx7gxBMfAJSVlcHPzw/ffvst/P39RcchIrJbZrMZPXv2xMyZMzF06FDRcazKaSc+APDw8EB0dDTmz58vOgoRkV3bt28fSktL8fjjj4uOYnVOPfEBQGlpKdRqNQ4fPgxfX1/RcYiI7NKjjz6Kxx9/HBMmTBAdxeqcvvgAIDY2FkVFRVi7dq3oKEREdufUqVMYMGAA8vPzoVKpRMexOkkU35UrV+Dv74+jR4+iXbt2ouMQEdmVcePGwc/PD7NmzRIdxSYkUXwAEBMTg6tXr2LVqlWioxAR2Y0ff/wRoaGhyMnJwT333CM6jk1IpviKi4sRGBiIjIwMeHl5iY5DRGQXpk+fjsrKSrz99tuio9iMZIoPAF5//XXo9XpJ/QMTEd1MWVkZfHx88MMPP8DHx0d0HJuRVPFdvHgRwcHBOHXqFFq3bi06DhGRUIsWLcL333+PTZs2iY5iU5IqPgCYMmUKZDIZFi9eLDoKEZEwBoMBvr6+2Lp1q+Qe3C254vvpp5/QoUMHZGZmomXLlqLjEBEJkZycjHXr1mH37t2io9ic5IoPAKKjo+Hm5oaFCxeKjkJEZFXFFVVIPVII3YUylOmN8FApENSqCd559Rkkxs/BI488IjqizUmy+AoLC9GxY0dkZWXB09NTdBwiIovLKCjFirRc7M2+DACoMtZcf59SXnuqc1CoF16KUKNT22aiYgohyeIDgBdffBF333039/EkIqez4VA+tNt10BtNuNUrvEwGqBQu0EQGYWwvb5vlE02yxXfu3Dl06dIFOTk5aN68ueg4REQWUVt6mag01Nz+g3/jppRDExksmfJz6qcz3Eq7du0wbNgwLF26VHQUIiKLyCgohXa7rk6lBwCVhhpot+twvLDUSsnsi2QnPgA4c+YMevTogdzcXBgVbn9zAdgDI7p64R53V9FRiYhua0LyD9iZefGWpzdvRiYDBoe0RNLYbpYPZmckXXwA8NS/p+Jyiy64KK/do+6PF4BVCjnMACICPREVLr0LwETkOIorqvDAW3tueA2rK1eFHN9O7+/0v+xL9lQnUHsu/GTLgThnbIoqY81fvmH0v71tx+mLGLX2EDYcyhcTlIjoNlKPFDb4GDIAqUcbfhx7J9niu3YBuMpkhkx+678GsxmoNJig3Z7J8iMiu6S7UNagaQ+o/WVfV1RuoUT2S5LFxwvARORsyvRGCx3HYJHj2DNJFt+KtFzojaZ6fa7eaMLKtFwLJyIiahgPlcJCx1Fa5Dj2THLFV1xRhb3Zl+u16gmoPe35ddZllFRUWTYYEVEDBLXygKuiYS/pKoUcQa2bWCiR/ZJc8fECMBE5ox6eNag2NOw0pRnA8C7O/6BuyRUfLwATkTMpKirCyy+/jIcf6gUv+c+Q1fM4MhnQL9DT6W9lACRYfLwATETOoKSkBNOnT0f79u3h6uoKnU6Hd158DCqlS72Op1K4ICpCbeGU9klyxccLwETkyMrLyxEXF4fAwED8/PPPOH78OBYtWgRPT090atsMmsgguCnr9tJeu1dnEDp6SWOTDskVHy8AE5EjqqysxKJFi6BWq5GdnY1Dhw4hKSkJXl43XpMb28sbmshguCldILvNeU+ZDHBTukhqg2pAgsU3vGvDL9zWmKVxAZiIxDMYDFi9ejX8/f2xf/9+7N69Gxs2bIBaffPTkmN7eSNlQi8MDmkJV4Ucqj/9sq9SyOGqkGNwSEukTOglqdIDJLpXZ0M2coW5BqZzxxDVUYmoqCg0bdrU4vmIiEwmEz766CPMmTMHfn5+iI+PR48ePep8nJKKKqQeLYSuqBxlegM8VEoEtW6C4V2kuwG/JIsvo6AUo9YeQqWh7jexuyld8ObAFti8dgm++uor/Oc//8HkyZP5JHcisgiz2YytW7di9uzZaNq0KbRaLSIiIkTHciqSO9UJoMEXgJ/s2wXJyck4fPgwiouLERgYiFdeeQUFBQVWSkxEzs5sNmPHjh3o2bMn5s6di7feegv79+9n6VmBJIsPsMwFYF9fXyQlJeHkyZNQKBTo1KkTxo8fj5ycHOuGJyKncuDAAfTr1w/R0dF47bXXcPToUQwZMgSy2704Ub1I8lTnHx0vLMXKtFx8nXUZMtTenH7Ntefx9Qv0RFSE+rZLfUtKSrB8+XKsWLECAwcOxMyZM9GxY0frfgFE5LDS09Mxa9YsnDhxAnPmzMGzzz4LhcIyt1zRzUm++K6x5AXg8vJyJCUlYfHixejWrRtiYmLQu3dvKyUnIkeTlZWF2NhY7Nu3DzExMZgwYQJcXaW50EQEFp8V6fV6fPDBB1i4cCG8vb2h0WgwYMAAnr4gkqhz585h7ty5+Pzzz/Hqq68iOjoajRs3Fh1LciR7jc8WVCoVXnzxRWRnZ+OFF17ApEmT0LNnT2zduhU1NQ3bL5SIHMeFCxcQHR2NLl26oE2bNsjJycGMGTNYeoKw+GxAqVTimWeewcmTJzFjxgzEx8cjNDQUGzZsgNFomb1Dicj+XLlyBTNnzkRISAgUCgUyMzMxb948NGsmja3B7BWLz4bkcjmGDRuG77//HkuWLMG7776LgIAArF69Gnq9XnQ8IrKQ8vJyxMfHIyAgACUlJcjIyMCSJUvQokUL0dEILD4hZDIZBg0ahLS0NCQnJ+Ozzz6Dn58fFi1ahIqKCtHxiKie9Ho9lixZAn9/f2RmZuLgwYNYs2YN2rZtKzoa/QGLT7AHHngAX375Jb788kscPnwYPj4+mDt3Lq5cuSI6GhHdIYPBgLVr18Lf3x9paWnYsWMHNm7cCH9/f9HR6G+w+OxEWFgYUlJScODAAZw/fx5qtRrTpk1DUVGR6GhEdBM1NTX48MMPERwcjJSUFKSmpmLbtm28f9fOsfjsTEBAAN577z2kp6ejuroa7du3R1RUFM6ePSs6GhH9xmw2Y9u2bQgLC8Py5cuxZs0a7Nq1Cz179hQdje4A7+Ozc5cuXcLSpUuxevVqDBkyBDNmzEBISIjoWESStXv3bsTExECv1yM+Ph6PPvoo7811MJz47FyLFi0wf/585OXlISgoCP369cOwYcPwww8/iI5GJCkHDx5E//798eKLL2LKlCk4duwYHnvsMZaeA2LxOYhmzZohJiYGZ8+eRUREBIYOHYrBgwdj79694NBOZD0ZGRl47LHHMHLkSIwZMwanT5/GqFGjIJfz5dNR8V/OwTRq1AiTJk1CXl4enn76aYwfPx4PPvggvvzySxYgkQVlZ2dj9OjRGDx4MB5++GFkZ2fjX//6FzeRdgK8xufgTCYTUlNTMX/+fMhkMsTExOCpp56Ci4uL6GhEDun8+fOIi4vD1q1bMXXqVEyaNAnu7u6iY5EFceJzcC4uLhg5ciTS09MRHx+PJUuWIDg4GO+//z6qq6tFxyNyGBcvXsTkyZPRuXNntGzZEjk5OYiJiWHpOSEWn5OQyWR49NFH8e2332LNmjXYtGkT1Go13n77bfz666+i4xHZratXryImJgYhISGQyWQ4ffo0tFot7r77btHRyEpYfE5GJpMhIiICO3bswObNm5GWlgZfX1+8+eab+Pnnn0XHI7IbFRUVmD9/PgICAnDp0iUcO3YMS5cuRcuWLUVHIytj8Tmx7t2749NPP8Xu3btx+vRp+Pn5QaPR4PLly6KjEQmj1+uxbNkyqNVqnDhxAgcOHMC7776L+++/X3Q0shEWnwS0b98eycnJOHz4MK5cuYLAwEC88sorKCgoEB2NyGaMRuP1J6Ls3r0b//vf//DRRx8hICBAdDSyMRafhPj6+mLVqlU4efIklEolOnXqhPHjxyMnJ0d0NCKrqampwaZNmxASEoIPP/wQKSkp+Oyzz9CpUyfR0UgQFp8E3XfffUhISEBOTg68vLzQp08fjBo1ChkZGaKjEVmM2WzG559/js6dO2PJkiVYtWoV9uzZg969e4uORoLxPj5CeXk5Vq9ejcWLF6NLly7QaDR8cSCHtmfPHmg0GlRUVECr1XJrMboBi4+u0+v1WLduHd566y14e3sjJiYGAwcO5AsGOYzvvvsOGo0G586dQ1xcHEaOHMmtxegvWHz0FwaDAZs2bcKbb76Jxo0bIyYmBk888QRfQMhuHT9+HLNnz8bRo0cRGxuL559/HkqlUnQsslMsPrqpmpoabNu2DVqtFpWVlZg5cyZGjRrFvQrJbuTk5GDOnDnYs2cPZsyYgf/85z9QqVSiY5Gd46/wdFNyuRxDhw7F999/j6VLl15fCp6UlAS9Xi86HklYQUEBJkyYgN69e6N9+/bIzc3FK6+8wtKjO8Lio9uSyWR4+OGHkZaWhuTkZHzxxRfw9fVFYmIiKioqRMcjCbl06RKmTJmCsLAw3HPPPcjOzoZGo+F+mlQnPNVJ9ZKeno4FCxZg9+7dePnllxEdHY3mzZuLjkV2qriiCqlHCqG7UIYyvREeKgWCWnlgRFcv3OPuetvPLy0tRWJiIlatWoUxY8YgJiYGrVq1skFyckYsPmqQ7OxsLFy4EFu2bMELL7yAqVOnonXr1qJjkZ3IKCjFirRc7M2u3Savylhz/X0qhRxmABGBnogKV6NT22Z/+fxffvkFy5cvx6JFi/D4448jNjYW7dq1s1V8clIsPrKIgoICJCYmIjk5GSNHjsTrr78OHx+fOh2joVMB2ZcNh/Kh3a6D3mjCrV5lZDJApXCBJjIIY3t5AwCqqqqwZs0azJ8/H+Hh4Zg7dy4CAwNtE5ycHouPLOrSpUtYtmwZVq9ejcjISMyYMQMhISG3/JyGTgVkf2pLLxOVhprbf/Bv3JRyzBgcCFNWGubOnYvQ0FDEx8cjLCzMiklJilh8ZBU///wzVq5ciaVLl+KBBx5ATEwMunXr9pePa8hUQPYpo6AUo9YeQqXBVPdPNlaj9elNWKSZjD59+lg+HBG4qpOspGnTppg5cybOnj2LiIgIDB06FIMHD8bevXtx7Xet36eCW5ceAJjNQKXBBO32TGw4lG/9L4DqbUVaLvTGepQeAJniLnQcPY2lR1bFiY9sorq6Ghs2bMCCBQvg6emJMdExePu0HPo6nAq7xk3pgpQJvdDRi6c97U1xRRUeeGvPDaer68pVIce30/vzui5ZDSc+som77roLL7zwAjIzMzFp0iQs/t8p6KuM9TqW3mjCyrRcCyckS0g9UtjgY8gApB5t+HGIboZ7T5FNubi4YMCQJxF7cg+M9ZwKzGbg66zLKKmocuqpwGQywWAwwGg0wmAw3PLP9vK+X0KHw3R/1wZ93XpjDXRF5Rb6WyT6KxYf2Zwlp4IJD/leLwhrvciLKhEAUCqVUCgUUCqV1//74/9b4n3X/qxSqRp8fO03JTj8Y2WD/33L9IYGH4PoZlh8ZHO6C2UNugYE1E4FsxJX4T/hi+Di4lLnF/n6vs/V1RXu7u4NKpg7fZ+Li4uF/sZt5z7dMcACxeeh4pMVyHpYfGRzZfr6Xdv7s0eHjsB7WxfycUl2JKiVB1wVFxr0i41KIUdQ6yYWTEV0I75ikM15qCzz+1azRq4sPTszvKtXg49hBjC8S8OPQ3QzfNUgm6udChr2rcepwD7d6+6K8ABPyGT1+3yZDOgX6OnUi5ZIPBYf2RynAuf2UoQaKkX9rk+qFC6IilBbOBHRjVh8ZHOcCpxbp7bNoIkMgpuybi8vbko5NJFB3JiArI7FR0JwKnBuY3t5QxMZDDely21/wZHJanfj0UQGcx9WsgluWUbC1HcHf75AOo7jhaVYmZaLr7MuQ4ba21CuufbkjX6BnoiKUHPSI5th8ZFQfDqDNJRUVCH1aCF0ReUo0xvgoVIiqHUTDO/CZy2S7bH4SDhOBURkSyw+shucCojIFlh8REQkKVzVSUREksLiIyIiSWHxERGRpLD4iIhIUlh8REQkKSw+IiKSFBYfERFJCouPiIgkhcVHRESSwuIjIiJJYfEREZGksPiIiEhSWHxERCQp/w/NYynSu9TxzwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"regular_g = nx.random_regular_graph(2, 10)\n",
"nx.draw(regular_g)\n",
"# This should really be a ring..."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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qK+l6E39WVWOXwF5P14W9aoKz7qcA51XVlL0z6bqc50+SB9O9adsMXEORbpfuD4U30N0Mde6WXks7En9BdXf2zkZNK4C9quoVs9Fer93t6Xace1bV92az7dmSZG/gvVX1mCnmm5N1tNAk+Qzdwf8lw65lriS5kO7GqW9NOe98hGKS/03XnbEd3R+O/qqqDp/zBWuL0rrIL6Q7Cnw13dnP/avqli29ltkOxdmU7iaGz9J1m76N7qzvETXfR8zSCJivr2p7EV2XzHfp+rb/eJ6Wqy3LY+i2kWvoujsOH0YgjmAtc+0wfv0lDXsCRxiIurOa9+5TSZJG1Rbxpd6SJM2HkfyS5rmyyy671LJly4ZdhiRtUb7yla9cU1WLp55zy3enCsVly5axevXqYZchSVuUJN+feq6Fwe5TSZIaQ1GSpMZQlCSpMRQlSWoMRUmSGkNRkqRmJEMxyfuSXJVk3C9vbf8y6m+TrEuyJskj5rtGSdLCM5KhSPd/wA6aZPrBdN/RuCewAnj3PNQkSVrgRjIUq+p84CeTzHIY8IHqXADslOS+81OdJGmh2lK/0WYJG/9Tzw1t3I8GZ2z/U20FwO67777JC/zwhT/Y5OdK0rA961Gbvv+7MxnJM8XZVFWnVdXyqlq+ePGd4qv7JEmbaEsNxSuA3XrDS9s4SZI22ZYaiiuB57S7UB8N3FBVd+g6lSRpJkbymmKSM4D9gV2SbADeANwVoKreA6wCDgHWATcDzx1OpZKkhWQkQ7GqjpxiegEvnadyJEl3Eltq96kkSbPOUJQkqTEUJUlqDEVJkhpDUZKkxlCUJKkxFCVJagxFSZIaQ1GSpMZQlCSpMRQlSWoMRUmSGkNRkqTGUJQkqTEUJUlqDEVJkhpDUZKkxlCUJKkxFCVJagxFSZIaQ1GSpMZQlCSpMRQlSWoMRUmSGkNRkqTGUJQkqTEUJUlqDEVJkhpDUZKkxlCUJKkxFCVJagxFSZKakQ3FJAcluTTJuiTHjTN99yTnJvlakjVJDhlGnZKkhWMkQzHJVsCpwMHAXsCRSfYamO11wFlV9XDgCOBd81ulJGmhGclQBPYF1lXVZVV1K3AmcNjAPAXs2B7fA/jhPNYnSVqARjUUlwDre8Mb2ri+E4FnJ9kArAJeNl5DSVYkWZ1k9dVXXz0XtUqSFohRDcXpOBI4vaqWAocAH0xyh9dTVadV1fKqWr548eJ5L1KStOUY1VC8AtitN7y0jet7PnAWQFV9CdgW2GVeqpMkLUijGooXAXsmuV+SrelupFk5MM8PgAMAkjyYLhTtH5UkbbKRDMWqug04FjgbuITuLtO1SU5Kcmib7VXAC5N8AzgDOKaqajgVS5IWgkXDLmAiVbWK7gaa/rgTeo8vBn5vvuuSJC1cI3mmKEnSMBiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUjOyoZjkoCSXJlmX5LgJ5nlGkouTrE3y4fmuUZK0sCwadgHjSbIVcCrwBGADcFGSlVV1cW+ePYHXAr9XVdcl+Y3hVCtJWihG9UxxX2BdVV1WVbcCZwKHDczzQuDUqroOoKqumucaJUkLzKiG4hJgfW94QxvX9yDgQUm+kOSCJAfNW3WSpAVpJLtPp2kRsCewP7AUOD/JQ6vq+v5MSVYAKwB23333+a5RkrQFGdUzxSuA3XrDS9u4vg3Ayqr6ZVV9D/g2XUhupKpOq6rlVbV88eLFc1awJGnLN6qheBGwZ5L7JdkaOAJYOTDPv9OdJZJkF7ru1Mvms0hJ0sIykqFYVbcBxwJnA5cAZ1XV2iQnJTm0zXY2cG2Si4FzgVdX1bXDqViStBCM7DXFqloFrBoYd0LvcQGvbD+SJG22kTxTlCRpGAxFSZKaOQ/FJHdv31AjSdJIm/VQTHKXJM9K8skkVwH/DfyofUfpW5M8cLaXKUnSbJiLM8VzgQfQfS/pfapqt6r6DeCxwAXAKUmePQfLlSRps8zF3acHVtUvB0dW1U+AjwEfS3LXOViuJEmbZdbPFMcCMcnJg9PGri2OF5qSJA3bXN5osyTJkWMD7V87nTOHy5MkabPM5R/vvwg4O8l3gQL+CXjNHC5PkqTNMuuhmOQDwFeBrwEvBT4M3AYcXlXrZnt5kiTNlrnoPj0dCPBc4EPAMuA64NlJnjYHy5MkaVbMRffpuVX1ubGBJIuABwP7APsCH02S9t2lkiSNjDn5O8UkL0uyO3T/8aKqvgmcRXeN8f3A0XOwXEmSNstcnCkeBDwPOCPJ/em6TrcFtgI+A7y9qr42B8uVJGmzzHooVtXPgXcB72p/pL8LcEtVXT/by5IkaTbNxXefHp3kmiQ/Af4BuMlAlCRtCebimuLrgScAvwX8AHjzHCxDkqRZNxfXFH/au2b4+iQXzsEyJEmadXMRivdNsoLuX0ZdAvjl35KkLcJchOIbgIcCR7Xf2ydZBXwDWFNVZ8zBMiVJ2mxzcffpaf3hJEvpwnFv4BDAUJQkjaS5/EJwAKpqA7AB+NRcL0uSpM0xl/86SpKkLYqhKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1IxsKCY5KMmlSdYlOW6S+Z6apJIsn8/6JEkLz0iGYpKtgFOBg4G9gCOT7DXOfDsALwf8R8aSpM02kqEI7Ausq6rLqupW4EzgsHHmeyNwCvDz+SxOkrQwjWooLgHW94Y3tHG3S/IIYLeq+uRkDSVZkWR1ktVXX3317FcqSVowRjUUJ5XkLsBfA6+aat6qOq2qllfV8sWLF899cZKkLdaohuIVwG694aVt3JgdgN8GzktyOfBoYKU320iSNseohuJFwJ5J7pdka+AIYOXYxKq6oap2qaplVbUMuAA4tKpWD6dcSdJCMJKhWFW3AccCZwOXAGdV1dokJyU5dLjVSZIWqkXDLmAiVbUKWDUw7oQJ5t1/PmqSJC1sI3mmKEnSMBiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUjOyoZjkoCSXJlmX5Lhxpr8yycVJ1iT5bJI9hlGnJGnhGMlQTLIVcCpwMLAXcGSSvQZm+xqwvKr2Bj4KvGV+q5QkLTQjGYrAvsC6qrqsqm4FzgQO689QVedW1c1t8AJg6TzXKElaYEY1FJcA63vDG9q4iTwf+NR4E5KsSLI6yeqrr756FkuUJC00oxqK05bk2cBy4K3jTa+q06pqeVUtX7x48fwWJ0naoiwadgETuALYrTe8tI3bSJIDgeOB/arqF/NUmyRpgRrVM8WLgD2T3C/J1sARwMr+DEkeDrwXOLSqrhpCjZKkBWYkQ7GqbgOOBc4GLgHOqqq1SU5Kcmib7a3A9sC/JPl6kpUTNCdJ0rSMavcpVbUKWDUw7oTe4wPnvShJ0oI2kmeKkiQNg6EoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEmNoShJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1hqIkSY2hKElSYyhKktQYipIkNYaiJEnNyIZikoOSXJpkXZLjxpm+TZKPtOkXJlk2/1VKkhaSkQzFJFsBpwIHA3sBRybZa2C25wPXVdUDgb8BTpnfKiVJC81IhiKwL7Cuqi6rqluBM4HDBuY5DHh/e/xR4IAkmccaJUkLzKJhFzCBJcD63vAG4FETzVNVtyW5AbgXcE1/piQrgBVt8KYkl25iTbsMtj0irGtmRrUuGN3arGtmRrKuozavrj1ms5ZRNqqhOGuq6jTgtM1tJ8nqqlo+CyXNKuuamVGtC0a3NuuaGevaso1q9+kVwG694aVt3LjzJFkE3AO4dl6qkyQtSKMaihcBeya5X5KtgSOAlQPzrASObo+fBnyuqmoea5QkLTAj2X3arhEeC5wNbAW8r6rWJjkJWF1VK4F/BD6YZB3wE7rgnEub3QU7R6xrZka1Lhjd2qxrZqxrCxZPriRJ6oxq96kkSfPOUJQkqTEUJ5Bk5yT/meQ77fc9J5l3xyQbkrxzFOpKskeSryb5epK1SV48InU9LMmXWk1rkjxzFOpq8306yfVJPjHH9Yzk1xdOo67Ht23qtiRPm4+aplnXK5Nc3LanzyaZl7+nm0ZdL07yzfYZ/Pw438g1lLp68z01SSXxTzQGVZU/4/wAbwGOa4+PA06ZZN53AB8G3jkKdQFbA9u0x9sDlwO7jkBdDwL2bI93BX4E7DTsutq0A4CnAJ+Yw1q2Ar4L3L+9R98A9hqY5yXAe9rjI4CPzMM2NZ26lgF7Ax8AnjbXNc2grt8HtmuP/3iE1teOvceHAp8ehbrafDsA5wMXAMvn473ckn48U5xY/2vk3g8cPt5MSX4HuDfwmVGpq6purapftMFtmJ8egenU9e2q+k57/EPgKmDxsOtq9XwWuHGOaxnVry+csq6quryq1gC/muNaZlrXuVV1cxu8gO5vmkehrp/2Bu8OzMcdjdPZvgDeSPdd0T+fh5q2OIbixO5dVT9qj6+kC76NJLkL8DbgT0epLoAkuyVZQ/dVeKe0EBp6Xb369qU7mv3uKNU1x8b7+sIlE81TVbcBY19fOOy6hmGmdT0f+NScVtSZVl1JXprku3S9FX8yCnUleQSwW1V9ch7q2SKN5N8pzpck5wD3GWfS8f2Bqqok4x3pvQRYVVUbZvNgfhbqoqrWA3sn2RX49yQfraofD7uu1s59gQ8CR1fVZp95zFZd2nIleTawHNhv2LWMqapTgVOTPAt4Hb/+spGhaAfxfw0cM8w6Rt2dOhSr6sCJpiX5cZL7VtWP2k78qnFmewzwuCQvobt2t3WSm6pqwgvc81RXv60fJvkW8Di67rih1pVkR+CTwPFVdcHm1DObdc2TmXx94YZ5/PrC6dQ1DNOqK8mBdAdA+/UuGwy9rp4zgXfPaUWdqeraAfht4Lx2EH8fYGWSQ6tq9TzUt0Ww+3Ri/a+ROxr4+OAMVXVUVe1eVcvoulA/sLmBOBt1JVma5G7t8T2BxwKb+t9BZrOurYF/o1tPmxXQs1nXPBrVry+cTl3DMGVdSR4OvBc4tKrm64BnOnXt2Rt8EvCdYddVVTdU1S5Vtaztsy6gW28GYt+w7/QZ1R+66zifpduYzwF2buOXA/8wzvzHMD93n05ZF/AEYA3d3WdrgBUjUtezgV8CX+/9PGzYdbXh/wKuBm6huxbzxDmq5xDg23TXUo9v406i2zkBbAv8C7AO+DJw/7l+76ZZ1yPbevkZ3Znr2hGp6xzgx73taeWI1PUOYG2r6VzgIaNQ18C85+Hdp3f48WveJElq7D6VJKkxFCVJagxFSZIaQ1GSpMZQlCSpMRQlSWoMRUmSGkNRGqIkByT54LDrkNQxFKXh2gf42rCLkNQxFKXh2gf4WpJtkpye5M3z8P8TJU3gTv1fMqQRsDfdf+44m+67WD805HqkOzW/+1QakiR3Ba4Bvg+8qKq+NOSSpDs9u0+l4Xkw3b/7uQ34nyHXIglDURqmfYAv0v3fu39Kcu8h1yPd6RmK0vDsA3yrqr4NvAY4q3WpShoSrylKktR4pihJUmMoSpLUGIqSJDWGoiRJjaEoSVJjKEqS1BiKkiQ1/x8cEDzVLKN/MgAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"regular_g = nx.random_regular_graph(5, len(coauthor.nodes()))\n",
"plot_degree_dist(regular_g, 'regular graph (degree=5)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Obviously, all nodes have same degree (5) **"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_clustering_dist(regular_g, 'regular')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Clustering coefficient is almost always 0, by definition. **\n",
"\n",
"(The generation algorithm may connect some neighbors to satisfy degree constraint.)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Do regular graphs have L =~ log(N) growth?\n",
"import math\n",
"Ls = []\n",
"ns = []\n",
"for n in range(50,1000)[::50]:\n",
" Ls.append(np.mean(get_shortest_paths(nx.random_regular_graph(2, n))))\n",
" ns.append(n)\n",
"\n",
"plt.plot(ns, Ls, 'bo-', label='regular')\n",
"plt.plot(ns, [math.log10(n) for n in ns], 'g-', label='log(N)')\n",
"plt.legend(loc='upper left')\n",
"plt.xlabel('N (number of nodes)')\n",
"plt.ylabel('L (mean shortest path)')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"** Clearly, regular graphs are not very realistic. Are they useful? **"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Source: [*Collective dynamics of 'small-world' networks.* Duncan J. Watts & Steven H. Strogatz](http://www.nature.com/nature/journal/v393/n6684/pdf/393440a0.pdf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- **Regular** graphs have low clustering and high distance\n",
"- **Random** graphs have low clustering and low distance\n",
"- **Real** graphs have high clustering and low distance.\n",
"\n",
"Need something in-between regular and random."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Idea:** randomly \"rewire\" edges in regular graph to become more random.\n",
"\n",
"**\"Watts Strogatz\" Model**"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Randomly rewire the edges of a regular graph, with probability $p$.\n",
"def rewire(G, p, seed=123):\n",
" nodes = G.nodes()\n",
" random.seed(seed)\n",
" for edge in list(G.edges()):\n",
" if random.random() < p:\n",
" G.remove_edge(*edge)\n",
" G.add_edge(edge[0], random.sample(nodes, 1)[0])\n",
" return G\n",
"\n",
"rewired = rewire(nx.random_regular_graph(2, 20), .1)\n",
"nx.draw(rewired)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Plot graphs with increasing rewiring.\n",
"for p in [0, .1, .5, .9]:\n",
" plt.figure()\n",
" rewired = rewire(nx.random_regular_graph(2, 20), p)\n",
" nx.draw(rewired)\n",
" plt.title('rewired, p=%.2f' % p)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Main result of Watts & Strogatz:** *Even a small amount of rewiring results in a small world (low distance).*\n",
"\n",
"\n",
"\n",
"$L \\approx$ distance\n",
"\n",
"$C \\approx$ clustering coefficient\n",
"\n",
"$p = $ rewiring probability\n",
"\n",
"\n",
"\n",
"Can fit $p$ on a real graph and get a model that has similar \n",
"- degree distribution\n",
"- clustering coefficient\n",
"- node distance\n",
"\n",
"This allows us to compare and reason about graphs."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"p = .2\n",
"k = 20\n",
"rewired_g = rewire(nx.random_regular_graph(k, len(coauthor.nodes())), p)\n",
"plot_clustering_dist(rewired_g, 'rewired, p=%g k=%d' % (p, k))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Better, but still not perfect (missing spike x=~1.0)** \n",
"([All models are wrong, but some are useful.](https://en.wikipedia.org/wiki/All_models_are_wrong))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Do rewired graphs obey L =~ log(N)?\n",
"Ls = []\n",
"ns = []\n",
"p = .5\n",
"for n in range(50,1000)[::50]:\n",
" Ls.append(np.mean(get_shortest_paths(\n",
" rewire(nx.random_regular_graph(2, n), p))))\n",
" ns.append(n)\n",
"\n",
"plt.plot(ns, Ls, 'bo-', label='rewired')\n",
"plt.plot(ns, [math.log(n) for n in ns], 'g-', label='log(N)')\n",
"plt.legend(loc='upper left')\n",
"plt.xlabel('N (number of nodes)')\n",
"plt.ylabel('L (mean shortest path)')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.core.display import HTML\n",
"HTML(open('../custom.css').read())"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
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