{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# [NTDS'19] tutorial 4: Manipulating graphs with NetworkX\n", "[ntds'19]: https://github.com/mdeff/ntds_2019\n", "\n", "[Effrosyni Simou](https://people.epfl.ch/effrosyni.simou), [EPFL LTS4](https://lts4.epfl.ch).\n", "Adapted from [NTDS'17 NetworkX demo](https://nbviewer.jupyter.org/github/mdeff/ntds_2017/blob/outputs/demos/04_networkx.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this session we will get introduced to NetworkX, explore some of the most common network models, look at their basic properties and compare them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1 Creating graphs using network models\n", "\n", "There are many libraries that deal with creation and manipulation of graph data.\n", "We will use NetworkX to create basic network models, as they are already implemented in the library.\n", "The full documentation of NetworkX 2.3 (installed in your `ntds_2019` environment) can be found [online](https://networkx.github.io/documentation/stable/)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import collections\n", "\n", "import numpy as np\n", "from scipy import spatial\n", "from matplotlib import pyplot as plt\n", "import networkx as nx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create an Erdős-Rényi graph with $N=100$ vertices, and a probability of connecting each pair of vertices equal to $p=0.15$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "N = 100 # number of nodes\n", "p = 0.15 # probability of connection\n", "er = nx.erdos_renyi_graph(N, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can retrieve the adjacency matrix of the graph, from the `Graph` object `er` as follows:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "er_adj = nx.adjacency_matrix(er, range(N))\n", "er_adj = er_adj.todense()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can now visualise the adjacency matrix:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.spy(er_adj);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2 Plotting graphs\n", "\n", "With NetworkX and Matplotlib we can also plot a graph. For example, we can plot the Erdős-Rényi graph that we created before as follows:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/michael/.conda/envs/ntds_2019/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n", "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n", " if not cb.iterable(width):\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nx.draw(er)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Exercise\n", "\n", "Create a Barabasi-Albert graph and a Watts-Strogatz graph and plot them." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a Barabasi-Albert graph.\n", "ba = # your code here" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Create a Watts-Strogartz graph.\n", "ws = # your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3 Modifying graphs\n", "\n", "It's easy to add or remove edges, but also nodes. If we add an edge between nodes that don't yet exist, they will be automatically created." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "er.add_node(100)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "NodeView((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "er.nodes()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, you can add and remove a collection of nodes or edges, and add and remove one node or edge:\n", "* Adding nodes with:\n", " * `G.add_node`: One node at a time\n", " * `G.add_nodes_from`: A container of nodes\n", "* Adding edges with:\n", " * `G.add_edge`: One edge at a time\n", " * `G.add_edges_from`: A container of edges\n", "* Removing nodes with:\n", " * `G.remove_node`: One node at a time\n", " * `G.remove_nodes_from`: A container of nodes\n", "* Removing edges with:\n", " * `G.remove_edge`: One edge at a time\n", " * `G.remove_edges_from`: A container of edges\n", "\n", "You can get the number of edges with `G.size()`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Add an edge between two non-existant vertices. Remove all nodes up to node 50. Draw the graph after each change." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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hgZJnRJmED+Auzz5xMEaGB6O3Z3tvkb09XTEyPBjPHHFKQyfzkGqAe1h/0LTTGfYexxIBbOLS9Gy8Oj4V5y/PRBFrm9PXrZ/H98Kx/jg9NOBKb5cQPoAtuD2/GOfemY7J6x/FXG0p+qo9MXj4QJw87gT23Ub4AEjF4hYAUhE+AFIRPgBSET4AUhE+AFIRPgBSET4AUhE+AFIRPgBSET4AUhE+AFIRPgBSET4AUhE+AFL5PxFw/WXx0047AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "er.add_edge(101, 102)\n", "nx.draw(er)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "NodeView((50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102))" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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IHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACRF+ABIivABkBThAyApwgdAUoQPgKQIHwBJET4AkiJ8ACSl1O4BAJ1rbGI6Dh0fiaEL4zE+VYnecikGNvbGJ+7dHOtW97R7eNCQQq1Wq7V7EEBnOXHucjx1ZDiOnhmNiIjpSvXqn5VLxahFxM6tfbF3R39s27K2TaOExggfcI0Dx87G/sGhmKrMxmKfDoVCRLnUFft2DcSe7bfkNj5olledwFVz0TsVkzPVG/5srRYxOTMb+wdPRUSIH8uGyS1ARMy93tw/OLSk6L3R5Ew19g8OxcmRyxmNDFpL+ICIiHjqyHBMVWYb+t2pymw8fWS4xSOCbAgfEGMT03H0zOii3+ktplaLOHx6NC5NTLd2YJAB4QPi0PGRpq9RiIhDLzR/Hcia8AExdGH8miULjZiqVGPo/JUWjQiyI3xAjE9VWnSdmZZcB7IkfED0lluzsqm33N2S60CWhA+IgY290VNq7uOgXCrGwKY1LRoRZEf4gNh97+amr1GLiN33NH8dyJrwAbF+dU/suKMvCoXGfr9QiLh/a5+Nq1kWhA+IiIjP7OyPcqmrod8tl7pi787+Fo8IsiF8QEREbNuyNvbtGohV3fV9LKzqLsa+XQNx92anNLA82KQauGp+o2mnM7CSOZYIeIuTI5fj6SPDcfj0aBRibnH6vPnz+O7f2hd7d/Z70mPZET7gui5NTMehF0Zi6PyVGJ+aid5ydwxsWhO773ECO8uX8AGQFJNbAEiK8AGQFOEDICnCB0BShA+ApAgfAEkRPgCSInwAJEX4AEiK8AGQFOEDICnCB0BShA+ApAgfAEkRPgCS8n+RavzAAURVjAAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "er.remove_nodes_from(range(50))\n", "nx.draw(er)\n", "er.nodes()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "212" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "er.size()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4 Degree distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`G.degree()` returns a ``DegreeView`` object with pairs of nodes and their degree.\n", "If we specify a node, `G.degree(node)` will return the degree of that node." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create an Erdős-Rényi network and plot a histogram of node degrees. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "N = 100 # number of nodes\n", "p = 0.15 # probability of connection\n", "er = nx.erdos_renyi_graph(N, p)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "d = er.degree()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[(0, 15), (1, 23), (2, 22), (3, 16), (4, 14), (5, 19), (6, 14), (7, 19), (8, 22), (9, 18), (10, 17), (11, 15), (12, 16), (13, 19), (14, 13), (15, 13), (16, 9), (17, 17), (18, 19), (19, 16), (20, 17), (21, 13), (22, 12), (23, 19), (24, 12), (25, 8), (26, 18), (27, 13), (28, 15), (29, 12), (30, 18), (31, 15), (32, 11), (33, 20), (34, 12), (35, 11), (36, 15), (37, 13), (38, 19), (39, 17), (40, 12), (41, 15), (42, 17), (43, 19), (44, 12), (45, 22), (46, 24), (47, 21), (48, 8), (49, 13), (50, 11), (51, 17), (52, 17), (53, 13), (54, 15), (55, 13), (56, 12), (57, 16), (58, 15), (59, 19), (60, 13), (61, 19), (62, 16), (63, 19), (64, 21), (65, 18), (66, 22), (67, 14), (68, 15), (69, 17), (70, 13), (71, 12), (72, 10), (73, 7), (74, 13), (75, 16), (76, 15), (77, 12), (78, 22), (79, 12), (80, 19), (81, 17), (82, 16), (83, 15), (84, 17), (85, 18), (86, 16), (87, 13), (88, 17), (89, 18), (90, 13), (91, 11), (92, 17), (93, 17), (94, 27), (95, 20), (96, 16), (97, 14), (98, 16), (99, 10)]\n" ] } ], "source": [ "print(d)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erdős-Rényi node degree histogram.\n", "degree_sequence = sorted([d for n, d in er.degree()], reverse=True) # degree sequence\n", "degreeCount = collections.Counter(degree_sequence)\n", "deg, cnt = zip(*degreeCount.items())\n", "\n", "fig, ax = plt.subplots()\n", "ax.bar(deg, cnt)\n", "ax.set_title(\"Degree Histogram\")\n", "ax.set_ylabel(\"Count\")\n", "ax.set_xlabel(\"Degree\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1 Fitting a distribution\n", "\n", "Try to fit a Poisson distribution." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Poisson distribution.\n", "def poisson(mu, k):\n", " return np.exp(-mu) * mu**k * (np.math.factorial(k)**-1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Erdős-Rényi node degree histogram.\n", "degree_sequence = sorted([d for n, d in er.degree()], reverse=True) # degree sequence\n", "degreeCount = collections.Counter(degree_sequence)\n", "deg, cnt = zip(*degreeCount.items())\n", "\n", "fig, ax = plt.subplots()\n", "ax.bar(deg, cnt, label='Histogram')\n", "\n", "# Poisson distribution\n", "mu = 2 * er.size() / 100\n", "k = np.linspace(1, 25, 25)\n", "deg = [100 * poisson(mu, i) for i in k]\n", "ax.plot(k, deg, color='r', label='Poisson distribution')\n", "\n", "ax.legend()\n", "ax.set_title(\"Degree Histogram\")\n", "ax.set_ylabel(\"Count\")\n", "ax.set_xlabel(\"Degree\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2 Exercise\n", "\n", "Do it for the Barabasi-Albert and Watts-Strogatz networks." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5 Creating a graph that approximates a manifold\n", "\n", "We can represent data laying on a manifold (sampled from a manifold) as a graph of connected samples.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate 100 two-dimensional data points from a uniform random distribution in $[0, 1]$.\n", "These will be the coordinates of your nodes." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "N = 100\n", "nodes_coords = np.random.rand(N, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two nodes are connected if the Euclidean distance between them is smaller than a threshold.\n", "In that case, the weight of the edge is set to\n", "$$w(i,j) = \\exp \\left( -{\\frac{\\operatorname{dist}^2(i,j)}{2\\sigma^2}} \\right),$$\n", "for some *kernel width* $\\sigma$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "sigma = 0.9\n", "threshold = 0.2" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def gaussian_kernel(dist, sigma):\n", " return np.exp(-dist**2 / (2*sigma**2))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "dist = spatial.distance.pdist(nodes_coords, metric='euclidean')\n", "dist = spatial.distance.squareform(dist)\n", "adj = gaussian_kernel(dist, sigma)\n", "adj -= np.identity(N)\n", "adj[dist > threshold] = 0" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.spy(adj);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the graph with NetworkX. \n", "\n", "Hints: \n", "* `nx.from_numpy_array(adj)` creates a graph object from an adjacency matrix (in numpy form)\n", "* `nx.draw(G,pos)` will draw vertices at coordinates specified in pos. Variable pos is a dictionary assigning a pair of coordinates to each node." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "g = nx.from_numpy_matrix(adj)\n", "plt.spy(nx.adjacency_matrix(g).todense());" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/michael/.conda/envs/ntds_2019/lib/python3.7/site-packages/networkx/drawing/nx_pylab.py:579: MatplotlibDeprecationWarning: \n", "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n", " if not cb.iterable(width):\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pos = dict(zip(range(N), nodes_coords))\n", "nx.draw(g, pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot a degree distribution of this graph. What can you say about the distribution?" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# node degree histogram\n", "degree_sequence = sorted([d for n, d in g.degree()], reverse=True) # degree sequence\n", "degreeCount = collections.Counter(degree_sequence)\n", "deg, cnt = zip(*degreeCount.items())\n", "\n", "fig, ax = plt.subplots()\n", "ax.bar(deg, cnt)\n", "ax.set_title(\"Degree Histogram\")\n", "ax.set_ylabel(\"Count\")\n", "ax.set_xlabel(\"Degree\");" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }