{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 1 Graphs" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "from pygsp import graphs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.1 Creation\n", "\n", "Most likely, the first thing you would like to do is to create a graph. In this toolbox, a graph is encoded as a weighted adjacency matrix. That is because it’s the most efficient representation to deal with when using spectral methods. As such, you can construct a graph from any adjacency matrix as follows." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "30 nodes, 50 edges\n" ] } ], "source": [ "W = np.random.uniform(size=(30, 30)) # Full graph.\n", "W[W < 0.93] = 0 # Sparse graph.\n", "W = W + W.T # Symmetric graph.\n", "np.fill_diagonal(W, 0) # No self-loops.\n", "\n", "G = graphs.Graph(W)\n", "\n", "print(f'{G.N} nodes, {G.Ne} edges')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Graphs can also be created from network models, such as the well-known [Erdős–Rényi](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "50 nodes, 238 edges\n" ] } ], "source": [ "G = graphs.ErdosRenyi(50, p=0.2)\n", "print(f'{G.N} nodes, {G.Ne} edges')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "2018-09-14 03:28:18,675:[INFO](pygsp.graphs.community.__init__): Constructed using eps-NN with eps = 2.23606797749979\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "100 nodes, 330 edges\n" ] } ], "source": [ "G = graphs.Community(N=100, Nc=5)\n", "print(f'{G.N} nodes, {G.Ne} edges')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, graphs can also be constructed from a set of points in $\\mathbb{R}^d$.\n", "\n", "Let $\\mathbf{X}$ be a data matrix $\\mathbf{X} = [\\mathbf{x}_1, \\ldots, \\mathbf{x}_N]^\\intercal \\in \\mathbb{R}^{N \\times d}$, where each $\\mathbf{x} \\in \\mathbb{R}^d$ is a sample for which we have $d$ features." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_points = 100\n", "dimensionality = 2\n", "points = np.random.uniform(size=(n_points, dimensionality))\n", "plt.scatter(points[:, 0], points[:, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may separate the task of building a graph from a set of points in two sub-tasks:\n", "* **Finding the structure (the existing edges)**. Two classical approaches are:\n", " * connecting a point to its $k$-nearest neighbors (kNN graph),\n", " * connecting a point to all points closer than $\\epsilon$ (in some measure); \n", "* **Associate a weight to each existing edge** (optional). In general, we want that the closer a pair of points, the larger the weight on the associated edge. A classical option is the Gaussian kernel:\n", "$$\\mathbf{W}[i,j] = \\exp(-\\frac{||\\mathbf{x}_i - \\mathbf{x}_j||^2_2 }{ \\sigma^2})$$ " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sigma=0.1" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 nodes, 127 edges\n" ] } ], "source": [ "G = graphs.NNGraph(points, NNtype='knn', k=2, sigma = sigma**2, rescale=False, symmetrize_type='maximum')\n", "print(f'{G.N} nodes, {G.Ne} edges')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100 nodes, 159 edges\n" ] } ], "source": [ "G = graphs.NNGraph(points, NNtype='radius', epsilon=0.1, sigma = sigma**2, rescale=False, symmetrize_type='maximum')\n", "print(f'{G.N} nodes, {G.Ne} edges')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.2 Properties" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The [pygsp.graphs.Graph](https://pygsp.readthedocs.io/en/stable/reference/graphs.html) class we just instantiated is the base class\n", "for all graph objects, which offers many methods and attributes.\n", "\n", "Given, a graph object, we can access and test some properties." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we've used before, there is the number of nodes and edges." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "100\n", "159\n" ] } ], "source": [ "print(G.N)\n", "print(G.Ne)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also test if the graph is connected or directed." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "False\n", "False\n" ] } ], "source": [ "print(G.is_connected())\n", "print(G.is_directed())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can retrieve the weighted adjacency matrix, which is stored in a sparse format." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<100x100 sparse matrix of type ''\n", "\twith 318 stored elements in LInked List format>" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G.W" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And visualize its sparsity pattern:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.spy(G.W, markersize=5);\n", "#plt.imshow(G.W.toarray());" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can access the [graph Laplacian](https://en.wikipedia.org/wiki/Laplacian_matrix), defined as\n", "$$ L = D - W $$\n", "for the combinatorial Laplacian, and\n", "$$ L = I - D^{-1/2} W D^{-1/2} $$\n", "for the normalized Laplacian, where $D$ is the diagonal degree matrix." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "<100x100 sparse matrix of type ''\n", "\twith 410 stored elements in Compressed Sparse Column format>" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G.compute_laplacian('combinatorial') \n", "#or G.compute_laplacian('normalized') ##the normalized Lap may yield an error if there exist a node with degree 0!\n", "G.L" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get another representation of a graph: the edge list.\n", "Note that if the graph is not directed the number of edges is half the number of non-zeros in the adjacency matrix." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(159,) (159,) (159,)\n" ] } ], "source": [ "v_in, v_out, weights = G.get_edge_list()\n", "print(v_in.shape, v_out.shape, weights.shape)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.3 Visualization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To be able to plot a graph, we need to embed its nodes in a 2D or 3D space. The process to find coordinates for each nodes is called [layout](https://en.wikipedia.org/wiki/Graph_drawing). Most included graph models define these. If that's not the case, or if you create the graph from an adjacency matrix, [`pygsp.graphs.Graph.set_coordinates()`](https://pygsp.readthedocs.io/en/stable/reference/graphs.html#pygsp.graphs.Graph.set_coordinates) can be used to set it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In our previous example, the nodes had a natural 2D embedding. It is thus logical to plot it using the 2D coordinates of each point in the point cloud:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nevertheless, the **same** graph could be drawn in many different ways. Below are two different options:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G2 = graphs.Graph(G.W)\n", "G2.set_coordinates(kind='ring2D') #here with a spring based algorithm\n", "G2.plot()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "G2 = graphs.Graph(G.W)\n", "G2.set_coordinates(kind='spring') #here with a spring based algorithm\n", "G2.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a more interactive visualization, you can use [Gephi](https://gephi.org/) or [Cytoscape](http://www.cytoscape.org/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.4 Exercise: The Barabasi-Albert model\n", "\n", "1. Create a graph from the [Barabási–Albert](https://en.wikipedia.org/wiki/Barab%C3%A1si%E2%80%93Albert_model) model.\n", "2. Compute and plot its degree distributions.\n", "3. Plot the graph in 2D with a force-directed layout." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Your code here.\n", "G = graphs.BarabasiAlbert(100, m0=2, m=2)\n", "plt.hist(G.dw)\n", "G.set_coordinates()\n", "G.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1.5 Exercise: connectedness phase transition in Erdös-Rényi graphs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Erdös Rényi graphs have a \"connectedness phase transition\" at $p=\\frac{\\log{N}}{N}$. That is, as $N\\rightarrow\\infty$:\n", "* if $p<\\frac{\\log{N}}{N}$ the graph is a.s. disconnected\n", "* if $p>\\frac{\\log{N}}{N}$ the graph is a.s. connected\n", "\n", "Illustrate this phase transition computationally" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "# Your code here." ] } ], "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": "3.7.0" } }, "nbformat": 4, "nbformat_minor": 2 }