From 20fc6d43231e9ca250b6eb9453120d4668933480 Mon Sep 17 00:00:00 2001 From: Andrew Date: Thu, 23 Jan 2025 14:30:05 +0000 Subject: [PATCH] [CS4423]: Add lecture materials --- .../CS4423/materials/CS4423-W01-1.pdf | Bin 0 -> 4064391 bytes .../CS4423/materials/CS4423-W01-2.ipynb | 2475 +++++++++++++++++ .../CS4423/materials/CS4423-W01-2.pdf | Bin 0 -> 901142 bytes .../CS4423/materials/CS4423-W02-1.ipynb | 786 ++++++ .../CS4423/materials/CS4423-W02-1.pdf | Bin 0 -> 68666 bytes .../CS4423/materials/CS4423-W02-2.ipynb | 984 +++++++ .../CS4423/materials/CS4423-W02-2.pdf | Bin 0 -> 459995 bytes 7 files changed, 4245 insertions(+) create mode 100644 year4/semester2/CS4423/materials/CS4423-W01-1.pdf create mode 100644 year4/semester2/CS4423/materials/CS4423-W01-2.ipynb create mode 100644 year4/semester2/CS4423/materials/CS4423-W01-2.pdf create mode 100644 year4/semester2/CS4423/materials/CS4423-W02-1.ipynb create mode 100644 year4/semester2/CS4423/materials/CS4423-W02-1.pdf create mode 100644 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    Table of Contents

    \n", + "
    " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### CS4423 - Networks\n", + "Niall Madden, \n", + "School of Mathematical and Statistical Sciences \n", + "University of Galway\n", + "\n", + "(These notes are adapted from Angela Carnecale's work)\n", + "\n", + "This notebook is at: https://www.niallmadden.ie/2425-CS4423/W01/CS4423-W01-2.ipynb\n", + "\n", + "# Week 1, Lecture 2: \n", + "# Graphs and `networkx`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "import networkx as nx" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## News\n", + "\n", + "1. Still working on confirming the lab times. We'll certainly have a lab session, Wednesday at 10am in CA116a.\n", + "\n", + "Tuesday at 4 in AC215 is suboptimal... let's see if we can improve on that...\n", + "\n", + "After that, we'll review some of the slides I didn't cover on Wednesday (see https://universityofgalway.instructure.com/courses/31889/files?preview=2325934)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Graphs\n", + "\n", + "\n", + "A **graph** can serve as a mathematical model of a network.\n", + "\n", + "Later, we will use the `networkx` package to work with examples of graphs and networks.\n", + "\n", + "This notebook gives an introduction into graph theory, along with some basic, useful\n", + " `networkx` commands.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### An example: the Internet (circa 1970)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "**Example.** The internet (more precisely, [ARPANET](https://en.wikipedia.org/wiki/ARPANET)) in December 1970. Nodes are computers,\n", + "connected by a link if they can directly communicate with each other.\n", + "At the time, only 13 computers participated in that network. \n", + "\n", + "![the internet in december 1970](https://d1vq4hxutb7n2b.cloudfront.net/system/files/53b5c1/66342b8248f70002ea/h_1536/f7dec1970.jpg)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "UCSB SRI UCLA\r\n", + "SRI UCLA STAN UTAH\r\n", + "UCLA STAN RAND\r\n", + "UTAH SDC MIT\r\n", + "RAND SDC BBN\r\n", + "MIT BBN LINC\r\n", + "BBN HARV\r\n", + "LINC CASE\r\n", + "HARV CARN\r\n", + "CASE CARN\r\n" + ] + } + ], + "source": [ + "!cat ../data/arpa.adj" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "The very first ARPANET network was even smaller, with node 1 being [UCLA](https://100.ucla.edu/timeline/the-internets-first-message-sent-from-ucla) and node 2 being SRI. The first ever message was sent on 29 October 1969. The intended message was \"Login\" but things didn't quite work and the computers crashed just after the more prophetic message \"Lo\" was displayed..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "The following **diagram**, built from the adjacencies in the list,\n", + "contains the same information, without the distracting details of the\n", + "US geography! (This is actually an important point: networks reflect only the *topology* of the object being studied). Also - don't worry about the syntax: we'll come back to that later!" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "H = nx.read_adjlist(\"../data/arpa.adj\")\n", + "opts = { \"with_labels\": True, \"node_color\": 'y' }\n", + "nx.draw(H, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Simple Graphs\n", + "\n", + "\n", + "**Definition.** A (simple) **graph**\n", + "is a pair $G = (X, E)$, consisting of a (finite) set $X$ of\n", + " objects, called **nodes** or **vertices** or **points**,\n", + "and $E$ is the of **links** or **edges**; every edge is a set consisting of two different vertices.\n", + " \n", + "We can also write $E \\subseteq \\binom{X}{2}$, where $\\binom{X}{2}$, pronounced as \"_$X$ choose 2_\", is the set of all $2$-element subsets of $X$. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Usually, $n$ is used to denote the number of vertices of a graph,\n", + "$n = |X|$,\n", + "and $m$ for the number of edges, $m = |E|$.\n", + "\n", + "$n = |X|$ is called the **order** of the graph $G$, and $m = |E|$ is called the **size** of $G$.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "The notation $\\binom{X}{2}$ for the set of all $2$-element subsets of $X$ is \n", + "motivated by the fact that if $X$ has $n$ elements then\n", + "$\\binom{X}{2}$ has $\\binom{n}{2} = \\frac{1}{2} n(n-1)$ elements:\n", + "$$\\left|\\binom{X}{2}\\right| = \\binom{|X|}{2}.$$\n", + "Obviously, $m \\leq \\binom{n}{2}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "**Example.**\n", + "\n", + "$G=(X,E)$ with $X = \\{ A, B, C, D \\}$ and $E = \\{ \\{AB\\}, \\{BC\\}, \\{BD\\}, \\{CD\\} \\}$. \n", + "**Notation:** usually we'll be a bit lazy and write $\\{ A, B \\}$) as just $AB$. So $E = \\{ AB, BC, BD, CD \\}$. \n", + "\n", + "So $G$ is a graph of order $4$ and size $4$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "G = nx.Graph()\n", + "G.add_edges_from([('A', 'B'), ('B', 'C'), ('B', 'D'), ('C', 'D')])" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Simple Graphs in `networkx`\n", + "\n", + "### Importing the package\n", + "We'll use the Python package `networkx` to work with graphs. So, from now on, every notebook with begin with:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "import networkx as nx\n", + "opts = { \"with_labels\": True, \"node_color\": 'y' } # show labels; yellow noodes" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Making a graph:\n", + "In `networkx`, we can construct this graph with the `Graph` constructor function, which takes the\n", + "node and edge sets $X$ and $E$ in a variety of formats. \n", + "\n", + "The simplest approach is to use $2$-letter strings for the edges: this implicitly defines the nodes too. \n", + "\n", + "Here is our graph from earlier: " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G = nx.Graph([\"AB\", \"BC\", \"BD\", \"CD\"])\n", + "G " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* The `python` object `G` representing the graph $G$ has lots of useful attributes. Firstly, it has `nodes` and `edges`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "NodeView(('A', 'B', 'C', 'D'))" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.nodes" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['A', 'B', 'C', 'D']" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(G.nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "EdgeView([('A', 'B'), ('B', 'C'), ('B', 'D'), ('C', 'D')])" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.edges" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('A', 'B'), ('B', 'C'), ('B', 'D'), ('C', 'D')]" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(G.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "A **loop** over a graph `G` will effectively loop over `G`'s nodes. As an example, (recall?) that the **degree** of a node is the number of edges incident to it (or, if you prefer, the number of neighbours)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "node A has degree 1\n", + "node B has degree 3\n", + "node C has degree 2\n", + "node D has degree 2\n" + ] + } + ], + "source": [ + "for node in G:\n", + " print(f\"node {node} has degree {G.degree(node)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "We can count the nodes, and the edges." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.number_of_nodes()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.order()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.number_of_edges()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.size()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "To draw the graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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Iyua0vapKK0tKtK6sTLtqauRq8ppFUlJ4uLL69NFtcXEa1quXWTG7RFVVVYvCuGPHDhUUFKi+vl6SFB0dLavVqnPPPbfZxt9DhgxRt27dTP4GAIJBXV2dCgsLmVACPsriany4LQgU2e1akp+v7PJyhUpytPPextczYmO1Ki1NiX48cXO5XDp8+HCL29Q7duzQnj173O8bOHBgs9vTjf/cv39/nm8EYKodO3Zo2LBh2rJli0aMGGF2HAAnCJoJ5fMlJVpeUCCH0ymp/TLZ9PUPyss1bNs2PZOSolvj4jo1o6ecTqeKi4tbPWbwyJEjkqRu3bopOTlZVqtVc+bMcZfH9PR0RUVFmfwNAKB1hmFIYssgwFcFRaFcUVysR4uKTutnHZIcTqcW5efrQH29HklI8G6401BbW6udO3e2uE2dl5cnu90uSerZs6e7KI4fP949bUxJSVGPHj1M/gYAcGoMw1BMTIz69etndhQArQj4Qvl8Sclpl8kTPVpUpLN69NAtAwZ45XonU1FR0WLSaBiGCgsL5fx20nrmmWfKarXqsssu07x589zFcfDgwRwzCCBgGIah9PR0Hr8BfFRAF8oiu13LCwpavrBhg/Szn/3v9927S5GRUkKCdMklUlaWFBvb6jWX7dyp0TExXnum0uVyqbS0tNXb1KWlpe73JSQkyGq1auLEic2eczzzzDO9kgMAfJlhGBo2bJjZMQC0IaAL5ZL8fPczk6164AEpPl5yOKTycumbb6S//lX629+kH/xAuvjiFj/icDq1JD9fm84//5SyOBwOFRUVtXrMYGVlpSSpe/fu7m14brnllmbHDPbs2fOUPg8AAoXL5ZJhGJo+fbrZUQC0IWAL5faqKmWXl7f/psREaejQ//1+xAhp5kzpzjuPF8r/9/+kEzbidkjKLi/XjqoqWVvZUqi6ulp5eXktpo07d+5UXV2dJKl3797usjht2jT3iuqkpCSFsgcmADRz4MABVVZWsiAH8GEB215WlpScdGugVvXvLy1dKj32mPTOO9L8+S3eEirpN7t2aV5FRYtb1cXFxe5jBgcMGKD09HSNGDFCt912m7tEDhgwgOeAAKCDWOEN+L6ALZTryspOvUw2uvxyKSRE+vrrVl92SFrz1Vdac9NNCgkJUVJSkqxWq2bNmtXs+caYmJjTTQAA+JZhGAoNDVVSUpLZUQC0ISAL5VGHQ7tqak7/AhERUnS0VFbW9nsGDtSnX32l89PSFB4efvqfBQBol2EYSk5OVvfu3c2OAqANAbmvTKHdrk4//sdiUVhiImUSADpZ45ZBAHxXQBbKWk9Pk7TbpYoKqU+fzv0cAMBJUSgB3xeQhTLM0wUvn34qOZ3SBRd07ucAANpVXV2t4uJiCiXg4wKyUKZEROi0q96BA9LKlVKvXtKkSW2+zfLt5wAAOk9+fr4kVngDvi4gF+VEhoYqKTxchSdbmFNUJDU0HP9VXi79+9/S+vVSt27S449L7azSTg4PVyR7RgJAp8rLy5MkDW26ZzAAnxOwjSirTx89t29f+1sHNR6/2Hj0Yny8dMMN0oQJ7ZZJORw6+O67evKDD3TzzTfrrLPO8mJyAEAjwzDUv39/xbZxHC4A32BxuQJzZcn2qiqdvW1bp11/yhtvaOPq1XI4HJoyZYoWL16sa6+9ViEhAfkUAQCY4oYbblBpaam2bNlidhQA7QjY9jOsVy9lxMZ6fQQbKikjNlZvPv20SkpK9Otf/1p5eXkaN26cUlJS9OSTT2r//v1e/lQACE6GYXC7G/ADAVsoJWlVWppCvTwxDA0J0aq0NElSbGysli9frq+//loff/yxRowYoccff1yDBw/WjBkztGnTJjmdTq9+PgAEC6fTqby8PBbkAH4goAtlYkSEnklJ8eo1n01NVeIJq7stFouuvPJK/fGPf1RJSYl+85vfKD8/n6klAHhgz549stvtFErADwR0oZSkW+Pi9ERioleutSIxUbcMGNDue2JiYrRs2bI2p5YbN25kagkAHWAYhiS2DAL8QcAXSkl6JCFBa9LSFB4ScsrPVIZKCg8J0fNDh+rhhIQO/1xbU8vx48crOTlZP/nJT5haAkA7DMNQeHi44uPjzY4C4CQCdpV3a4rsdi3Jz1d2eblCpXa3FGp8PSM2VqvS0lrc5j4dLpdLn376qVavXq1XXnlF9fX1mjx5shYvXqyMjAxWiANAE0uXLtXHH3+sr776yuwoAE4iqAplo+1VVVpZUqL1ZWUqrKlR0/8BLDq+aXlmnz5aGhcna69enZLBZrPppZde0qpVq/TNN99oyJAhWrRokW6++WYNOMltdQAIBqNHj1bfvn31yiuvmB0FwEkEZaFs6pjDoQK7XbUul8IsFqVERHTpCTgul0ufffaZVq1axdQSAJqIi4vTokWL9Nhjj5kdBcBJBH2h9CU2m01//vOftWrVKv373/9magkgaFVUVCgmJkZ/+ctfdMMNN5gdB8BJMP7yITExMbrjjjv01Vdf6ZNPPtHIkSP1xBNPaPDgwZo+fTorxAEEDc7wBvwLhdIHWSwWXXHFFe4V4k8//bQKCgrcK8RXrFih0tJSs2MCQKdp3DIo7duDJAD4Ngqljztxajlq1CitWLHCPbXcsGEDU0sAAccwDA0ePFiRkZFmRwHQARRKP9E4tfzDH/7QbGqZmZmppKQkrVixQiUlJWbHBACvMAyDDc0BP0Kh9EMnTi1Hjx6tFStWKD4+nqklgIBAoQT8C4XSjzWdWpaWljK1BBAQHA6HCgoKKJSAH6FQBojo6Gj31PLTTz9tNrWcNm2aNmzYoIaGBrNjAsBJFRUVqb6+nkIJ+BEKZYCxWCy6/PLL3VPL3/72t9q1a5cyMzPdK8SZWgLwZY0rvCmUgP+gUAaw6Oho3X777fryyy/16aefasyYMfrJT37inlquX7+eqSUAn2MYhiIjIznQAfAjFMog0Di1fOGFF1RSUuKeWmZlZSk5OVlPPPEEU0sAPqNxQY7FYjE7CoAOolAGmdamlk8++SRTSwA+gxXegP+hUAYpppYAfJHL5dKOHTsolICfoVCi2dTys88+Y2oJwDSHDx9WeXk5hRLwMxRKuFksFl122WXuqeUzzzyjoqIippYAugwrvAH/RKFEq6Kjo7V06VL961//ajG1nDp1KlNLAJ0iLy9PISEhSklJMTsKgFNAoUS7Wpta7t69W1lZWUpKStLjjz/O1BKA1xiGoaSkJIWFhZkdBcApsLhcLpfZIeBfXC6Xtm3bptWrV+uvf/2ramtrNXHiRC1ZskRjx45Vt27dzI4IwE9NnDhRFotF77zzjtlRAJwCJpQ4ZY1Ty+eff77NqeW+ffvMjgnADxmGoaFDh5odA8ApolDCIyc+a5mRkaGf/vSnSkhI0NSpU7Vu3TqetQTQITU1NSoqKmJBDuCHKJTwiqZTy9LSUvfUcsKECUwtAXRIQUGBnE4nhRLwQxRKeF1UVJR7arl161amlgA6hC2DAP9FoUSnsVgsuvTSS91Ty2effVbFxcVMLQG0yjAM9enTR2eeeabZUQCcIgolukRUVJRuu+02ffHFF9q6davGjh2rn/3sZ4qPj9eUKVOYWgLgDG/Aj1Eo0aUap5Zr1qxRSUmJfve73+m///2vJkyYoMTERP34xz9magkEqby8PAol4KcolDDNiVPLcePG6ec//7l7arl27VqmlkCQcLlcTCgBP0ahhOnamlpOnDiRqSUQJEpKSnTs2DEKJeCnKJTwKUwtgeDUuMKbTc0B/0ShhE86cWr5+9//Xnv27Gk2tdy7d6/ZMQF4iWEY6t69uxITE82OAuA0UCjh86KiorRkyRJ9/vnn2rZtm3tqmZCQoMmTJzO1BAKAYRhKTU1VaGio2VEAnAYKJfyGxWLRJZdc0mxquXfvXvfU8rHHHmNqCfgpFuQA/o1CCb904tRy/Pjx+sUvfsHUEvBTFErAv1Eo4dcap5arV69magn4qWPHjmnv3r0USsCPUSgRMBqnll988UWrU8t3332XqSXgg/Lz8yVxhjfgzyiUCEiNU8vS0lL31HLSpEkaMmQIU0vAx7BlEOD/KJQIaL1793ZPLf/5z38qMzOTqSXgYwzDUFxcnKKiosyOAuA0USgRNC6++GL31PK5557Tvn37mk0t9+zZY3ZEICgZhsF0EvBzFEoEnd69e2vx4sX6/PPP9c9//lNZWVn65S9/qSFDhmjSpElMLYEuxgpvwP9RKBHULr74Yq1atUolJSV67rnnVFJS4p5a/uhHP2JqCXSyhoYG5efnUygBP0ehBNT61PJXv/qVe2r5zjvvyOFwmB0TCDjFxcWqra2lUAJ+jkIJnODEqWVpaakmT56sxMREppaAlzWu8KZQAv6NQgm0oXFq+c9//pOpJdBJDMNQz549NWjQILOjAPAAhRLogKZTy5UrVzK1BLwkLy9PQ4cOVUgIfx0B/ow/wcAp6N27txYtWsTUEvASVngDgYFCCZwmppaA59iDEggMFErAQydOLSdMmOCeWk6cOJGpJdCGI0eO6ODBg0wogQBAoQS86OKLL9bKlSvdU8sDBw5o8uTJGjJkiH74wx8ytQSayMvLk8QKbyAQUCiBTtA4tdy2bZs+//xzTZw4Ub/+9a/dU8u3336bqSWCnmEYslgsSk1NNTsKAA9RKIFOdtFFF7mfsWycWk6ZMsU9tfzvf/9rdkTAFIZhKCEhQT179jQ7CgAPWVwul8vsEECw+eKLL7R69Wr9+c9/VnV1tTIzM7V48WJlZWUpNDTU7HhAl5gyZYrq6uq0fv16s6MA8BATSsAETC2B489Q8vwkEBgolICJIiMjmz1rOWnSJP3mN7/RkCFDNGHCBJ61RMCqr69XYWEhhRIIEBRKwEdcdNFFeu6551RSUqLVq1fr4MGDTC0RsAoLC+VwOCiUQICgUAI+JjIyUrfeeitTSwQ0wzAkiU3NgQBBoQR82IlTy0OHDmnKlClKSEjQD37wA6aW8FuGYSg6Olr9+/c3OwoAL6BQAn6gcWq5detWffHFF5o8ebKeeuop99TyrbfeYmoJv9J4hrfFYjE7CgAvoFACfubCCy9sMbWcOnWqe2pZXFxsdkTgpBoLJYDAQKEE/FRbU8vExESmlvBpLpeLQgkEGAolEACaTi3XrFnD1BI+7cCBA6qoqKBQAgGEQgkEkMjISN1yyy2tTi2zsrKYWsIn5OXlSRKFEgggFEogQJ04tSwrK3NPLb///e8ztYRpDMNQaGiokpOTzY4CwEsolECAa5xafvbZZ/rXv/6lKVOm6Omnn3ZPLd98802mluhShmEoOTlZ3bt3NzsKAC+hUAJB5IILLtDvf//7ZlPLadOmKT4+nqkluoxhGGxoDgQYCiUQhE6cWk6dOpWpJboMK7yBwEOhBIJc49SytLS01anl7t27zY6IAFJdXa3i4mIKJRBgKJQAJEm9evVqNrWcNm2afvvb3yopKUmZmZl68803VV9fb3ZM+LmdO3fK5XJRKIEAQ6EE0MIFF1yg3/3udyopKdHzzz+vI0eOaNq0ae4V4kwtcboMw5AknqEEAgyFEkCbevXqpYULFzK1hNcYhqF+/frpjDPOMDsKAC+iUALokBOnluXl5e6p5aOPPsrUEh2Sl5fH7W4gAFEoAZySxqnlp59+qi+//FLTpk3TM888455avvHGG0wt0SZWeAOBiUIJ4LSdf/75LaaW06dPZ2qJVjmdTiaUQICiUALwGFNLdMTevXtVXV3NghwgAFEoAXhV06nlCy+8wNQSbo0rvJlQAoGHQgmgU/Tq1Us333xzq1PL8ePHM7UMQoZhKCwsTAkJCWZHAeBlFEoAne7EqWVFRYWmT5+u+Ph4PfLII0wtg4RhGEpLS1O3bt3MjgLAyyiUALpM49Tyk08+0ZdffqkZM2bo2WefZWoZJFjhDQQuCiUAU5x//vl69tln25xaFhUVmR0RXkahBAIXhRKAqdqaWiYnJ2v8+PF6/fXXmVoGgMrKSpWWllIogQBFoQTgM1qbWs6YMYOpZQDIy8uTxApvIFBRKAH4nKZTy6+++oqpZQBo3DIoLS3N5CQAOgOFEoBPO++889xTyz/84Q9MLf2UYRgaNGiQIiMjzY4CoBNQKAH4hV69emnBggXuqeXMmTP1u9/9TsnJyRo3bhxTSx/HghwgsFEoAfid8847T88884x7allZWakZM2Zo8ODBevjhh5la+iAKJRDYKJQA/FbPnj2bTS1nzZql3//+90pKStK4ceP02muvMbX0AQ6HQzt37qRQAgGMQgkgIDSdWv7xj3/U0aNHNXPmTPfUcteuXWZHDFpFRUWqr6+nUAIBjEIJIKA0Ti0//vhjff311+6pZeOzlkwtux5bBgGBj0IJIGCde+657qnln/70J6aWJjEMQ5GRkYqLizM7CoBOQqEEEPB69uyp+fPntzq1HDt2LFPLTta4IMdisZgdBUAnoVACCConTi2PHTvmnlo+9NBDTC07gWEYGjp0qNkxAHQiCiWAoHTi1PK6667Tc889x9SyE7BlEBD4KJQAgt65556r3/72t+6pZVVVVbOpZWFhodkR/dbhw4dVVlZGoQQCHIUSAL7VOLX8xz/+0WxqmZKSorFjx+rVV19lanmKGs/wplACgY1CCQCtaG1qOWvWLKaWp8gwDIWEhCglJcXsKAA6EYUSANrRdGr573//u9WpZV1dndkxfZZhGEpMTFR4eLjZUQB0IgolAHTQOeec455avvjii0wtOyAvL4/b3UAQoFACwCnq2bOn5s2b555aXn/99Vq5cqVSUlKUkZHB1LIJVngDwYFCCQAeOOecc/T0009r3759evHFF1VdXe2eWj744INBPbWsra3Vrl27KJRAEKBQAoAXtDa1XLVqlXtq+fe//z3oppYFBQVyOp1sag4EAQolAHhZ49Sy8VlLu92u6667LuimlmwZBAQPCiUAdJKIiAjNmzdPubm5QTm1NAxDZ5xxhs4880yzowDoZBRKAOgCTaeW//d//9diallQUGB2RK9rXJBjsVjMjgKgk1EoAaALRURE6KabblJubq6++eYb99QyNTU14KaWrPAGggeFEgBMcvbZZwfs1NLlclEogSBCoQQAk504tbzhhhvcU8trr73WL6eWpaWlOnbsGIUSCBIUSgDwIWeffbaeeuop99SytrZW1113nQYNGqQHHnjAb6aWrPAGgguFEgB8UOPUMicnR998841uvPFGrV692j21/Nvf/ubTU0vDMNS9e3clJiaaHQVAF6BQAoCPa21qOXv2bJ+eWhqGoZSUFIWGhpodBUAXoFACgJ9oOrX8z3/+oxtvvFFr1qzxyaklC3KA4EKhBAA/NGzYMD311FPat2+fT04tKZRAcKFQAoAfO3FqOWfOHPfUcsyYMV06tTzmcOjLo0f1wf792tOjh4ZYrV3yuQDMZ3G5XC6zQwAAvMdut+u1117TqlWrlJubq759+2rBggVatGiRUlNTvfpZ26uqtLKkROvKyrSrpkZN/0KxSEoKD1dWnz66LS5Ow3r18upnA/AdFEoACGDbt2/XmjVr9OKLL6q8vFyjR4/W4sWLNW3aNPXo0eO0r1tkt2tJfr6yy8sVKsnRznsbX8+IjdWqtDQlRkSc9ucC8E0USgAIAo1Ty9WrVysnJ8ejqeXzJSVaXlAgh9PZbpE8Uaik0JAQPZOSolvj4k7pMwH4NgolAASZtqaWU6dOVVhYWLs/u6K4WI8WFXmc4YnERD2SkODxdQD4BgolAASpmpoavfrqq+6p5Zlnnqmbb765zanl8yUlWpSf77XPf37oUN0yYIDXrgfAPBRKAIB27Nih1atXtzm1LLLbNWzbNtU4nS1/eMMG6Wc/a/7fRUdLQ4ZIs2dLV17Z6meGh4Ro+6WX8kwlEAAolAAAt5qaGvcK8aZTy4+nTdNntbWtPzPZWCgfeECKj5dcLunIEemNN6R//UtasUL6znda/FiopFGxsdp0/vmd/bUAdDL2oQQAuIWHh2vOnDn66KOPtH37ds2dO1erNmzQP9oqk00lJkrDhklnny0NHy49+aTUvbv03nutvt0hKbu8XDuqqrz9NQB0MQolAKBVVqtVv/nNbzTnb39TyOnczOrR43ihbOc871BJz5WUnH5IAD6BQgkAaNcmm01Oi+Xkb2xoOP7L4ZAOHZKefVaqqZHGjGnzRxyS1peVeS8sAFO0/X8bAQBB76jDoV01NR178x13NP999+7SnXdKl13W7o8V1tTomMOhyHYmmQB8G396AQBtKrTb1eGb3Q89JDXuLVlRIeXkSE8/LTmd0rRpbf6YS1KB3a4Levf2NC4Ak1AoAQBtqj2VZycTEqShQ//3+8sukw4ckFatkjIypMhI73wOAJ/DM5QAgDaFdeTZyfYkJUm1tdKePZ37OQBMRaEEALQpJSJCHlW9wsLj/xkT0+ZbLN9+DgD/xS1vAECbIkNDlRQersKOLMwpKjq+ylv63zOU//zn8T0p2zliMTk8nAU5gJ/jTzAAoF1ZffrouX37Tr6xedPjF3v1Ol4ib79dmjKlzR8JlZTZp483YgIwEUcvAgDatb2qSmdv29Z517/0Ull79eq06wPofDxDCQBo17BevZQRG+v1W1qhkjJiYymTQACgUAIATmpVWppCQ7z7V0ZoSIhWpaV59ZoAzEGhBACcVGJEhJ5JSfHqNZ9NTVUiq7uBgEChBAB0yK1xcXoiMdEr1zrr3Xc1gzIJBAwKJQCgwx5JSNCatDSFh4Sc8jOVoZLCQ0L0WGSk6v74R02YMEFVVVWdERNAF2OVNwDglBXZ7VqSn6/s8nKFSu1uKdT4ekZsrFalpSkxIkJbt27VmDFj9J3vfEdvv/22wsLCuiY4gE5BoQQAnLbtVVVaWVKi9WVlKqypUdO/UCw6vml5Zp8+WhoX12I19wcffKDMzExNnDhRL7/8skLZ3BzwWxRKAIBXHHM4VGC3q9blUpjFopSIiJOegPP2229r+vTpmj9/vp5//nlZONMb8EsUSgCAqV566SXddNNNuueee/SrX/2KUgn4Ie4vAABMNXfuXFVUVGjZsmWKjY3V97//fbMjAThFFEoAgOnuuOMO2Ww2Pfroo4qJidHy5cvNjgTgFFAoAQA+4eGHH5bNZtOdd96p6OhozZs3z+xIADqIQgkA8AkWi0U///nPZbPZtHDhQkVFRWnq1KlmxwLQASzKAQD4lIaGBt1444168803tW7dOo0ZM8bsSABOgkIJAPA5dXV1mjJlinJycrR582ZdccUVZkcC0A4KJQDAJ1VXV2vcuHH6z3/+ow8//FDnnnuu2ZEAtIFCCQDwWRUVFRo1apRKS0uVk5OjlJQUsyMBaAWFEgDg0w4ePKjhw4errq5Oubm5GjhwoNmRAJwgxOwAAAC0p1+/ftq8ebOcTqcyMjJ0+PBhsyMBOAGFEgDg8wYPHqzs7GyVlZUpMzNTlZWVZkcC0ASFEgDgF9LS0rRp0ybt3LlTkydPlt1uNzsSgG9RKAEAfuP888/X2rVrtW3bNs2aNUv19fVmRwIgCiUAwM9cddVVev3117Vp0ybNnz9fDQ0NZkcCgh6FEgDgd8aNG6e//OUveuWVV7Rs2TKxYQlgLgolAMAvzZw5U2vWrNHKlSv1yCOPmB0HCGqhZgcAAOB0LVy4UBUVFbr33nsVHR2tBx54wOxIQFCiUAIA/No999wjm82mBx98UDExMVqyZInZkYCgQ6EEAPi9H/3oRyovL9fSpUsVHR2t66+/3uxIQFChUAIA/J7FYtFTTz2liooK3XTTTerdu7cmTJhgdiwgaHCWNwAgYDgcDs2aNUsbNmzQxo0bdc0115gdCQgKFEoAQECpqanRxIkTtXXrVn3wwQe6+OKLzY4EBDwKJQAg4Bw7dkzXXnutCgsL9dFHH8lqtZodCQhoFEoAQEA6cuSIRowYofLycuXm5mrIkCFmRwICFoUSABCwSktLNXz4cElSbm6uzjrrLJMTAYGJk3IAAAFrwIAB2rx5s+x2u8aOHavy8nKzIwEBiUIJAAhoQ4YMUXZ2tkpKSpSVlaVjx46ZHQkIOBRKAEDAGzZsmDZs2KD//Oc/mjZtmmpra82OBAQUCiUAIChccskleuedd5Sbm6sbbrhBDofD7EhAwKBQAgCCxogRI/Tqq6/qnXfe0aJFi+R0Os2OBAQECiUAIKhMmDBB//d//6cXX3xR99xzj9jsBPAcZ3kDAILODTfcoIqKCi1dulSxsbH60Y9+ZHYkwK9RKAEAQem2226TzWbTQw89pJiYGN19991mRwL8FoUSABC0HnzwQdlsNt1zzz2Kjo7WzTffbHYkwC9RKAEAQe3JJ5+UzWbTrbfequjoaE2fPt3sSIDf4ehFAEDQa2ho0Ny5c/Xaa6/p3Xff1dixY82OBPgVCiUAAJLq6+s1bdo0ffDBB8rOztZ3vvMdsyMBfoNCCQDAt+x2u8aPH6+vv/5aW7Zs0fnnn292JMAvUCgBAGiisrJSo0eP1p49e5Sbm6vU1FSzIwE+j0IJAMAJDh8+rOHDh6u6ulq5ubkaPHiw2ZEAn0ahBACgFXv37tXVV1+t8PBw5eTkqG/fvmZHAnwWRy8CANCKQYMGafPmzbLZbBo/frwqKirMjgT4LAolAABtSElJ0aZNm7Rr1y5NmjRJ1dXVZkcCfBKFEgCAdpx33nlav369vvjiC82cOVN1dXVmRwJ8DoUSAICTuOKKK/Tmm2/qvffe07x589TQ0GB2JMCnUCgBAOiAa6+9Vi+//LL+/ve/a+nSpWJNK/A/FEoAADpo2rRp+sMf/qA1a9bogQceoFQC3wo1OwAAAP5k/vz5stlsuvvuuxUbG6uHHnrI7EiA6SiUAACcorvuuksVFRV6+OGHFRMTo6VLl5odCTAVhRIAgNPw/e9/X+Xl5brjjjsUFRWlOXPmmB0JMA2FEgCA02CxWPSrX/1KFRUVmj9/vqKiojRp0iSzYwGm4OhFAAA84HA4NHv2bK1du1YbNmzQyJEjzY4EdDkKJQAAHqqtrdWkSZP0ySef6P3339ell15qdiSgS1EoAQDwgqqqKo0dO1aGYeijjz7S2WefbXYkoMtQKAEA8JLy8nKNHDlShw4dUm5urpKSksyOBHQJCiUAAF504MABXX311XI6ncrNzdWAAQPMjgR0Ok7KAQDAi/r376/Nmzerrq5OGRkZKisrMzsS0OkolAAAeFlCQoKys7N14MABZWVl6ejRo2ZHAjoVhRIAgE6Qnp6ujRs3yjAMTZ06VTU1NWZHAjoNhRIAgE5y0UUX6d1339XHH3+s66+/Xg6Hw+xIQKegUAIA0ImGDx+u119/XWvXrtXChQvldDrNjgR4HYUSAIBOlpmZqZdeekkvvfSS7rrrLrHBCgINZ3kDANAFZs+ercrKSi1evFgxMTF6/PHHzY4EeA2FEgCALrJo0SLZbDbdf//9iomJ0X333Wd2JMArKJQAAHSh733ve7LZbPrud7+rmJgY3XLLLWZHAjxGoQQAoIs98cQTstlsWrx4saKiojRr1iyzIwEeoVACANDFLBaLnnnmGdlsNs2ZM0e9e/fW+PHjzY4FnDbO8gYAwCT19fWaMWOGNm/erE2bNunqq682OxJwWiiUAACYqKamRpmZmfriiy+0ZcsWXXjhhWZHAk4ZhRIAAJMdPXpUY8aM0e7du5WTk6OhQ4eaHQk4JRRKAAB8QFlZma655hodPXpUubm5io+PNzsS0GEUSgAAfMS+ffs0fPhwde/eXTk5OerXr5/ZkYAO4ehFAAB8xMCBA7V582YdPXpU48aNk81mMzsS0CEUSgAAfEhSUpI2bdqk4uJiTZw4UVVVVWZHAk6KQgkAgI8555xztGHDBn311VeaMWOG6urqzI4EtItCCQCAD7rsssv01ltvacuWLZozZ44aGhrMjgS0iUIJAICPGj16tF555RW98cYbWrJkiVhHC19FoQQAwIdNmTJFf/rTn/TCCy/ou9/9LqUSPomzvAEA8HFz586VzWbT8uXLFRsbq0cffdTsSEAzFEoAAPzAsmXLVFFRoUcffVQxMTFatmyZ2ZEANwolAAB+4uGHH1Z5ebmWL1+uqKgozZs3z+xIgCQKJQAAfsNisegXv/iFbDabFi5cqOjoaE2ZMsXsWABHLwIA4G8aGhp0ww036K233tK6des0ZswYsyMhyFEoAQDwQ3V1dZoyZYpycnL03nvv6fLLLzc7EoIYhRIAAD9VXV2tsWPHavv27froo490zjnnmB0JQYpCCQCAH7PZbBo1apT279+v3NxcJScnmx0JQYhCCQCAnzt48KCGDx+u+vp65eTkaODAgWZHQpDhpBwAAPxcv379lJ2dLYfDobFjx+rw4cNmR0KQoVACABAA4uPjtXnzZh06dEiZmZmqrKw0OxKCCIUSAIAAkZaWpk2bNmnnzp2aPHmy7Ha72ZEQJCiUAAAEkAsuuEBr167V1q1bdd1116m+vt7sSAgCFEoAAALMVVddpTfeeEMbN27UggUL5HQ6zY6EAEehBAAgAI0bN05/+ctf9PLLL2vZsmViUxd0JgolAAABaubMmVqzZo2ee+45PfLII2bHQQALNTsAAADoPAsXLpTNZtN9992nmJgY3X///WZHQgCiUAIAEODuvfde2Ww2PfDAA4qJidHixYvNjoQAQ6EEACAIPPbYY7LZbLrtttsUHR2t2bNnmx0JAYRCCQBAELBYLHrqqadks9k0d+5c9e7dW1lZWWbHQoDgLG8AAIKIw+HQrFmztGHDBm3cuFHXXHON2ZEQACiUAAAEmZqaGk2YMEHbtm3TBx98oIsvvtjsSPBzFEoAAILQ0aNHlZGRocLCQuXk5Cg9Pd3sSPBjFEoAAILUkSNHNGLECJWXlys3N1dDhgwxOxL8FIUSAIAgVlpaqquvvlohISHKycnRWWedZXYk+CFOygEAIIgNGDBAmzdvVnV1tcaNG6fy8nKzI8EPUSgBAAhyiYmJys7O1r59+zRhwgRVVVWZHQl+hkIJAAA0bNgwbdiwQd98842mTZum2tpasyPBj1AoAQCAJOmSSy7R22+/rY8++kg33nijHA6H2ZHgJyiUAADAbeTIkXr11Vf19ttva9GiRXI6nWZHgh+gUAIAgGYmTpyoF198US+++KLuvfdesSEMToazvAEAQAs33nijKioqdPvttys2NlY//OEPzY4EH0ahBAAArVq6dKkqKir00EMPKSYmRnfddZfZkeCjKJQAAKBNDz74oMrLy3X33XcrOjpaCxYsMDsSfBCFEgAAtOunP/2pbDabbrnlFkVFRWn69OlmR4KP4ehFAABwUg0NDZozZ47eeOMNvfvuu8rIyDA7EnwIhRIAAHRIXV2dpk2bpi1btmjz5s268sorzY4EH0GhBAAAHVZdXa3x48fr3//+tz788EOdd955ZkeCD6BQAgCAU1JRUaHRo0dr3759ysnJUWpqqtmRYDIKJQAAOGWHDh3SNddcI7vdrtzcXA0aNMjsSDARJ+UAAIBT1rdvX2VnZ0uSMjIydOjQIZMTwUwUSgAAcFoGDRqk7OxslZeXa/z48aqoqDA7EkxCoQQAAKctNTVVmzZt0q5duzRp0iRVV1ebHQkmoFACAACPnHfeeVq3bp0+//xzzZo1S3V1dWZHQhejUAIAAI9deeWVevPNN7V582bNmzdPDQ0NZkdCF6JQAgAAr8jIyNBf//pX/f3vf9ftt98uNpIJHhRKAADgNdOnT9cLL7yg1atX66GHHjI7DrpIqNkBAABAYFmwYIEqKip09913KyYmRg8++KDZkdDJKJQAAMDr7rrrLtlsNj300EOKjo7W0qVLzY6ETkShBAAAneIHP/iBysvLdccddyg6Olo33nij2ZHQSSiUAACgU1gsFv36179WRUWF5s2bp6ioKE2cONHsWOgEnOUNAAA6lcPh0OzZs7Vu3TqtX79eI0eONDsSvIxCCQAAOl1tba0mTZqkTz75RO+//74uvfRSsyPBiyiUAACgS1RVVSkjI0N5eXnKycnRsGHDzI4EL6FQAgCALlNeXq6RI0fq8OHDys3NVWJiotmR4AUUSgAA0KX279+v4cOHy+l0Kjc3VwMGDDA7EjzESTkAAKBLnXXWWdq8ebNqa2s1duxYHTlyxOxI8BCFEgAAdLmEhARlZ2dr//79ysrK0rFjx8yOBA9QKAEAgCmsVqs2btyoHTt2aOrUqaqpqTE7Ek4ThRIAAJjmoosu0jvvvKN//OMfuv766+VwOMyOhNNAoQQAAKa65ppr9Nprr2nt2rVauHChnE6n2ZFwiiiUAADAdFlZWXrppZf00ksv6e677xab0PgXzvIGAAA+Yfbs2aqoqNCSJUsUExOjH//4x2ZHQgdRKAEAgM9YvHixbDabHnjgAcXExOjee+81OxI6gEIJAAB8yv333y+bzab77rtPMTExWrhwodmRcBIUSgAA4HNWrFghm82mRYsWKSoqSjNnzjQ7EtpBoQQAAD7HYrHo2WefVUVFhW688Ub17t1b48aNMzsW2sBZ3gAAwGfV19dr+vTpeu+995Sdna2rrrrK7EhoBYUSAAD4NLvdrszMTH355ZfasmWLLrjgArMj4QQUSgAA4PMqKys1ZswYFRcXKzc3V2lpaWZHQhMUSgAA4BcOHz6sESNG6OjRo8rNzVV8fLzZkfAtCiUAAPAb+/bt09VXX60ePXooJydH/fr1MzsSxNGLAADAjwwcOFCbN29WZWWlxo0bJ5vNZnYkiEIJAAD8THJysrKzs1VcXKyJEyequrra7EhBj0IJAAD8zjnnnKP169fryy+/1IwZM1RXV2d2pKBGoQQAAH7p8ssv11tvvaX3339fc+fOVUNDg9mRghaFEgAA+K0xY8bolVde0euvv64lS5aItcbmoFACAAC/NnXqVP3xj3/UCy+8oO9973uUShNwljcAAPB7N910kyoqKrR8+XLFxsbqkUceMTtSUKFQAgCAgLBs2TLZbDY9+uijio6O1rJly8yOFDQolAAAIGA88sgjKi8v1/LlyxUTE6O5c+eaHSkoUCgBAEDAsFgs+uUvf6mKigotWLBAvXv31pQpU8yOFfA4ehEAAASchoYGXX/99XrnnXe0bt06jR492uxIAY1CCQAAAlJtba2mTJmi3Nxcvf/++7rsssvMjhSwKJQAACBgVVVVady4cdqxY4c+/PBDnXPOOWZHCkgUSgAAENBsNptGjRqlAwcOKCcnR8nJyWZHCjgUSgAAEPAOHjyo4cOHq76+Xrm5uYqLizM7UkDhpBwAABDw+vXrp+zsbDkcDmVkZKisrMzsSAGFQgkAAIJCfHy8srOzdejQIWVmZuro0aNmRwoYFEoAABA0hg4dqo0bNyo/P1+TJ0+W3W43O1JAoFACAICgcuGFF2rt2rX67LPPNHv2bNXX15sdye9RKAEAQNC56qqr9Prrr2vDhg1asGCBnE6n2ZH8GoUSAAAEpfHjx+vPf/6zXn75ZS1fvlxsfHP6OMsbAAAErVmzZqmyslK33nqrYmJitGLFCrMj+SUKJQAACGq33HKLbDabvvvd7yomJkbf+973zI7kdyiUAAAg6N13332y2Wy6//77FRMTo0WLFrX7/mMOhwrsdtW6XAqzWJQSEaHI0OCtVcH7zQEAAJr48Y9/LJvNpiVLligqKkqzZ89u9vr2qiqtLCnRurIy7aqpUdMnLi2SksLDldWnj26Li9OwXr26NLvZOHoRAADgW06nUwsWLNBf//pXvfXWW8rKylKR3a4l+fnKLi9XqCRHOz/f+HpGbKxWpaUpMSKia4KbjEIJAADQhMPh0MyZM7Vx40bduWGDfmuxyOF0tlskTxQqKTQkRM+kpOjWIDg3nEIJAABwgpqaGp395JPaNWqUx9d6IjFRjyQkeCGV72IfSgAAgBO8dOSIV8qkJD1aVKQXSku9ci1fxYQSAACgiSK7XcO2bVONF0/PCQ8J0fZLLw3YZyqZUAIAADSxJD9fjo6Uyddek0aNkm6++aRvdTidWpKf74V0volCCQAA8K3tVVXKLi/v2AKc9euP/+fu3dL27e2+1SEpu7xcO6qqPEzomyiUAAAA31pZUtKxTbrz8qTCQumKK47/ft26k/5IqKTnSko8ieezKJQAAADfWldW1rHpZGOBXLxYOvts6YMPpJqadn/EIWl9WZmnEX0ShRIAAEDSUYdDu05SCiVJtbXSe+9J6elSYqKUmSlVV0tbtpz0RwtranTMcSo7WvoHCiUAAICkQrtdHdr65sMPpaqq40VSkkaPliIi/vdMZTtckgrsdk9i+iQKJQAAgKTaju6kuG6dFBZ2vEhKx8vkiBHS119Le/d673P8CIUSAABAUpjFcvI37dt3vDg2LsY5duz4rxEjjv++A1PKDn2On+nQQiYAAIBAlxIRIYvU/m3vdeskl+v4be8PP2z5+saN0sKFUrdurf645dvPCTQUSgAAAEmRoaFKCg9XYVsLcxoapE2bpLg46Xvfa/n6J59If/ubtHWrdOWVrV4iOTxckaGBV78C7xsBAACcpqw+ffTcvn2tbx20dat0+PDxrYIuuKDl64mJ0htvHJ9itlIoQyVl9unj5cS+gWcoAQAAvnVbXFzb+1CuWyd17/6/1d0nio6Whg8/Pqk8cqTFyw5JS+PivBXVp1hcrgBcagQAAHCaxn71lT7o6PGLHRQqaVRsrDadf74Xr+o7mFACAAA0sSotTaEh3q1IoSEhWpWW5tVr+hIKJQAAQBOJERF6JiXFq9d8NjVViQG4ursRhRIAAOAEt8bF6YnERK9ca0Viom4ZMMAr1/JVPEMJAADQhudLSrS8oEAOp/OUnqkM1fHb3M+mpgZ8mZQolAAAAO0qstu1JD9f2eXlCpXaLZaNr2fExmpVWlpA3+ZuikIJAADQAdurqrSypETry8pUWFPT7EQdi45vWp7Zp4+WxsXJ2quXWTFNQaEEAAA4RcccDhXY7ap1uRRmsSglIiIgT8DpKAolAAAAPMIqbwAAAHiEQgkAAACPUCgBAADgEQolAAAAPEKhBAAAgEcolAAAAPAIhRIAAAAeoVACAADAIxRKAAAAeIRCCQAAAI9QKAEAAOARCiUAAAA8QqEEAACARyiUAAAA8AiFEgAAAB6hUAIAAMAjFEoAAAB4hEIJAAAAj1AoAQAA4BEKJQAAADxCoQQAAIBHKJQAAADwCIUSAAAAHqFQAgAAwCMUSgAAAHiEQgkAAACPUCgBAADgEQolAAAAPEKhBAAAgEcolAAAAPAIhRIAAAAeoVACAADAIxRKAAAAeIRCCQAAAI9QKAEAAOARCiUAAAA8QqEEAACAR/4/zXSOH5ZjChgAAAAASUVORK5CYII=", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(G, **{ \"with_labels\": True, \"node_color\": 'c'})" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "The example also illustrates a typical way how diagrams of graphs are drawn:\n", + "nodes are represented by small circles, and edges by lines connecting the nodes." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Adding and removing nodes and edges\n", + "A graph `G` can be modified, by adding nodes one at a time ..." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G.add_node(1)\n", + "list(G.nodes)\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "or many nodes at once ..." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G.add_nodes_from([2, 3, 5])\n", + "list(G.nodes)\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* ... or even as nodes of another graph `H`" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['A',\n", + " 'B',\n", + " 'C',\n", + " 'D',\n", + " 1,\n", + " 2,\n", + " 3,\n", + " 5,\n", + " 'UCSB',\n", + " 'SRI',\n", + " 'UCLA',\n", + " 'STAN',\n", + " 'UTAH',\n", + " 'RAND',\n", + " 'SDC',\n", + " 'MIT',\n", + " 'BBN',\n", + " 'LINC',\n", + " 'HARV',\n", + " 'CASE',\n", + " 'CARN']" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.add_nodes_from(H)\n", + "list(G.nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(21, 4)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.order(), G.size()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Adding edges works in a similar fashion" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G=nx.Graph( [\"AB\", \"BC\", \"BD\", \"DC\"] )\n", + "G.add_edge(1,2)\n", + "#G.add_edge(1,'C')\n", + "#G.add_edge(1,'A')\n", + "list(G.edges)\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "#edge = (2,3)\n", + "#G.add_edge(*edge)\n", + "#list(G.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "source": [ + "Add edges from a list:" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('A', 'B'),\n", + " ('B', 'C'),\n", + " ('B', 'D'),\n", + " ('C', 'D'),\n", + " (1, 2),\n", + " (1, 5),\n", + " (2, 5),\n", + " (5, 3)]" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.add_edges_from([(1,5), (2,5), (3,5)])\n", + "list(G.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Add edges from another graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('A', 'B'),\n", + " ('B', 'C'),\n", + " ('B', 'D'),\n", + " ('C', 'D'),\n", + " (1, 2),\n", + " (1, 5),\n", + " (2, 5),\n", + " (5, 3),\n", + " ('UCSB', 'SRI'),\n", + " ('UCSB', 'UCLA'),\n", + " ('SRI', 'UCLA'),\n", + " ('SRI', 'STAN'),\n", + " ('SRI', 'UTAH'),\n", + " ('UCLA', 'STAN'),\n", + " ('UCLA', 'RAND'),\n", + " ('UTAH', 'SDC'),\n", + " ('UTAH', 'MIT'),\n", 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "There are corresponding commands for **removing** nodes or edges from a graph `G`" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(21, 25)" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.order(), G.size()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(21, 24)" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.remove_edge(3,5)\n", + "G.order(), G.size()" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(21, 7)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.remove_edges_from(H.edges())\n", + "G.order(), G.size()" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "That is, `networkx` is ensuring what we get is a proper graph, which is a subgraph of the original one.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "
    Finished here Thursday
    " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Subgraphs and Induced subgraphs\n", + "\n", + "Given $G=(X,E)$, a **subgraph** of $G$ is $H=(Y,E_H)$ with $Y\\subseteq X$ and $E_H\\subseteq E\\cap \\binom{Y}{2}$.\n", + "\n", + "So, all the nodes in $H$ are also in $G$. And any edge in $H$ was also in $G$, and is incident only to vertices in $Y$.\n", + "\n", + "One of the most important subgraphs of $G$ is the **induced subgraph** on $Y\\subseteq X$ is the graph $H=\\left(Y,E\\cap \\binom{Y}{2}\\right)$. That is, given a subset $Y$ of $X$, we include *all possible edges* from $G$ too.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Each node has a list of **neighbours**, the nodes it is\n", + " directly connected to by an edge of the graph." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['A', 'C', 'D']" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(G.neighbors('B'))" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "scrolled": true, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "AtlasView({'A': {}, 'C': {}, 'D': {}})" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G['B']" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['A', 'C', 'D']" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(G['B'])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "As mentioned earlier, the number of neighbours of a node $x$ is its **degree**" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.degree('B')" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "DegreeView({'A': 1, 'B': 3, 'C': 2, 'D': 2})" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G.degree" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[('A', 1), ('B', 3), ('C', 2), ('D', 2)]" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(G.degree)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "Anybody knows/remembers a fundamental relationship between (the sum of) the degrees and the size of a graph?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Important Graphs" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "### Complete Graphs\n", + "\n", + "The [**complete graph**](https://en.wikipedia.org/wiki/Complete_graph)\n", + "on a vertex set $X$ is the graph with edge set all of $\\binom{X}{2}$. E.g., if $X=\\{0,1,2,3\\}$, then $E=\\{01, 02, 03, 12, 13, 23\\}$." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3]" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nodes = range(4)\n", + "list(nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]\n" + ] + } + ], + "source": [ + "E4 = [(x, y) for x in nodes for y in nodes if x < y]\n", + "print(E4)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "K4 = nx.Graph(E4)\n", + "nx.draw(K4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "While it is somewhat straightforward to find all $2$-element\n", + "subsets of a given set $X$ with a short `python` program,\n", + "it is probably more convenient (and possibly efficient) to use a function from the\n", + "`itertools` package for this purpose." + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from itertools import combinations\n", + "nodes5 = range(5)\n", + "combinations(nodes5, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]\n" + ] + } + ], + "source": [ + "print(list(combinations(nodes5, 2)))" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "K5 = nx.Graph(combinations(nodes5, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(K5, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "We can turn this procedure into a `python` function that\n", + "constructs the complete graph for an arbitrary vertex set $X$." + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "def complete_graph(nodes):\n", + " return nx.Graph(combinations(nodes, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", 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", 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(complete_graph(\"ABCD\"), **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "In fact, `networkx` has its own implementation of complete graphs." + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(nx.complete_graph(\"NETWORKS\"), **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Petersen Graph\n", + "\n", + "The [Petersen Graph](https://en.wikipedia.org/wiki/Petersen_graph)\n", + "is a graph on $10$ vertices with $15$ edges.\n", + "\n", + "It can be constructed \n", + "as the complement of the line graph of the complete graph $K_5$,\n", + "i.e.,\n", + "as the graph with vertex set\n", + "$$X = \\binom{\\{0,1,2,3,4\\}}{2}$$ (the edge set of $K_5$) and\n", + "with an edge between $x, y \\in X$ whenever $x \\cap y = \\emptyset$." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(K5, **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[(0, 1), (0, 2), (0, 3), (0, 4), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)]\n" + ] + } + ], + "source": [ + "lines = K5.edges\n", + "print(list(lines))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[((0, 1), (0, 2)), ((0, 1), (0, 3)), ((0, 1), (0, 4)), ((0, 1), (1, 2)), ((0, 1), (1, 3)), ((0, 1), (1, 4)), ((0, 1), (2, 3)), ((0, 1), (2, 4)), ((0, 1), (3, 4)), ((0, 2), (0, 3)), ((0, 2), (0, 4)), ((0, 2), (1, 2)), ((0, 2), (1, 3)), ((0, 2), (1, 4)), ((0, 2), (2, 3)), ((0, 2), (2, 4)), ((0, 2), (3, 4)), ((0, 3), (0, 4)), ((0, 3), (1, 2)), ((0, 3), (1, 3)), ((0, 3), (1, 4)), ((0, 3), (2, 3)), ((0, 3), (2, 4)), ((0, 3), (3, 4)), ((0, 4), (1, 2)), ((0, 4), (1, 3)), ((0, 4), (1, 4)), ((0, 4), (2, 3)), ((0, 4), (2, 4)), ((0, 4), (3, 4)), ((1, 2), (1, 3)), ((1, 2), (1, 4)), ((1, 2), (2, 3)), ((1, 2), (2, 4)), ((1, 2), (3, 4)), ((1, 3), (1, 4)), ((1, 3), (2, 3)), ((1, 3), (2, 4)), ((1, 3), (3, 4)), ((1, 4), (2, 3)), ((1, 4), (2, 4)), ((1, 4), (3, 4)), ((2, 3), (2, 4)), ((2, 3), (3, 4)), ((2, 4), (3, 4))]\n" + ] + } + ], + "source": [ + "print(list(combinations(lines, 2)))" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "15" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "edges = [e for e in combinations(lines, 2) \n", + " if not set(e[0]) & set(e[1])]\n", + "len(edges)" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "P = nx.Graph(edges)" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(P, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Even though there is no parameter involved in this example,\n", + "it might be worth wrapping the construction up into a `python`\n", + "function." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "def petersen_graph():\n", + " nodes = combinations(range(5), 2)\n", + " G = nx.Graph()\n", + " for e in combinations(nodes, 2):\n", + " if not set(e[0]) & set(e[1]):\n", + " G.add_edge(*e)\n", + " return G" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw(petersen_graph(), **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Code Corner" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### `python`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* **list unpacking** operator `*e`: if `e` is a list, an\n", + "argument `*e` passes the elements of `e` as individual arguments\n", + "to a function call." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* **dictionary unpacking** operator `**opts`: `python` function calls take **positional** arguments and **keyword** arguments. The keyword arguments can be collected in a dictionary `opts` (with the keywords as keys). This dictionary can then be passed into the function call in its \"unwrapped\" form `**opts`." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* **set intersection**: if `a` and `b` are sets then `a & b` represents the intersection of `a` and `b`. In a boolean context, an empty set counts as `False`, and a non-empty set as `True`." + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{3}" + ] + }, + "execution_count": 62, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = set([1,2,3])\n", + "b = set([3,4,5])\n", + "a & b" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(False, True)" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "bool({}), bool({3})" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* `list` [[doc]](https://docs.python.org/3/library/stdtypes.html#list) turns its argument into a `python` list (if possible)." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['n', 'e', 't', 'w', 'o', 'r', 'k', 's']" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "list(\"networks\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "source": [ + "* **list comprehension** [[doc]](https://docs.python.org/3/tutorial/datastructures.html#list-comprehensions) allows the construction of new list from old ones\n", + "without explicit `for` loops (or `if` statements)." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[(x, y) for x in range(4) for y in range(4) if x < y]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### `networkx`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* the `read_adjlist` command [[doc]](https://networkx.org/documentation/stable/reference/readwrite/generated/networkx.readwrite.adjlist.read_adjlist.html#networkx.readwrite.adjlist.read_adjlist) constructs a graph from a text file in `adj` format." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* `Graph` constructor and applicable methods [[doc]](https://networkx.org/documentation/stable/reference/classes/graph.html): if `G` is `Graph` object then\n", + " * `G.nodes` returns the nodes of a graph `G` (as an iterator),\n", + " * `G.edges` returns the edges of a graph `G` (as an iterator),\n", + " * ..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* `complete_graph` [[doc]](https://networkx.org/documentation/stable//reference/generated/networkx.generators.classic.complete_graph.html)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### `itertools`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* `combinations` [[doc]](https://docs.python.org/3/library/itertools.html#itertools.combinations) returns the $k$-element combinations of a given list (as an iterator)." + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['ne', 'nt', 'nw', 'no', 'nr', 'nk', 'ns', 'et', 'ew', 'eo', 'er', 'ek', 'es', 'tw', 'to', 'tr', 'tk', 'ts', 'wo', 'wr', 'wk', 'ws', 'or', 'ok', 'os', 'rk', 'rs', 'ks']\n" + ] + } + ], + "source": [ + "print([\"\".join(c) for c in combinations(\"networks\", 2)])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "hide_code_all_hidden": false, + "kernelspec": { + 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    Table of Contents

    \n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + " # CS4423 : Week 02 - Lecture 1 - Networks \n", + "# More on Graphs, and `networkx`\n", + "\n", + "[//]: $\\color{red}{\\text{DRAFT}}$\n", + "Niall Madden, \n", + "School of Mathematical and Statistical Sciences \n", + "University of Galway\n", + "\n", + "(These notes are adapted from Angela Carnevale's work)\n", + "\n", + "This notebook is at https://www.niallmadden.ie/2425-CS4423/W02/CS4423-W02-1.ipynb\n", + "You can read the HTML version at https://www.niallmadden.ie/2425-CS4423/W02/CS4423-W02-1.html\n", + "\n", + "
    This version of this notebook was written by Niall Madden, adapted from notebooks by Angela Carnevale.
    " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## News: \n", + "### Labs\n", + "\n", + "Labs start next week, and an (reintroduction) to Python. This will run:\n", + "* Tuesday at 4 in AC215 (slight chance this might get moved to Tuesday at 3), and\n", + "* Wednesday at 10am in CA116a. \n", + "\n", + "These rooms are not labs: BYoD! (Bring Your Own Device)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Website\n", + "I now plan to post all notes to https://www.niallmadden.ie/2425-CS4423/ as well as to Canvas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## `networkx`\n", + "Last week we learned a little about the `networkx` package. We'll return to that now, while also revisiting some key ideas about graphs." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As ever, we'll start with importing the `networkx` module, as well as `numpy`: more about that later. And we'll define the `opts` option dictionary." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "import networkx as nx\n", + "import numpy as np\n", + "opts = { \"with_labels\": True, \"node_color\": 'y' } # show labels; yellow noodes" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "To create a graph with nodes $1$, $2$, $3$, $4$, $5$, and edges between all even and odd labelled nodes:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "K32 = nx.Graph() # makes THE empty graph\n", + "K32.add_edges_from([(1, 2), (1,4), (2,3), (2,5), (3,4), (4,5)])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We'll later learn this is the graph $K_{3,2}$. Now draw it:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "nx.draw(K32, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "We can also be lazy, and just give $2$-letter strings for the edges: this implicitly defines the nodes too. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "K33 = nx.Graph([\"A1\", \"A2\", \"A3\", \"B1\", \"B2\", \"B3\", \"C1\", \"C2\", \"C3\"])\n", + "nx.draw(K33, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Check basic properties:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(f\"K33 has {K33.number_of_nodes()} nodes and {K33.number_of_edges()} edges\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "print(f\"This is the same as saying K33 order {K33.order()} and size {K33.size()}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To list the nodes and edges (as lists)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "list(K33.nodes)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "list(K33.edges)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "A **loop** over a graph `G` will effectively loop over `G`'s nodes. As an example, (recall?) that the **degree** of a node is the number of edges incident to it (or, if you prefer, the number of neighbours)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "for node in K33:\n", + " print(f\"node {node} has neighbours {list(K33.neighbors(node))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Adding and removing nodes and edges\n", + "\n", + "We say that \n", + "* `G.add_node('v')` adds a node to $G$ called 'v'\n", + "* `G.add_nodes_from([2, 3, 5])` adds all the nodes from a list\n", + "* `G.add_nodes_from(H])` adds all the nodes from Graph $H$ to Graph $G$\n", + "* `G.add_edge('x','y')` add edge from Node $x$ to Node $y$, adding one or both nodes, if needed.\n", + "* `G.add_edges_from([(1,5), (2,5), (3,5)])` add edges from a list\n", + "* `G.add_edges_from(H.edges)` add edges from another graph\n", + "* `G.remove_edge('x','y')` remove edge from $x$ to $y$, but keep the nodes\n", + "* `G.remove_node('x')` remove node $x$ and any edge it was incident to." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Neighbours and degree\n", + "\n", + "(As we've seen) \n", + "* The **neighbours** of a node are those that it shares an edge with;\n", + "* If nodes $a$ and $b$ are neighbours, we say they are **adjacent**.\n", + "* the **degree of a node** is the number of edges incident to it (or, if you prefer, the number of neighbours).\n", + "\n", + "Let's look at an example:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Edges1 = [('Aoife', 'Brian'), ('Aoife', 'Ciara'), ('Aoife', 'Daire'), ('Aoife', 'Ella'), \n", + " ('Aoife', 'Finn'), ('Brian', 'Ciara'), ('Brian', 'Finn'), ('Ciara', 'Daire'), \n", + " ('Daire', 'Ella'), ('Ella', 'Finn') ]\n", + "G1 = nx.Graph(Edges1)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "nx.draw(G1, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "This is example, which is known as a *wheel graph* is chosen because it exhibits a famous concept in Network Science: *The Friendship Paradox*: your friends (probably) have more friends, on average, than you do!\n", + "\n", + "Explanation:\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "#pos = nx.nx_agraph.graphviz_layout(G1)\n", + "#nx.draw(G1, pos=pos,**opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Important Graphs\n", + "\n", + "In this section we'll discuss some important examples of graphs, which we'll return to later as key examples of networks. These include\n", + "* Complete Graphs\n", + "* Bipartite and complete bipartite graphs\n", + "* Path graphs" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Complete Graphs\n", + "\n", + "The [**complete graph**](https://en.wikipedia.org/wiki/Complete_graph)\n", + "on a vertex set $X$ is the graph with edge set all of $\\binom{X}{2}$. That is: every node is a neighbour of every other node. It is denoted $K_n$ where $n=|X|$. E.g., if $X=\\{0,1,2,3\\}$, then $K_4$ (\"the complete graph on 4 nodes\") has edges $E=\\{01, 02, 03, 12, 13, 23\\}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "nodes = range(4)\n", + "list(nodes) " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "E4 = [(x, y) for x in nodes for y in nodes if x < y]\n", + "print(E4)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "K4 = nx.Graph(E4)\n", + "nx.draw(K4, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "While it is somewhat straightforward to find all $2$-element\n", + "subsets of a given set $X$ with a short `python` program,\n", + "it is probably more convenient (and possibly efficient) to use a function from the\n", + "`itertools` package for this purpose." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "from itertools import combinations\n", + "nodes5 = range(5)\n", + "combinations(nodes5, 2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "print(list(combinations(nodes5, 2)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "K5 = nx.Graph(combinations(nodes5, 2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "nx.draw(K5, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "`networkx` has a built-in function to create complete graphs: `complete_graph` [[doc]](https://networkx.org/documentation/stable//reference/generated/networkx.generators.classic.complete_graph.html)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [], + "source": [ + "nx.draw(nx.complete_graph(\"NETWORKS\"), **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "nx.draw(nx.complete_graph(22), **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Bipartite Graphs\n", + "\n", + "A graph is **bipartite** if we can divide the node set, $X$, into two subsets $X_1$ and $X_2$ such that \n", + "* $X_1 \\cap X_2 = \\emptyset$ (the sets have no edge in common)\n", + "* $X_1 \\cup X_2 = X$ \n", + "* For any edge $(u_1,u_2)$ we have $u_1 \\in X_1$ and $u_2 \\in X_2$. That is we only ever have edges between nodes from different sets. \n", + "\n", + "Such graphs are very common in Network Science, where nodes in the network represent two different types of entities. For example, we might have a graph where nodes represent students and modules, with edges between students and modules they are enrolled in, often called an **affiliation network**." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "Edges2 = [('Aoife', 'CS4423'), ('Aoife', 'CS319'), ('Aoife', 'MA432'), \n", + " ('Brian', 'CS4423'), ('Brian', 'CS319'), \n", + " ('Ciara', 'CS319'), ('Ciara', 'MA432'), \n", + " ('Daire', 'MA432') ]\n", + "G2 = nx.Graph(Edges2)\n", + "nx.draw(G2, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Somehow that previous graph did not catch the essence of the network: there are two different types of node. We could make that clearer, by colouring the nodes. Here we'll do it manually (later, automatically)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "print(G2.nodes)\n", + "color_list= ['c','y','y','y','c', 'c','c'] # y=yellow; c=cyan\n", + "nx.draw(G2, node_color=color_list, with_labels=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Complete Bipartite Graphs\n", + "\n", + "A **complete bipartite graph** is a particular bipartite graph where there is an edge between every node in $X_1$ and every node in $X_2$. Such graphs are denoted $K_{m,n}$ where $|X_1|=m$ and $|X_2|=n$. (We met $K_{2,2}$ and $K_{3,3}$ earlier). \n", + "\n", + "As usual, there is a built-in generator: `complete_bipartite_graph` [[doc]](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.generators.complete_bipartite_graph.html)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "K33 = nx.complete_bipartite_graph(3,3)\n", + "nx.draw(K33,**opts) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Path Graphs\n", + "\n", + "The **Path Graph** with $n$ nodes, denoted $P_n$, is one where two nodes have degree 1, and the other $n-2$ have degree 2:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P4 = nx.Graph([\"ab\", \"bc\", \"cd\", \"de\"])\n", + "nx.draw(P4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "The built-in `nerworkx`generator is called `path_graph` [[doc]](https://networkx.org/documentation/stable/reference/generated/networkx.generators.classic.path_graph.html)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "P10 = nx.path_graph(10)\n", + "nx.draw(P10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercises\n", + "\n", + "1. For what values of $n$ is $K_n$ bipartite?\n", + "2. For what values of $m$ and $n$ is $K_{m,n}$ bipartite?\n", + "3. For what values of $n$ is $P_n$ bipartite?\n", + "5. (Based on Q2(a) from the 2023/2024 CS4423 Exam paper) Let $G$ be the graph on the set of nodes \n", + "$\\{1, 2, 3, 4, 5, 6\\}$ with edges $1-2$, $1-3$, $2-$4, $3-4$, $3-6$, $4-5$, $4-6$. Draw the graph $G$.\n", + "Is $G$ bipartite? Justify your answer. (Note saying $a-b$ is an edge in $G$ is the same as saying $(a,b)$ is an element of its edge set).\n", + "\n", + "6. (Based on Q1(b) of the 2019/2019 CS4423 paper) At a party with $n=5$ people, some people know each other already while others don’t. Each of the 5 guests is asked how many friends they have at this party. Two report that they have one friend each. Two other guests have two friends each, and the fifth guest has three friends at the party. Understanding friendship as a symmetric relation, is this network possible? Why, or why not?\n", + "(*Hint: recall that the sum of all node degrees is twice the number of edges in the graph*).\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    Finished here Wednesday
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    \n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + " # CS4423-Networks : Week 02 - Lecture 2 [$\\color{red}{\\text{DRAFT}}$]\n", + "# From Graphs to Matrices\n", + "Niall Madden, \n", + "School of Mathematical and Statistical Sciences \n", + "University of Galway\n", + "\n", + "(These notes are adapted from Angela Carnevale's nodes)\n", + "\n", + "This Jupyter notebook, and a HTML version, can be found at https://www.niallmadden.ie/2425-CS4423/#Week02\n", + "\n", + "
    This version of this notebook was written by Niall Madden, adapted from notebooks by Angela Carnevale.
    " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Preliminaries\n", + "### Reminder\n", + "\n", + "Labs start next week, and an (reintroduction) to Python. This will run:\n", + "* Tuesday at 4 in AC215 (slight chance this might get moved to Tuesday at 3), and\n", + "* Wednesday at 10am in CA116a. \n", + "\n", + "These rooms are not labs: BYoD! (Bring Your Own Device)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes \n", + "(Revised) Notes from yesterday's class are at https://www.niallmadden.ie/2425-CS4423/#Week02. As well as the material we covered, there is a set of exercises at the end of the notebook, including some based on past exam papers." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "### Modules for this notebook" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "import networkx as nx\n", + "import numpy as np\n", + "opts = { \"with_labels\": True, \"node_color\": 'pink' } # show labels; pink noodes\n", + "from itertools import combinations" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Important Graphs (continued)\n", + "\n", + "Yesteryday, we discussed \n", + "* Complete Graphs, which can be built using, for example `nx.complete_graph(\"NETWORKS\")`\n", + "* Bipartite and complete bipartite graphs, the latter of which can be built using `nx.complete_bipartite_graph(m,n)`. One can also use *list comprehension* to make the edge set: `E = [(x, y) for x in X1 for y in X2 if x < y]`\n", + "* Path graphs, built with `nx.path_graph(10)`. Can also use list comprehension to make the edge set (next week's lab)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Cycle Graphs\n", + "\n", + "Our last example: the **cycle** graph on $n \\geq 3$ nodes, denoted $C_n$, (slightly informally) is formed by adding an edge between to to nodes of degree 1 in a path graph if we delete any one edge is a es is connected, which as a path graph, but with an edge between the two \"end\" nodes. You can make one with `cycle_graph(n)`, but here we'll do it manually.\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "C5 = nx.Graph(['01', '12', '23', '34', '40'])\n", + "nx.draw(C5, **opts) " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "C7 = nx.path_graph(7) # not a cycle graph... yet\n", + "C7.add_edge(0,6)\n", + "nx.draw(C7)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## New Graphs from old\n", + "\n", + "### Complement Graph\n", + "\n", + "The **complement of a graph** $G$ is a graph $H$ with the same nodes as $G$, and two nodes in $H$ are adjacent if and only if they are *not* adjacent in G. \n", + "\n", + "For example, the complement of a complete graph is an empty graph.\n", + "\n", + "In `networkx`, the `complement` function returns to complement of a graph." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[(1, 4), (1, 5), (2, 4), (2, 5), (4, 5)]" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)])\n", + "G_complement = nx.complement(G)\n", + "list( G_complement.edges() ) # This shows the edges of the complemented graph" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "**Tip**: `nx.draw` uses a (semi-random) algorithm, called `spring_layout` for deciding the position of nodes when we draw a graph. Usually, a graph and its complement will be drawn with nodes in different places, making them hard to compare. But we can record the positions determined by the algorithm, and reuse them, as in the next example..." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pos = nx.spring_layout( G)\n", + "nx.draw(G, **opts, pos=pos)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "nx.draw_networkx(G_complement, **opts, pos=pos)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Line Graphs\n", + "\n", + "A graph, $G$, is made from \"things\" that have connections to each other. The \"things\" are nodes, and their connections are represented by an edge.\n", + "\n", + "But we can think of edges as \"things\" too, with connections to any other edge that has a vertex in common. This leads to the idea of a _line graph_.\n", + "\n", + "The **line graph** of $G$, is denoted $L(G)$: every node in $L(G)$ corresponds to an edge in $G$, and for every two edges in $G$ that have a node in common, $L(G)$ has an edge between their corresponding nodes." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Examples" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G = nx.Graph([\"AB\", \"AC\", \"AD\", \"BD\"])\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "LG = nx.line_graph(G)\n", + "nx.draw(LG, **opts, node_size=800) # large nodes to label easier to read" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Line graph of $C_4$" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G = nx.cycle_graph(4)\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "LG = nx.line_graph(G)\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Petersen Graph\n", + "\n", + "Everyone who has a favourite graph has as their favourite graph the [Petersen Graph](https://en.wikipedia.org/wiki/Petersen_graph). It is a graph on $10$ nodes with $15$ edges.\n", + "\n", + "One way to construct it, is as the **complement** of the **line graph** of the complete graph $K_5$." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "K5 = nx.complete_graph(5)\n", + "nx.draw(K5, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Next we make the line graph, $L(K_5)$:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "LK5 = nx.line_graph(K5)\n", + "nx.draw(LK5, **opts, node_size=800)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "And (almost) finally, we take the complement of $L(K_5)$." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "hideCode": false, + "hidePrompt": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Petersen = nx.complement(LK5)\n", + "nx.draw(Petersen, **opts, node_size=800)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "While the graph is correct, we have to be quite careful with the positioning of the nodes to get a proper view of the graph:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "pos = nx.circular_layout(Petersen)\n", + "pos[(0,1)]=[0,5]; pos[(0,2)]=[3,1]; pos[(0,3)]=[2,-2]; pos[(0,4)]=[-3,-4]\n", + "pos[(1,2)]=[3,-4]; pos[(1,3)]=[-2,-2]; pos[(1,4)]=[-3,1]\n", + "pos[(2,3)]=[-5,2]; pos[(2,4)]=[0,3]\n", + "pos[(3,4)]=[5,2]\n", + "nx.draw(Petersen, pos=pos,node_size=800, width=3, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Matrices of Graphs\n", + "\n", + "There are various ways the represent a network/graph, including:\n", + "* The node set and edge set, or\n", + "* a drawing of the graph.\n", + "But, computationally, the most useful way is as a matrix. Three important matrix representations are\n", + "1. **The Adjacency Matrix** (most important)\n", + "2. **Incidence Matrix** (has its uses)\n", + "3. **The Graph Laplacian** (the coolest)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Adjacency Matrix\n", + "\n", + "**Definition** The __adjacency matrix__ of a graph, $G$ of order $n$, is a square $n\\times n$ matrix, $A=(a_{ij})$, \n", + "with rows and columns corresponding to the nodes of the graph. That is, we number the nodes $1, 2, \\dots, n$. Then $A$ is given by \n", + "$$\n", + " a_{ij}=\\begin{cases} 1 & \\mbox{if node $i$ and $j$ are joined by an edge},\\\\\n", + "0 &\\mbox{otherwise}.\\end{cases}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example\n", + "Let $G=G(X,E)$ be the graph with $X=\\{a,b,c,d,e\\}$ and edges $a-b$, $b-c$, $b-d$, $c-d$ and $d-e$.\n", + "Then $$A = \n", + "\\begin{pmatrix}\n", + "0&1&0&0&0\\\\\n", + "1&0&1&1&0\\\\\n", + "0&1&0&1&0\\\\\n", + "0&1&1&0&1\\\\\n", + "0&0&0&1&0\n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Example\n", + "The adjacency matrix of $K_4$ is \n", + "$$ A = \\begin{pmatrix} \n", + "0 & 1 & 1 &1 \\\\\n", + "1 & 0 & 1 &1 \\\\\n", + "1 & 1 & 0 &1 \\\\\n", + "1 & 1 & 1 &0 \n", + "\\end{pmatrix}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Properties of Adjacency matrices \n", + "1. $\\sum_{i=1}^N \\sum_{j=1}^N a_{ij} = \\sum_{u \\in X} \\mathrm{deg}(u)$, where $\\mathrm{deg}(u)$ is the degree of $u$.\n", + "2. All graphs we've seen so far are _undirected_. For all such graphs, $A$ is symmetric: $A=A^T$; equivalently $a_{ij}=a_{ji}$\n", + "4. $a_{ii}=0$ for all $i$.\n", + "3. In real-world examples, $A$ would usually be **sparse**, which means that $\\sum_{i=1}^N \\sum_{j=1}^N a_{ij} \\ll n^2$. (I.e., the vast majority of the entries are zero)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Sparse matrices\n", + "Sparse matrices have huge importance in computational linear algebra. The main idea is that it is much more efficient to just store the location of the non-zero entries. That is what `networkx` does:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Coords\tValues\n", + " (0, 1)\t1\n", + " (0, 3)\t1\n", + " (1, 0)\t1\n", + " (1, 2)\t1\n", + " (2, 1)\t1\n", + " (2, 3)\t1\n", + " (3, 0)\t1\n", + " (3, 2)\t1\n" + ] + } + ], + "source": [ + "C4 = nx.cycle_graph(4)\n", + "A_C4 = nx.adjacency_matrix(C4)\n", + "print(A_C4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "This matrix is internally represented as a `scipy` sparse matrix. It needs to be converted (e.g. by the `toarray` method) in order to be displayed as a matrix as usual.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "scipy.sparse._csr.csr_array" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(A_C4)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "numpy.ndarray" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "type(A_C4.toarray())" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 0 1]\n", + " [1 0 1 0]\n", + " [0 1 0 1]\n", + " [1 0 1 0]]\n" + ] + } + ], + "source": [ + "print(A_C4.toarray())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Another example\n", + "Here is another example, we introduce to look at the idea of creating a graph from a matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "G = nx.Graph([\"ab\", \"bc\", \"bd\", \"cd\", \"de\"])\n", + "nx.draw(G, **opts)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0 1 0 0 0]\n", + " [1 0 1 1 0]\n", + " [0 1 0 1 0]\n", + " [0 1 1 0 1]\n", + " [0 0 0 1 0]]\n" + ] + } + ], + "source": [ + "A = nx.adjacency_matrix(G)\n", + "print(A.toarray())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Now let's make a graph from that matrix:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "H = nx.from_numpy_array(A.toarray())\n", + "nx.draw(H, **opts)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So the graph is more or less the same, but the labels have changed!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "#### More about Adjacency Matrices\n", + "\n", + "Next week we'll learn more about these matrices. In particular, even though they are created just as a table of numbers representing a graph, matrix algebra is really important! Examples:\n", + "* Matrix-vector products can tell us about neighbours of a vertex\n", + "* Matrix-matrix produces can let us compose the actions to two networks\n", + "* Matrix powers tell us about paths of given lengths\n", + "* Even the eigenvalues of $A$ give us information about the network" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "hideCode": false, + "hidePrompt": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercises\n", + "\n", + "1. For what values of $n$ is $C_n$ bipartite?\n", + "2. In this class we looked at a few graph generators in `networkx`. Explore the following: `barbell_graph`, `ladder_graph`, `lollipop_graph`, `star_graph` and `wheel_graph`.\n", + "3. We say two graphs are **equal** if they have the same node and edge sets. We say they are **isomorphic** if there is a relabling of their nodes that makes them equal. Verify that $C_5$ is isomorphic to its complement.\n", + "4. Convince yourself that $C_n$ is always isomorphic to $L(C_n)$, the line graph of $C_n$.\n", + "5. Is the Petersen graph bipartite?\n", + "6. Write down the adjacency matrix of $K_{3,3}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
    Finished here Thursday
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