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  "name": "",
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##todo\n",
      "\n",
      "- Is this form of code the most recent one?\n",
      "- How can I make this more educational?\n",
      "- Write something about setup\n",
      "- Write more about conclusions\n",
      "- Divide code into smaller snippets and comment it a lot"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "\n",
      "import numpy as np\n",
      "import networkx as nx\n",
      "from collections import Counter\n",
      "from matplotlib import pyplot as plt\n",
      "from numpy.random import random_sample\n",
      "from hypergraph.generators import uniform_hypergraph\n",
      "from hypergraph import converters\n",
      "from hypergraph import utils\n",
      "\n",
      "\n",
      "def create_markov_matrix(edges):\n",
      "    a_matrix = np.zeros((len(edges), len(edges)))\n",
      "\n",
      "    for i, edge_1 in enumerate(edges):\n",
      "        for j, edge_2 in enumerate(edges):\n",
      "            if i != j:\n",
      "                a_matrix[i][j] = len(set(edge_1) & set(edge_2))\n",
      "\n",
      "    for i, edge_1 in enumerate(edges):\n",
      "        a_matrix[i] = a_matrix[i] / float(sum(a_matrix[i]))\n",
      "\n",
      "    return a_matrix\n",
      "\n",
      "\n",
      "def weighted_values(values, probabilities, size):\n",
      "    bins = np.add.accumulate(probabilities)\n",
      "    bins[-1] = max(1, bins[-1])\n",
      "    index = np.digitize(random_sample(size), bins)\n",
      "    return values[index]\n",
      "\n",
      "\n",
      "def step_diffusion(current_state, markov_matrix):\n",
      "    values_size = len(markov_matrix)\n",
      "    values = range(values_size)\n",
      "    probs = markov_matrix[current_state]\n",
      "    next_state = weighted_values(values, probs, 1)\n",
      "    return next_state\n",
      "\n",
      "\n",
      "def simulate(current_state, markov_matrix, t_max):\n",
      "    c = Counter()\n",
      "    states = []\n",
      "    for _ in range(t_max):\n",
      "        current_state = step_diffusion(current_state, markov_matrix)\n",
      "        visited_hyperedge = current_state\n",
      "        c[visited_hyperedge] += 1\n",
      "        states.append(visited_hyperedge)\n",
      "    return c.most_common(), states\n",
      "\n",
      "\n",
      "def count_nodes(nodes, edges, occurences):\n",
      "    c = Counter()\n",
      "    for index, count in occurences:\n",
      "        for edge in edges[index]:\n",
      "            c[edge] += count\n",
      "    for node in nodes:\n",
      "        if node not in c:\n",
      "            c[node] = 0\n",
      "    return c\n",
      "\n",
      "def plot_nodes_frequencies(most_common_nodes, title):\n",
      "    plt.bar(list(most_common_nodes.keys()),\n",
      "             list(most_common_nodes.values()),\n",
      "             alpha=0.7, color='magenta')\n",
      "\n",
      "    plt.title(title)\n",
      "    plt.show()\n",
      "\n",
      "\n",
      "def plot_different_representations(nodes, hyperedges):\n",
      "    print(\"Drawing different representations of hypergraph\")\n",
      "\n",
      "    print(\"Bipartite graph\")\n",
      "    nx_bipartite = converters.convert_to_nx_bipartite_graph(nodes, hyperedges)\n",
      "    utils.draw_bipartite_graph(nx_bipartite,\n",
      "                               *utils.hypergraph_to_bipartite_parts(nx_bipartite))\n",
      "\n",
      "    print(\"Graph of hypereges as nodes\")\n",
      "    custom_hyper_g = converters.convert_to_custom_hyper_G(nodes, hyperedges)\n",
      "    plt.figure()\n",
      "    nx.draw(custom_hyper_g)\n",
      "\n",
      "    print(\"Clique graph\")\n",
      "\n",
      "    clique_graph = converters.convert_to_clique_graph(nodes, hyperedges)\n",
      "    plt.figure()\n",
      "    nx.draw(clique_graph)\n",
      "\n",
      "def plot_hyperedges_frequencies(most_common, hyperedges, title):\n",
      "    hyperedges_indexes, occurences = zip(*most_common)\n",
      "    plt.bar(hyperedges_indexes, occurences)\n",
      "    plt.title(title)\n",
      "    plt.xticks(range(len(hyperedges)), hyperedges)\n",
      "\n",
      "\n",
      "def compare_hypergraph_with_cliques(number_of_nodes,\n",
      "                                    cardinality, fraction, t_max, plot_representations=False):\n",
      "    HG = uniform_hypergraph(\n",
      "        n=number_of_nodes,\n",
      "        k=cardinality,\n",
      "        number_of_edges=int(\n",
      "            number_of_nodes *\n",
      "            fraction))\n",
      "\n",
      "    nodes = HG.nodes()\n",
      "    hyperedges = HG.hyper_edges()\n",
      "\n",
      "    all_nodes = []\n",
      "    for hyperedge in hyperedges:\n",
      "        all_nodes += hyperedge\n",
      "    c = Counter(all_nodes)\n",
      "    xs, ys = zip(*c.items())\n",
      "    #plt.bar(xs, ys)\n",
      "\n",
      "    if plot_representations:\n",
      "        plot_different_representations(nodes, hyperedges)\n",
      "\n",
      "    markov_matrix = create_markov_matrix(hyperedges)\n",
      "    print(markov_matrix)\n",
      "    current_state = 1\n",
      "    most_common, states = simulate(current_state, markov_matrix, t_max)\n",
      "\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    plot_hyperedges_frequencies(most_common, hyperedges,\n",
      "                                'Ocurrences of hyperedges in a hypergraph')\n",
      "\n",
      "    most_common_nodes = count_nodes(nodes, hyperedges, most_common)\n",
      "\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    plot_nodes_frequencies(most_common_nodes, 'Nodes in a hypergraph')\n",
      "\n",
      "    clique_graph = converters.convert_to_clique_graph(nodes, hyperedges)\n",
      "    clique_markov_matrix = create_markov_matrix(clique_graph.edges())\n",
      "\n",
      "    print(\"clique markov matrix\")\n",
      "    print(clique_markov_matrix)\n",
      "    most_common, states = simulate(current_state, clique_markov_matrix, t_max)\n",
      "\n",
      "    plt.figure(figsize=(8, 4))\n",
      "    plot_hyperedges_frequencies(most_common, clique_graph.edges(),\n",
      "                                'Ocurrences of edges in a graph')\n",
      "\n",
      "    most_common_nodes = count_nodes(clique_graph.nodes(), clique_graph.edges(),\n",
      "                                    most_common)\n",
      "    plt.figure(figsize=(12, 10))\n",
      "    plot_nodes_frequencies(most_common_nodes, 'Nodes in a graph')\n",
      "\n",
      "\n",
      "def demo():\n",
      "    n = 10\n",
      "    k = 3\n",
      "    fraction = 2.0 / 3\n",
      "\n",
      "    for simulation_time in [100]:\n",
      "        compare_hypergraph_with_cliques(n, k, fraction, simulation_time)\n",
      "\n",
      "\n",
      "if __name__ == '__main__':\n",
      "    demo()\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.          0.14285714  0.28571429  0.28571429  0.28571429]\n",
        " [ 0.2         0.          0.4         0.          0.4       ]\n",
        " [ 0.28571429  0.28571429  0.          0.14285714  0.28571429]\n",
        " [ 0.5         0.          0.25        0.          0.25      ]\n",
        " [ 0.28571429  0.28571429  0.28571429  0.14285714  0.        ]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f47a92b38>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f47a9e630>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "clique markov matrix\n",
        "[[ 0.          0.14285714  0.14285714  0.14285714  0.14285714  0.\n",
        "   0.14285714  0.          0.14285714  0.14285714]\n",
        " [ 0.2         0.          0.2         0.2         0.          0.          0.2\n",
        "   0.2         0.          0.        ]\n",
        " [ 0.2         0.2         0.          0.2         0.          0.2         0.\n",
        "   0.          0.2         0.        ]\n",
        " [ 0.2         0.2         0.2         0.          0.          0.          0.\n",
        "   0.2         0.          0.2       ]\n",
        " [ 0.2         0.          0.          0.          0.          0.2         0.2\n",
        "   0.          0.2         0.2       ]\n",
        " [ 0.          0.          0.33333333  0.          0.33333333  0.          0.\n",
        "   0.          0.33333333  0.        ]\n",
        " [ 0.16666667  0.16666667  0.          0.          0.16666667  0.          0.\n",
        "   0.16666667  0.16666667  0.16666667]\n",
        " [ 0.          0.25        0.          0.25        0.          0.          0.25\n",
        "   0.          0.          0.25      ]\n",
        " [ 0.16666667  0.          0.16666667  0.          0.16666667  0.16666667\n",
        "   0.16666667  0.          0.          0.16666667]\n",
        " [ 0.16666667  0.          0.          0.16666667  0.16666667  0.\n",
        "   0.16666667  0.16666667  0.16666667  0.        ]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f47b38fd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x7f3f50154e48>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#How can we represent hypergraphs in code?\n",
      "\n",
      "A very good representation is bipartite graph of nodes and hyperedges.\n",
      "Another representation is a graph with hyperedges as nodes connected if hyperedges have common nodes.\n",
      "Is it a good representation for our diffusion problem? Can we use it as a reference model?\n",
      "\n",
      "#How different are hypergraphs from graphs with cliques?\n",
      "\n",
      "Cliques are sets of nodes in which every node is connected to every other node.\n",
      "They are a bit similar to hypergraphs, but how the nodes are connected is conceptually different from\n",
      "hypergraphs.\n",
      "\n",
      "How is it different in diffusion simulation with markov chain?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}