bonus-3-matrices-instructor.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "In this notebook, we will explore the use of matrix representations of graphs, and show how their are direct matrix parallels for some of the algorithms that we have investigated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ericmjl/anaconda/envs/nams/lib/python3.6/importlib/_bootstrap.py:219: RuntimeWarning: numpy.dtype size changed, may indicate binary incompatibility. Expected 96, got 88\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx\n",
    "from networkx import bipartite\n",
    "import matplotlib.pyplot as plt\n",
    "import nxviz as nv\n",
    "from custom.load_data import load_university_social_network, load_amazon_reviews\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "import numpy as np\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this notebook, we will specifically see the connection between matrix operations and pathfinding between nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy Example: Linear Chain\n",
    "\n",
    "To start, let us use a simple four-node network, in which nodes are joined in a chain. Convince yourself that this is is a linear chain by running the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = list(range(4))\n",
    "G1 = nx.Graph()\n",
    "\n",
    "G1.add_nodes_from(nodes)\n",
    "G1.add_edges_from(zip(nodes, nodes[1:]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph Form\n",
    "\n",
    "When visualized as circles and lines, the graph looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 479
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G1, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Form\n",
    "\n",
    "When represented in matrix form, it looks like the plot below. (Explain row by columns = node by nodes.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 344,
       "width": 344
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nv.MatrixPlot(G1).draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Playing with the matrix form\n",
    "\n",
    "NetworkX provides a `to_numpy_array()` function that will return a numpy array of the graph. That is used behind-the-scenes in `nxviz` to generate the MatrixPlot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [0., 1., 0., 1.],\n",
       "       [0., 0., 1., 0.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = nx.to_numpy_array(G1, nodelist=sorted(G1.nodes()))\n",
    "A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One neat result is that if we take the adjacency matrix, and matrix-matrix multiply it against itself (\"matrix power 2\"), we will get back a new matrix that has interesting properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 1., 0.],\n",
       "       [0., 2., 0., 1.],\n",
       "       [1., 0., 2., 0.],\n",
       "       [0., 1., 0., 1.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# One way of coding this up\n",
    "np.linalg.matrix_power(A1, 2)\n",
    "\n",
    "# Another equivalent way, that takes advantage of Python 3.5's matrix multiply operator\n",
    "A1 @ A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Firstly**, if we look at the off-diagonals of the new matrix, this corresponds to the number of paths of length 2 that exist between those two nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 2., 1.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(A1 @ A1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, one path of length 2 exists between node 0 and node 2, and one path of length 2 exists between node 1 and node 3.\n",
    "\n",
    "**Secondly**, you may notice that the diagonals look like the degree of the nodes. This is a unique property of the 2nd adjacency matrix power: for every node, there are $ d $ degree paths of length two to get back to that same node.\n",
    "\n",
    "Not convinced? To get from a node and back, that's a path length of 2! :-)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if the following statment is true: The $ k^{th} $ matrix power of the graph adjacency matrix indicates how many paths of length $ k $ exist between each pair of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 2., 0., 1.],\n",
       "       [2., 0., 3., 0.],\n",
       "       [0., 3., 0., 2.],\n",
       "       [1., 0., 2., 0.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_power(A1, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, if we think about it, there is, by definition, no way sequence of graph traversals that will allow us to go back to a node within 3 steps. We will always end up at some neighboring node.\n",
    "\n",
    "In addition, to get to the neighboring node in 3 steps, there are two ways to go about it:\n",
    "\n",
    "- node -> neighbor -> node -> neighbor\n",
    "- node -> neighbor -> neighbor's neighbor -> neighbor\n",
    "\n",
    "Or for the case of this chain graph:\n",
    "\n",
    "- 0 -> 1 -> 0 -> 1\n",
    "- 0 -> 1 -> 2 -> 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy Example: Directed Linear Chain\n",
    "\n",
    "Let's see if the same properties hold for a directed graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9/q233iq55thjjy0KxO3t7Tn11FNTX19f4ScAoNKEZQBg1Ojr68uGDRuKusRr1qzJzp07S66ZMmVK5s2bV9QtPvnkk51RDHAUE5YBgJpz4MCBrFu3rigUd3Z2Zs+ePSXXzJgxo2SneMaMGUIxAEWEZQBgxNq7d29eeOGFoo22urq6sn///pJrTj755KJNttra2vKRj3ykwtUDUMuEZQCg6np7e9PV1VXUKV67dm36+vpKrjnttNOKusRtbW057rjjKlw9AKORsAwAVMzOnTsP6hK/+/369etTKBSKrq+rq8ucOXOKQnFLS0uOOeaYKjwBAEcLYRkAGHZvvfVWyTOKX3rppZLXjxkzJnPnzi3aZKu5uTkTJkyocPUAICwDAEfgjTfeKHlG8auvvlry+nHjxqWlpaWoUzxnzpyMGzeuwtUDwPsTlgGAD1QoFLJ58+ai84k7OjqyZcuWkmsmTJhQ1CVua2vL6aefnjFj/PUDgJHP/60AgCQDoXjTpk0lO8VvvfVWyTXHHHPMn4PwvHnz/hyMTzvttNTX11f4CQBg+AjLAHCU6e/vT09PT9EmWx0dHdm5c2fJNccff/xBYfjdr5NPPtkZxQCMSsIyAIxSBw4cyPr164u6xJ2dnent7S25ZsaMGQedT/zu1wknnCAUA3BUEZYBoMbt27cvL7zwQlEo7u7uzr59+0quOemkk0qeUfyRj3ykwtUDwMgkLANAjejt7U1XV1fRJlsvvPBC+vr6Sq457bTTDgrD7/56/PHHV7h6AKgtwjIAjDA7d+5MZ2dnUad4/fr1KRQKRdfX1dXljDPOKOoUt7a25phjjqnCEwBA7ROWAaBK3nrrrT93id/bLd6wYUPJ6xsaGjJ37tyi0emWlpZMmDChwtUDwOgmLANAmb355pslj2N65ZVXSl4/bty4NDc3F3WK586dm3HjxlW4egA4OgnLADAMCoVCXnvttaJAvGbNmrz++usl1zQ2NhbtOt3e3p7TTz89Y8b4XzQAVJP/EwPAEBQKhWzatKlok62Ojo5s27at5JpjjjmmaJOt9vb2nHbaaWloaKjwEwAAgyEsA0AJ/f392bBhQ8lO8Y4dO0quOf7444u6xO3t7Zk1a5YzigGgxgjLABzVDhw4kPXr1x8Uht/9tbe3t+Sa6dOnlzyj+MQTTxSKAWCUEJYBOCrs27cva9euLeoUd3V1Zd++fSXXzJw5s2Qonj59eoWrBwAqTVgGYFTZs2dPurq6ikanX3jhhRw4cKDkmlNPPbVkKD7++OMrXD0AMFIIywDUpJ07d6azs7Noo63169env7+/6Pq6urqcccYZRZtstba25thjj63CEwAAI1ldoVAoVLsIAHg/27dvL7nz9IYNG0pe39DQkDlz5hR1iltaWjJhwoQKVw8A1CqdZQBGhDfffLNodLqjoyMvv/xyyevHjh2blpaWoiOZ5s6dm/Hjx1e4egBgtBGWAaiYQqGQ119/vahL3NHRkddff73kmsbGxrS2thZ1ik8//fSMHTu2wk8AABwthGUAhl2hUMjLL79cMhRv27at5JpJkyaV3GSrqakpDQ0NFX4CAOBoJywDcNj6+/uzYcOGg8am3/3asWNHyTXHHXdcUShub2/PrFmzUl9fX+EnAAAoTVgG4EP19fVl/fr1RV3izs7O7N69u+SaadOmZd68eUWh+MQTT0xdXV2FnwAAYGiEZQD+bN++fVm7dm3RRltdXV3Zu3dvyTUzZ84sOo6pvb0906dPr3D1AADDR1gGOArt2bMn3d3dRZ3iF154IQcOHCi55pRTTin5TvGUKVMqXD0AQPkJywCj2K5du9LZ2VkUitevX5/+/v6i6+vq6nL66acXBeLW1tZMnjy5Ck8AAFAddYVCoVDtIgA4Mtu3b8+aNWuKNtnq6ekpeX1DQ0POOOOMok5xS0tLJk6cWNniAQBGIJ1lgBqydevWkscxvfzyyyWvHzt2bJqbm4tC8dy5czN+/PgKVw8AUDuEZYARplAo5PXXXy/aZKujoyOvvfZayTWNjY1pbW0t2mTrjDPOyNixYyv8BAAAtU9YBqiSQqGQV155pWSneOvWrSXXTJo0qSgQt7e3p6mpKQ0NDRV+AgCA0UtYBiiz/v7+vPTSS0WBeM2aNXn77bdLrjnuuOOKNtlqb2/PKaeckvr6+go/AQDA0UdYBhgmfX19Wb9+fdEmW2vWrMnu3btLrpk2bVpRl7i9vT0zZ85MXV1dhZ8AAIB3CcsAQ7R///6sXbu2qFPc1dWVvXv3llxz4oknlgzF06dPr3D1AAAMhrAM8D727NmT7u7uok22uru7c+DAgZJrZs2aVRSI29raMnXq1ApXDwDAkRCWgaPe7t2709nZWdQpXrduXfr7+0uumT17dlEobm1tzeTJkytcPQAA5VBXKBQK1S4CoBLefvvtoveJOzo6smHDhpT6T2F9fX3mzJlTtPt0S0tLJk2aVIUnAACgUnSWgVFn69atJUPxpk2bSl4/ZsyYNDc3F3WK586dm8bGxgpXDwDASCAsAzWpUChky5YtJc8ofu2110quGT9+fFpbW4uOY5ozZ07Gjh1b4ScAAGAkE5aBEa1QKOSVV14p2mSro6Mjb775Zsk1EydOLBqdbm9vz+zZs9PQ0FDhJwAAoBYJy8CI0N/fn40bN5bsFL/99tsl10yePLnkcUynnHJK6uvrK/wEAACMJsIyUFF9fX158cUXiwJxZ2dndu3aVXLN1KlTM2/evKJu8UknnZS6uroKPwEAAEcDYRkoi/3792ft2rVFo9OdnZ3Zu3dvyTUnnHBCyU7x9OnThWIAACpKWKb29PQkf/pTsnp18tRTydatyb59ybhxydSpydlnJwsWJOeemzQ1VbvaUW/v3r3p7u4u6hR3d3fnwIEDJdfMmjWraJOttra2TJs2rcLVAwBAac5Zpjb09iY/+lFyxx3JE08Mft155yVf+1py2WXJhAnlq+8osHv37nR2dh4UiNesWZO1a9emv7+/5JqmpqaiLnFra2uOO+64ClcPAABDIywzsvX1JStWJMuWDXSQD9fUqcl11yVLlyZ2Q/5AO3bsKHlGcU9PT0r956K+vj5nnHFGUShuaWnJpEmTqvAEAABw5IRlRq7OzuRLX0r++Mfh+8zzz0/uuSdpbR2+z6xR27ZtK7nz9KZNm0peP2bMmDQ3NxdtstXc3JzGxsYKVw8AAOUlLDMy3Xdf8jd/k7zPRlBHZPz45O67kyuuGP7PHmEKhUK2bNlStMlWR0dHNm/eXHLNuHHj0traWtQpnjNnTsaOHVvhJwAAgOoQlhl5fvCD5N/9u/Leo64u+f73k7/92/Lep0IKhUJeffXVkp3iN998s+SaiRMnpq2trahTPHv27IwZY+8/AACObsIyI8t99yV/8ReVuVddXXLvvTXVYe7v78/GjRuLNtnq6OjI9u3bS6459thjSx7HdOqpp6a+vr7CTwAAALVBWGbk6OxM5s//0NHrHUl+m+SJJH9659d3e6drkgzpbeTx45Onnx5x7zD39fWlp6enqEu8Zs2a7Nq1q+SaKVOmZN68eQcdx9Te3p6TTz7ZGcUAADBEZi0ZGfr6BjbzGsQ7yr9O8rnhuu/evclf/3WyatWH7pL9hz/8IbfcckuuueaaLFq0aFhuv3///qxbt64oFHd1dWXPnj0l18yYMaNkp3jGjBlCMQAADBNhmZFhxYoh7Xo9I8m5Sc5LcnKSI3rz+NFHB+7/7/99yT8+cOBAbrrppnzrW99Kf39/GhsbhxyW9+7dm+7u7qJNtrq7u7N///6Sa04++eSiQNzW1pZp06YN+REBAIChMYZN9fX2JrNmDfoc5b4k7+0B9ySZ/c73Qx7DftfUqcmmTcmECQf99ksvvZQrrrgi//zP//zn3zvrrLPyzDPPlPyY3bt3p6urq6hTvG7duvT19ZVc09TUVLTJVltbW4477rjDeRIAAGAY6CxTfT/60aCDcnJwUB42W7cmDzyQXHnln3/rxz/+cf7tv/23eeuttw66tKurK2+99Va6u7uLNtl68cUXU+rnT/X19ZkzZ05Rp7ilpSXHHHNMOZ4IAAA4AjrLVN/ChckTTxz28p4MQ2f53Toeeyy7du3K3/3d3+Wuu+4a8keMGTMmc+fOPahD3N7enubm5kw4pGsNAACMXDrLVFdPzxEF5WH1+OP54/3351Nf/Wq2bdv2gZeOGTOmaHS6vb09c+bMybhx4ypUMAAAUC7CMtX1pz9Vu4KD/Pg//scPDcpJcuONN+a6666rQEUAAEA11Fe7AI5yq1dXu4KDfOPii3PRRRdlxowZH3hdZ2dnhSoCAACqQVimup56qtoVHOSEl1/Ob37zm2zevDlPPfVU/tN/+k+ZP39+0XXPP/98FaoDAAAqRVimuoawC3ZFvDOCXVdXl/nz5+fv//7v89RTT6Wnpye33XZbLr744jQ0NOSEE06ocqEAAEA52Q2b6po/P3mfM4sHqyfDtBt2kvyLf5E8/fQHXrJ79+6MHTs2Y8eOPZI7AQAAI5gNvqiukbZz9PjxH3rJxIkTK1AIAABQTcawqa6pU6tdwcGmTKl2BQAAwAggLFNdZ59d7QoOds451a4AAAAYAYxhU10LFhzWsjfe8/17T0V+65A/m5oh/kToMOsBAABGFxt8UV09Pcns2R962aHqBnndi0mahvLBL76YNA1pBQAAMAoZw6a6mpqS886rdhUDFi4UlAEAgCTCMiPBV7865CWFQX41lbkOAABgdDKGTfX19iazZiVbt1avhqlTk5dfThobq1cDAAAwYugsU30TJiTXXVfdGq67TlAGAAD+TGeZkaGvL7ngguSPf6z8vRctSlatShoaKn9vAABgRBKWGTk6O5P585O9eyt3z/Hjk2eeSVpaKndPAABgxDOGzcjR2prcfXdSN9iDoY5QXd3A/QRlAADgEMIyI8sVVyTf/375A3Nd3cB9rriivPcBAABqkjFsRqb77kv+5m/KM5Ld2Jj84z8KygAAwPsSlhm5OjuTL31peDf9WrQoueceo9cAAMAHMobNyNXamvzzPye33DJwDvKRmDp14HNWrRKUAQCAD6WzTG3o7U0eeCC5447k8ccHv27hwuRrX0suvXTgPGcAAIBBEJapPT09yerVyerVeePhh7Nu9ep85JhjckZ7ezJlSnLOOcmCBQNfTU3VrhYAAKhBwjI17Ze//GU+/elP55Of/GT+6Z/+qdrlAAAAo4R3lqlpBw4cSJKMHTu2ypUAAACjibBMTdu/f3+SZMyYMVWuBAAAGE2EZWrau51lYRkAABhOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA7CMjXNGDYAAFAOwjI1zRg2AABQDsIyNc0YNgAAUA51hUKhUO0i4HAUCoXU1w/8vKe/vz91dXVVrggAABgtdJapWX19fUmShoYGQRkAABhWwjI1ywg2AABQLsIyNcvmXgAAQLkIy9Qsx0YBAADlIixTs4xhAwAA5SIsU7OMYQMAAOUiLFOzjGEDAADlIixTs4xhAwAA5SIsU7OMYQMAAOUiLFOzjGEDAADlIixTs4xhAwAA5SIsU7OMYQMAAOUiLFOzjGEDAADlIixTs4xhAwAA5SIsU7OMYQMAAOUiLFOz3g3LDQ0NVa4EAAAYbYRlata7Y9g6ywAAwHATlqlZxrABAIByEZapWXbDBgBIzSEVAAAgAElEQVQAykVYpmbZDRsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKBdhmZplDBsAACgXYZmaZQwbAAAoF2GZmmUMGwAAKJe6QqFQqHYRMFSFQiH19QM/6+nv709dXV2VKwIAAEYTnWVqUl9fX5KkoaFBUAYAAIadsExNMoINAACUk7BMTbITNgAAUE7CMjXJTtgAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOQnL1CRj2AAAQDkJy9QkY9gAAEA5CcvUJGPYAABAOUka1IQdO3bkP//n/5ydO3dm7NixeeaZZ5Ik/+N//I9873vfy9ixYzNp0qRceumlOf7446tcLQAAUOvqCoVCodpFwIe5//7782/+zb/50OtuvPHG3HDDDRWoCAAAGM2MYVMTPvGJT2TSpEkfet3HP/7xClQDAACMdsIyNWHatGn58pe//IHXfOpTn8q//Jf/skIVAQAAo5kxbGrGq6++mqampuzbt6/knz/55JM5++yzK1wVAAAwGuksUzNmzpyZv/7rvy75Z5deeqmgDAAADBudZWrKiy++mLlz56avr+/Pv1dfX5/nn38+ra2tVawMAAAYTXSWqSmzZ8/O5ZdfftDv/dVf/ZWgDAAADCudZWrOmjVr0t7eniRpaGjI2rVr09TUVN2iAACAUUVnmZrT1taWtra2JMkFF1wgKAMAAMNOWKYmPfjgg7n00ktz//33V7sUAABgFDKGTW3o6Un+9Kdk9erkqaeSrVuTffuSceOSqVOTs89OFixIzj030WkGAACOkLDMyNXbm/zoR8kddyRPPDH4deedl3zta8lllyUTJpSvPgAAYNQSlhl5+vqSFSuSZcsGOsiHa+rU5LrrkqVLk4aG4asPAAAY9YRlRpbOzuRLX0r++Mfh+8zzz0/uuSdxvBQAADBINvhi5LjvvmT+/OENysnA582fP/D5AAAAgyAsMzL84AfJX/xFsndveT5/797kL/9y4D4AAAAfwhg21XfffQNBuRLq6pJ7702uuKIy9wMAAGqSsEx1dXYOjEh/SEf5pST/NcmvkzyT5LUk45KcnuR/TbIkyczB3nP8+OTpp73DDAAAvC9hmerp60suuOBD31HemOS0JO/9F3Vykl1J+t755ylJfpLkosHee9GiZNUqu2QDAAAleWeZ6lmxYlCbeb0biD+d5P9JsjXJ9iS7k/wyyewk25L870k2D/bejz46cH8AAIASdJapjt7eZNasQZ2jvD1JT5J/8T5/3pnk7CR7kvynJH8/2BqmTk02bUomTBjsCgAA4Cihs0x1/OhHgwrKSXJc3j8oJ0lrkvPf+X71UGrYujV54IGhrAAAAI4SwjLVcccdw/px0975te8Dryp/HQAAwOggLFN5PT3JE08M28cdSPKHd74/c6iLH398oB4AAID3EJapvD/9aVg/7v/OwMZe9Un+6nA+YPWQhrcBAICjgLBM5Q1jOH02yXXvfP9/JJlX5XoAAIDRQVim8p56alg+5tUMHBe1O8mCJDcf7gc9+eSw1AMAAIwewjKVN8hdsD/wI5JckuTFJHOT/CJJ4+F+2LZtR1wPAAAwugjLVN6+fUe0fHuSf5XkuSSnJvlVkhOO5AP37j2iegAAgNFHWKbyxo077KW7knwqyZ+SnJiBoHzqkdYzfvyRfgIAADDKCMtU3tSph7WsN8lnkzySgXOVf5WBEewjNmXKcHwKAAAwigjLVN7ZZw95yb4k/zrJb5Mcn+ThHObO16Wcc85wfRIAADBKCMtU3oIFQ7q8L8nlSR5KcmySf0oyrPF2iPUAAACjX12hUChUuwiOMj09yezZg77890n+p3e+b0xy3Adce0qSJ4Zaz4svJk1NQ10FAACMYmOqXQBHoaam5LzzkicGF2v73/P9nne+3s+Qj49auFBQBgAAihjDpjq++tVBX/o/JykM8qunjHUAAABHD2PYVEdvbzJrVrJ1a9VK2D1hQgobN2bStGlVqwEAABiZdJapjgkTkuuuq8qt3/3p0P/Z25vW+fNz//33x8+MAACA99JZpnr6+pILLkj++MeK3/rtM8/M/zJuXJ548skkyYUXXpiVK1dm/vz5Fa8FAAAYeXSWqZ6GhuSee5Lx4yt73/HjM/nHP86jjz+eu+66Kx/5yEeyatWqLFiwIF/5ylfyxhtvVLYeAABgxBGWqa7W1uTuu5O6usrcr65u4H4tLWloaMhVV12VF154IUuXLk1dXV2+//3vp7m5Of/wD/+QAwcOVKYmAABgxDGGzcjwgx8kX/5yUs5/Hevqku9/P/nbvy35xx0dHVmyZEl+9atfJUnOPPPMrFy5MhdddFH5agIAAEYknWVGhr/92+Tee8s3kt3YOPD57xOUk6S9vT0PP/xwHnzwwTQ1NeW5557LxRdfnMsuuywbNmwoT10AAMCIpLPMyNLZmXzpS8O76deiRQPvRre0DHpJb29vli9fnmXLlqW3tzeNjY259tprc80112TChAnDVxsAADAiCcuMPH19yYoVybJlR3YO89SpA8dTLV06sJnYYdi4cWOuueaa3H///UmS0047Lbfccks+//nPp65S71kDAAAVJywzcvX2Jg88kNxxR/L444Nft3Bh8rWvJZdeOnCe8zD4/e9/n8WLF+eZZ55Jklx00UVZuXJlzjzzzGH5fAAAYGQRlqkNPT3J6tUDX08+mWzbluzdO/CO85QpyTnnJAsWDHw1NZWlhL6+vtx111355je/ma1bt6ahoSFf/epXc+ONN2bKlClluScAAFAdwjIM0datW3PDDTfkzjvvTH9/f6ZNm5abbropV111VRoOc9wbAAAYWYRlOEzPPvtslixZkt/97ndJkvnz5+f222/PBRdcUN3CAACAI+boKDhMZ511Vn7zm9/kgQceyCmnnJKnn346F154YS6//PJs2rSp2uUBAABHQGcZhsHu3btz880357vf/W727NmTiRMn5pvf/GauvvrqNDY2Vrs8AABgiIRlGEY9PT35+te/np/85CdJktNPPz233nprPvvZzzpqCgAAaoiwDGXw61//OkuWLMnzzz+fJLnkkkuyYsWKtLW1VbkyAABgMLyzDGXw8Y9/PE899VRuu+22HH/88Xn44Ydz1lln5eqrr8727durXR4AAPAhdJahzLZs2ZLrr78+d911VwqFQmbMmJFvf/vb+eIXv5j6ej+vAgCAkUhYhgp58skns3jx4vzhD39Ikpx33nlZuXJlzj///CpXBgAAHEpbCyrknHPOyapVq3LfffflpJNOyhNPPJFFixblyiuvzKuvvlrt8gAAgPfQWYYq2LlzZ5YtW5bly5dn3759OeaYY3LDDTdkyZIlGTduXLXLAwCAo56wDFW0bt26XH311fnZz36WJGlubs6tt96aT33qU1WuDAAAjm7CMowADz30UJYuXZqurq4kyac//enceuutmTt3bpUrAwCAo5N3lmEE+OQnP5lnn302y5cvz7HHHptf/OIXmTdvXq699trs2LGj2uUBAMBRR2cZRpjNmzfnuuuuyz333JMkmTlzZm6++eZcccUVjpoCAIAKEZZhhHr88cezePHiPPbYY0mSRYsWZeXKlTn33HOrXBkAAIx+2lQwQi1cuDCPPPJIfvjDH+aEE07Io48+moULF+aqq67K66+/Xu3yAABgVBOWYQSrr6/PlVdeme7u7nzjG9/ImDFjcvfdd6e5uTkrVqzI/v37q10iAACMSsawoYZ0dXVl6dKleeihh5IkbW1tue222/KJT3yiypUBAMDoorMMNaSlpSW//OUv8/Of/zxz5szJmjVrcskll+Rzn/tc1q9fX+3yAABg1BCWocbU1dXlM5/5TJ577rl85zvfyaRJk/LTn/407e3tuf7667Nr165qlwgAADXPGDbUuFdeeSX/4T/8h/yX//JfkiSzZs3K9773vXzhC19IXV1dlasDAIDaJCzDKPHII49k8eLFWb16dZLkwgsvzMqVKzN//vwqVwYAALXHGDaMEh/96Efz2GOP5a677spHPvKRrFq1KgsWLMhXvvKVvPHGG9UuDwAAaoqwDKNIQ0NDrrrqqrzwwgtZunRp6urq8v3vfz/Nzc35h3/4hxw4cKDaJQIAQE0whg2jWEdHR5YsWZJf/epXSZIzzzwzK1euzEUXXVTlygAAYGTTWYZRrL29PQ8//HAefPDBNDU15bnnnsvFF1+cyy67LBs2bKh2eQAAMGLpLMNRore3N8uXL8+yZcvS29ubxsbGXHvttbnmmmsyYcKEapcHAAAjirAMR5mNGzfmmmuuyf33358kOe2003LLLbfk85//vKOmAADgHcIyHKV+//vfZ/HixXnmmWeSJBdddFFWrlyZM888s8qVAQBA9XlnGY5SH/vYx7J69erceeedmTp1an77299m/vz5Wbx4cbZt21bt8gAAoKp0loFs3bo1N9xwQ+6888709/dn2rRpuemmm3LVVVeloaGh2uUBAEDFCcvAnz377LNZsmRJfve73yVJ5s+fn9tvvz0XXHBBdQsDAIAKM4YN/NlZZ52V3/zmN3nggQdyyimn5Omnn86FF16Yyy+/PJs2bap2eQAAUDE6y0BJu3fvzs0335zvfve72bNnTyZOnJhvfvObufrqq9PY2Fjt8gAAoKyEZeAD9fT05Otf/3p+8pOfJElOP/303HrrrfnsZz/rqCkAAEYtYRkYlF//+tdZsmRJnn/++STJJZdckhUrVqStra3KlQEAwPDzzjIwKB//+Mfz1FNP5bbbbsvxxx+fhx9+OGeddVauvvrqbN++vdrlAQDAsNJZBoZsy5Ytuf7663PXXXelUChkxowZ+fa3v50vfvGLqa/3MzgAAGqfsAwctieffDKLFy/OH/7whyTJeeedl5UrV+b888+vcmUAAHBktICAw3bOOedk1apVue+++3LSSSfliSeeyKJFi3LllVfm1VdfrXZ5AABw2HSWgWGxc+fOLFu2LMuXL8++fftyzDHH5IYbbsiSJUsybty4apcHAABDIiwDw2rdunW5+uqr87Of/SxJ0tzcnFtvvTWf+tSnqlwZAAAMnrAMlMVDDz2UpUuXpqurK0ny6U9/Orfeemvmzp1b5coAAODDeWcZKItPfvKTefbZZ7N8+fIce+yx+cUvfpF58+bl2muvzY4dO6pdHgAAfCCdZaDsNm/enOuuuy733HNPkmTmzJm5+eabc8UVVzhqCgCAEUlYBirm8ccfz+LFi/PYY48lSRYtWpSVK1fm3HPPrXJlAABwMC0doGIWLlyYRx55JD/84Q9zwgkn5NFHH83ChQtz1VVX5fXXX692eQAA8GfCMlBR9fX1ufLKK9Pd3Z1vfOMbGTNmTO6+++40NzdnxYoV2b9/f7VLBAAAY9hAdXV1dWXp0qV56KGHkiRtbW257bbb8olPfKLKlQEAcDTTWQaqqqWlJb/85S/z85//PHPmzMmaNWtyySWX5HOf+1zWr19f7fIAADhKCctA1dXV1eUzn/lMnnvuuXznO9/JpEmT8tOf/jTt7e25/vrrs2vXrmqXCADAUcYYNjDivPLKK7n22mtz7733JklmzZqV733ve/nCF76Qurq6KlcHAMDRQFgGRqxHHnkkixcvzurVq5MkF154YVauXJn58+dXuTIAAEY7Y9jAiPXRj340jz32WO66665Mnz49q1atyoIFC/KVr3wlb7zxRrXLAwBgFNNZBmrCW2+9lRtvvDG33357+vr6MmXKlHzrW9/Kl7/85YwZM6ba5QEAMMoIy0BN6ejoyJIlS/KrX/0qSXLmmWdm5cqVueiii6pcGQAAo4kxbKCmtLe35+GHH86DDz6YpqamPPfcc7n44otz2WWXZcOGDdUuDwCAUUJnGahZvb29Wb58eZYtW5be3t40Njbm2muvzTXXXJMJEyZUuzwAAGqYsAzUvI0bN+aaa67J/fffnyQ57bTTcsstt+Tzn/+8o6YAADgswjIwavz+97/P4sWL88wzzyRJLrrooqxcuTJnnnlmlSsDAKDWeGcZGDU+9rGPZfXq1bnzzjszderU/Pa3v838+fOzePHibNu2rdrlAQBQQ3SWgVFp69atueGGG3LnnXemv78/06ZNy0033ZSrrroqDQ0N1S4PAIARTlgGRrVnn302S5Ysye9+97skyfz583P77bfnggsuqG5hAACMaMawgVHtrLPOym9+85s88MADOeWUU/L000/nwgsvzOWXX55NmzZVuzwAAEYonWXgqLF79+7cfPPN+e53v5s9e/Zk4sSJ+eY3v5mrr746jY2N1S4PAIARRFgGjjo9PT35+te/np/85CdJktNPPz233nprPvvZzzpqCgCAJMIycBT79a9/nSVLluT5559PklxyySVZsWJF2traqlwZAADV5p1l4Kj18Y9/PE899VRuu+22HH/88Xn44Ydz1lln5eqrr8727durXR4AAFWkswyQZMuWLbn++utz1113pVAoZMaMGfn2t7+dL37xi6mv93NFAICjjbAM8B5PPvlkFi9enD/84Q9JkvPOOy8rV67M+eefX+XKAACoJO0SgPc455xzsmrVqtx333056aST8sQTT2TRokW58sor8+qrr1a7PAAAKkRnGeB97Ny5M8uWLcvy5cuzb9++HHPMMbnhhhuyZMmSjBs3rtrlAQBQRsIywIdYt25drr766vzsZz9LkjQ3N+fWW2/Npz71qSpXBgBAuQjLAIP00EMPZenSpenq6kqSfPrTn86tt96auXPnVrkyAACGm3eWAQbpk5/8ZJ599tksX748xx57bH7xi19k3rx5ufbaa7Njx45qlwcAwDDSWQY4DJs3b851112Xe+65J0kyc+bM3HzzzbniiiscNQUAMAoIywBH4PHHH8/ixYvz2GOPJUkWLVqUlStX5txzz61yZQAAHAntD4AjsHDhwjzyyCP54Q9/mBNOOCGPPvpoFi5cmKuuuiqvv/56tcsDAOAwCcsAR6i+vj5XXnlluru7841vfCNjxozJ3Xffnblz52bFihXZv39/tUsEAGCIjGEDDLOurq4sXbo0Dz30UJKkra0tt912Wz7xiU9UuTIAAAZLZxlgmLW0tOSXv/xlfv7zn2fOnDlZs2ZNLrnkknzuc5/L+vXrq10eAACDICwDlEFdXV0+85nP5Lnnnst3vvOdTJo0KT/96U/T3t6e66+/Prt27ap2iQAAfABj2AAV8Morr+Taa6/NvffemySZNWtWvve97+ULX/hC6urqqlwdAACHEpYBKuiRRx7J4sWLs3r16iTJhRdemJUrV2b+/PlVrgwAgPcyhg1QQR/96Efz2GOP5a677sr06dOzatWqLFiwIF/5ylfyxhtvVLs8AADeobMMUCVvvfVWbrzxxtx+++3p6+vLlClT8q1vfStf/vKXM2bMmGqXBwBwVBOWAaqso6MjS5Ysya9+9askyZlnnpmVK1fmoosuqnJlAABHL2PYAFXW3t6ehx9+OA8++GCampry3HPP5eKLL85ll12WDRs2VLs8AICjks4ywAjS29ub5cuXZ9myZent7U1jY2OuvfbaXHPNNZkwYUK1ywMAOGoIywAj0MaNG3PNNdfk/vvvT5KcdtppueWWW/L5z3/eUVMAABUgLAOMYL///e+zePHiPPPMM0mSiy66KCtXrsyZZ55Z5coAAEY37ywDjGAf+9jHsnr16tx5552ZOnVqfvvb32b+/PlZvHhxtm3bVu3yAABGLZ1lgBqxdevW3HDDDbnzzjvT39+fadOm5aabbspVV12VhoaGapcHADCqCMsANebZZ5/NkiVL/r/27j7Gq/reE/h7gCsPaldofLiKW0qkykMI5amOC02QSBsfsrGN2iu7i0ZyL9a9M2SuIhcoW0yKik6AIZGuU6wbl2wlNRqNhlKxxLlgAQeQIoopFFeuLugFreIALrJ/DNt6T70ygzOcmeH1Sn6Z4Tffc86bP9+/z/f8TtasWZMkGTFiRJYsWZJx48aVGwwAoAuxDRugkxk+fHheeOGFrFixIhdffHG2bNmS8ePH5+abb86ePXvKjgcA0CWYLAN0Yh9//HHuv//+LFiwIIcOHUqfPn0ye/bs1NTUpFevXmXHAwDotJRlgC5g9+7dufPOO/PEE08kSQYOHJiFCxfmuuuu86gpAICToCwDdCGrV69OdXV1Xn311STJpEmTsmjRogwePLjkZAAAnYt7lgG6kIkTJ2bz5s1ZvHhxzjnnnKxatSrDhw9PTU1NPvjgg7LjAQB0GibLAF3Uu+++mzlz5qS+vj7Hjh3Leeedl3vvvTe33HJLunXzWSkAwBdRlgG6uE2bNqWqqipr165NkowZMyZ1dXW5/PLLS04GANBxGS0AdHEjR45MQ0NDli9fngsvvDAbN25MZWVlpkyZknfeeafseAAAHZLJMsBp5KOPPsr8+fNTW1ubI0eO5KyzzsrcuXNTXV2dM844o+x4AAAdhrIMcBrauXNnampq8vTTTydJvvGNb2ThwoW5+uqrS04GANAxKMsAp7GVK1dm+vTp2bFjR5LkmmuuycKFCzNo0KCSkwEAlMs9ywCnse9+97vZunVramtrc/bZZ+fZZ5/N0KFDc/fdd+fDDz8sOx4AQGlMlgFIkuzduzezZs3KI488kiS54IILsmDBgkyePNmjpgCA046yDMC/smHDhlRVVWX9+vVJksrKytTV1WX06NElJwMAOHWMCgD4V8aOHZt169bl0Ucfzfnnn5+XXnopY8eOzdSpU7Nv376y4wEAnBLKMgB/oVu3bpkyZUreeOON3HXXXenRo0eWLVuWQYMGZdGiRfnkk0/KjggA0K5swwbghHbs2JHp06dn5cqVSZLBgwdn8eLFueqqq0pOBgDQPkyWATihSy+9NM8991yeeeaZXHLJJXnttdcyadKkXH/99dm1a1fZ8QAA2pyyDECLVFRU5Nprr822bdty33335cwzz8xTTz2VIUOGZM6cOTl48GDZEQEA2oxt2ACclLfffjszZ87MY489liTp379/Hnjggdx0002pqKgoOR0AwJejLAPwpaxbty5VVVVpbGxMkowfPz51dXUZMWJEyckAAE6ebdgAfClXXHFF1q9fn/r6+px77rlpaGjIqFGjcvvtt+e9994rOx4AwEkxWQagzbz//vuZN29elixZkqNHj6Zv37655557Mm3atPTo0aPseAAALaYsA9Dmtm/fnurq6jz//PNJkmHDhqWuri4TJkwoORkAQMvYhg1AmxsyZEhWrVqVJ598MgMGDMi2bdty5ZVX5sYbb8ybb75ZdjwAgBMyWQagXTU1NaW2tjbz589PU1NTevXqlZkzZ2bGjBnp3bt32fEAAD6XsgzAKfHWW29lxowZ+cUvfpEk+drXvpYHH3ww3//+9z1qCgDocJRlAE6pF198MVVVVXnllVeSJBMmTEhdXV2GDRtWcjIAgD9zzzIAp9S3v/3tNDY2ZunSpenXr19+85vfZMSIEamqqsqBAwfKjgcAkMRkGYAS7d+/P3Pnzs3SpUvz6aef5qtf/Wp+8pOfZOrUqenevXvZ8QCA05iyDEDptm7dmurq6qxZsyZJMmLEiCxZsiTjxo0rNxgAcNqyDRuA0g0fPjwvvPBCVqxYkYsvvjhbtmzJ+PHjc/PNN2fPnj1lxwMATkMmywB0KB9//HHuv//+LFiwIIcOHUqfPn0ye/bs1NTUpFevXmXHAwBOE8oyAB3S7t27c+edd+aJJ55IkgwcODALFy7Mdddd51FTAEC7U5YB6NBWr16d6urqvPrqq0mSSZMmZdGiRRk8eHDJyQCArsw9ywB0aBMnTszmzZuzePHinHPOOVm1alWGDx+empqafPDBB2XHAwC6KJNlADqNd999N3PmzEl9fX2OHTuW8847L/fee29uueWWdOvm818AoO0oywB0Ops2bUpVVVXWrl2bJBkzZkzq6upy+eWXl5wMAOgqfAwPQKczcuTINDQ0ZPny5bnwwguzcePGVFZWZsqUKXnnnXfKjgcAdAEmywB0ah999FHmz5+f2traHDlyJGeddVZ+9KMfpbq6Oj179iw7HgDQSSnLAHQJO3fuTE1NTZ5++ukkyaBBg7Jo0aJcffXVJScDADojZRmALuVXv/pVqqurs2PHjiTJNddck4ULF2bQoEElJwMAOhP3LAPQpXznO9/J1q1bU1tbm7PPPjvPPvtshg4dmrvvvjsffvhh2fEAgE7CZBmALmvv3r2ZNWtWHnnkkSTJBRdckAULFmTy5MkeNQUAfCFlGYAub8OGDamqqsr69euTJJWVlamrq8vo0aNLTgYAdFQ+Vgegyxs7dmzWrVuXRx99NBLvhs0AAAn3SURBVOeff35eeumljB07NlOnTs2+ffvKjgcAdEDKMgCnhW7dumXKlCl54403ctddd6VHjx5ZtmzZn741+5NPPik7IgDQgdiGDcBpaceOHZk+fXpWrlyZJBk8eHAWL16cq666quRkAEBHYLIMwGnp0ksvzXPPPZdnnnkml1xySV577bVMmjQp119/fXbt2lV2PACgZMoyAKetioqKXHvttdm2bVvuu+++nHnmmXnqqacyZMiQzJkzJwcPHiw7IgBQEtuwAeC4t99+OzNnzsxjjz2WJOnfv38eeOCB3HTTTamoqCg5HQBwKinLAFCwbt26VFVVpbGxMUkyfvz41NXVZcSIESUnAwBOFduwAaDgiiuuyPr161NfX59zzz03DQ0NGTVqVG6//fa89957ZccDAE4Bk2UA+ALvv/9+5s2blyVLluTo0aPp27dv7rnnnkybNi09evQoOx4A0E6UZQBoge3bt6e6ujrPP/98kmTYsGGpq6vLhAkTSk4GALQH27ABoAWGDBmSVatW5cknn8yAAQOybdu2XHnllbnxxhvz5ptvlh0PAGhjJssA0EpNTU2pra3N/Pnz09TUlF69emXmzJmZMWNGevfuXXY8AKANmCwDQCv17t07c+bMyY4dO/KDH/wghw4dyo9//OMMHjw4v/zlL/N5n0OvX78+N9xwQ3bt2lVCYgCgtUyWAeBLevHFF1NVVZVXXnklSTJhwoTU1dVl2LBhSZLDhw9n6NCh2blzZyorK9PQ0JDu3buf3MV2705efjlpbEw2b07270+OHEnOOCPp1y/55jeTUaOS0aOTAQPa5j8IAKchZRkA2sDRo0dTX1+f2bNnZ//+/enevXt++MMfZt68eXn44Yczc+bMP61dtGhRqqurW37ypqbk8ceThx5KNm5s+XFjxiR33JHceGNiezgAtIqyDABtaP/+/Zk7d26WLl2aTz/9NH379s3Bgwdz5MiRP63p06dPfve732XgwIFffLKjR5NFi5L585snyCerX79k1qxk+vTkZCfaAHCaUZYBoB1s3bo11dXVWbNmzef+feLEifn1r3+dioqKzz/B668nt96a/Pa3bRfq8suTn/88ueyytjsnAHRRyjIAtJO1a9dm3Lhx/+bf6+vrM3Xq1L/8w/LlyW23JYcPt32onj2TZcuSyZPb/twA0IUoywDQDo4ePZpvfetbaWxs/DfXfOUrX8n27dtz0UUX/fnNhx9O/u7v2jdcRUXy058mf/u37XsdAOjEPDoKANrB8uXLv7AoJ8kf//jHfO973/vzo6aWL2//opwkx44l06Y1Xw8A+FzKMgC0g71797Zo3YYNG/L4448336N8220nXP9ykh8l+W6SS5L8uyQ9k1yU5D8meaqlAY8da77e66+39AgAOK3Yhg0A7eDYsWP5/e9/n3379uXAgQN/8dq/f3+2bNmSgwcPZs3q1bn4b/6mRV/mNS3Jf//Mv89K8n+THPrMe99P8r+S/FVLglZWJg0NviUbAAqUZQAoW21tcuedLVr6P5IcSPLtJN9Ic1lOkreSLEnywPF/35PmCXSLPPhg8g//0NLVAHBaUJYBoExNTUn//l/uOcqf8Z+T/M8kA5PsbOlB/fole/YkvXu3SQYA6ArcswwAZXr88TYrykky5vjPt1tz0P79yYoVbZYBALoCZRkAyvTQQ216unXHf3695BwA0NkpywBQlt27k40bv/RpPkqyNckdSR4//t5/be1JNmxozgMAJEl6lB0AAE5bL7980ofuSXLx57zfK8msJD88mZM2NiYDBpx0JgDoSkyWAaAsjY0nfWj3JOcff51x/L0eSf4xJzFVboM8ANDVKMsAUJbNm0/60L9O8n+Ov5qS7EjyX5L8tyQjkrx6MifdtOmk8wBAV6MsA0BZ2uhbsLul+ZnLy5LUJPnfSf5Tkk9be6IDB9okDwB0BcoyAJTlyJE2P+XfH/+5JUmr59aHD7dtGADoxJRlACjLGWeceE0rXfSZ33e29uCePdswCQB0bsoyAJSlX782P+UfPvP7Wa09uG/fNkwCAJ2bsgwAZfnmN1u1/GiSYydY88Dxnz2SVLY2z8iRrT0CALosZRkAyjJqVKuWv5VkdJJH0vyc5f/v0zTfozw5yc+Ov/f3SVo9J25lHgDoyiqOHTt2og+pAYD2sHt38vWvt3x5ks+u7pXmrdYfJvnsV3PdkqQ+zdPlVvnDH5IBA1p7FAB0ScoyAJRp7Nhk48YWLT2S5Kkkq5NsSPJOkn9Jc2n+92nedn1rkv9wsjnWrz+ZIwGgS1KWAaBMjz6a3Hpr2Smac0yZUnYKAOgwlGUAKFNTU9K/f7J/f3kZ+vVL/vmfk169yssAAB2ML/gCgDL17p3MmlVuhlmzFGUAKDBZBoCyHT2ajBuX/Pa3p/7alZVJQ0PSvfupvzYAdGDKMgB0BK+/nowYkRw+fOK1baVnz+SVV5JLLz111wSATsI2bADoCC67LFm2LKmoODXXq6hovp6iDACfS1kGgI5i8uTkpz9t/8JcUdF8ncmT2/c6ANCJ2YYNAB3N8uXJbbe1z5bsXr2Sn/1MUQaAE1CWAaAjev315ucvt+WXflVWJj//ua3XANACtmEDQEd02WXJP/1T8uCDzc9B/jL69Ws+T0ODogwALWSyDAAdXVNTsmJF8tBDyYYNLT9u7NjkjjuSG25ofp4zANBiyjIAdCa7dyeNjc2vTZuSAwea723u2TPp2zcZOTIZNar5NWBA2WkBoNNSlgEAAKDAPcsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUKAsAwAAQIGyDAAAAAXKMgAAABQoywAAAFCgLAMAAECBsgwAAAAFyjIAAAAUKMsAAABQoCwDAABAgbIMAAAABcoyAAAAFCjLAAAAUPD/AGpduNlD7lY7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 485
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "G2 = nx.DiGraph()\n",
    "G2.add_nodes_from(nodes)\n",
    "G2.add_edges_from(zip(nodes, nodes[1:]))\n",
    "nx.draw(G2, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that in a directed graph, the matrix representation is not guaranteed to be symmetric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2 = nx.to_numpy_array(G2)\n",
    "A2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the 2nd matrix power: the number of paths of length 2 between any pair of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_power(A2, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that there's only one path from node 0 to node 2 of length 2, and one path from node 1 to node 3. If you're not convinced of this, trace it for yourself!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "In this directed graph, how many paths are there from node 0 to node 3 of length 3? Compute the 3rd matrix power and verify your answer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_power(A2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Real Data\n",
    "\n",
    "Now that we've looked at a toy example, let's play around with a real dataset!\n",
    "\n",
    "This dataset is a residence hall rating dataset. From the [source website](http://konect.uni-koblenz.de/networks/moreno_oz):\n",
    "\n",
    "> This directed network contains friendship ratings between 217 residents living at a residence hall located on the Australian National University campus. A node represents a person and edges contain ratings of one friend to another.\n",
    "\n",
    "For the purposes of this exercise, we will treat the edges as if they were unweighted.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = load_university_social_network()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Use nxviz's MatrixPlot to draw the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 344,
       "width": 344
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nv.MatrixPlot(G).draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Using what you know from the previous material, find out how many connected component subgraphs there are in the subgraph.\n",
    "\n",
    "**Hint:** You may need to convert the graph to an undirected one first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<networkx.classes.graph.Graph at 0x1a1fcfc3c8>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.connected_component_subgraphs(G.to_undirected()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Since there is only one connected component subgraph, pick two nodes in the graph and see how many shortest paths there exist between those two nodes.\n",
    "\n",
    "**Hint:** You will first need to know what the shortest path length is between those two nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[30, 196, 115, 100]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(G, 30, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = nx.to_numpy_array(G)\n",
    "np.linalg.matrix_power(A, 4)[29, 99]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Message Passing\n",
    "\n",
    "Message passing on graphs is a fascinating topic to explore. It's a neat way to think about a wide variety of problems, including the spread of infectious disease agents, rumours, and more. As it turns out, there's a direct matrix interpretation of the message passing operation.\n",
    "\n",
    "To illustrate this more clearly, let's go back to the directed chain graph, `G2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ATEXwpSrY5wsAAEzFHl+qQn9/f1pbW7Ns2bIMDg6msbGx6JIAAIAyoeNLVWhpack111yTkZGR7Nmzp+hyAACAMiL4UjXOLHe2zxcAAHgzwZeq4YArAABgMvb4UjUOHjyYrq6utLS05OWXX059vd/rAAAAOr5Ukc7OznR0dKS/vz9PP/100eUAAABlQvClqtjnCwAAvJ3gS1URfAEAgLcTfKkqDrgCAADezuFWVJWxsbG0trZmcHAwBw8eTEdHR9ElAQAABdPxparU19dnw4YNSXR9AQCACYIvVcc+XwAA4M0EX6qOfb4AAMCb2eNL1Tlx4kSamppy8uTJ9PX1pbm5ueiSAACAAun4UnUaGxuzbt26jI+PZ8eOHUWXAwAAFEzwpSrZ5wsAAJwh+FKVBF8AAOAMe3ypSv39/WltbU1DQ0MGBwfT0NBQdEkAAEBBdHypSi0tLbnmmmsyPDyc3bt3F10OAABQIMGXqmW5MwAAkAi+VDHBFwAASOzxpYodOHAg3d3daWlpycsvv5z6er/nAQCAWiQJULW6urrS0dGR/v7+PPPMM0WXAwAAFETwpaqdWe68bdu2gisBAACKIvhS1ezzBQAABF+qmuALAAA43IqqNjY2ltbW1gwODubgwYPp6OgouiQAAGCR6fhS1err67Nhw4Ykyfbt2wuuBgAAKILgS9VzwBUAANQ2wZeqZ58vAADUNnt8qXonTpxIU1NTTp48mb6+vjQ3NxddEgAAsIh0fKl6jY2NWbduXcbHx7Nz586iywEAABaZ4EtNsM8XAABql+BLTbDPFwAAapc9vtSEvr6+tLW1paGhIYODg2loaCi6JAAAYJHo+FITWltbc/XVV2d4eDh79uwpuhwAAGARCb7UjI0bNyax3BkAAGqN4EvNcMAVAADUJnt8qRkHDhxId3d3Wlpa8vLLL6e+3u99AACgFvjJn5rR2dmZ9vb29Pf355lnnim6HAAAYJEIvtSMuro6+3wBAKAGCb7UFPN8AQCg9gi+1BQHXAEAQO1xuBU1ZXR0NG1tbRkcHMzBgwfT0dFRdEkAAMAC0/GlpixZsiQ33HBDkmT79u0FVwMAACwGwZea44ArAACoLYIvNcc+XwAAqC32+FJzTpw4kaamppw8eTJ9fX1pbm4uuiQAAGAB6fhScxobG3PddddlfHw8O3fuLLocAABggQm+1CTzfAEAoHYIvtQkB1wBAEDtsMeXmtTX15e2trY0NDRkcHAwDQ0NRZcEAAAsEB1falJra2uuvvrqDA8PZ8+ePUWXAwAALCDBl5plny8AANQGwZeaJfgCAEBtsMeXmnXgwIF0d3entbU1x44dS3293wMBAEA18pM+NauzszPt7e3p6+vLM888U3Q5AADAAhF8qVl1dXWWOwMAQA0QfKlpgi8AAFQ/wZeatnHjxiSCLwAAVDOHW1HTRkdH09bWlsHBwRw6dCjt7e1FlwQAAJSYji81bcmSJbnhhhuS6PoCAEC1Enypefb5AgBAdRN8qXmCLwAAVDd7fKl5J06cSFNTU06ePJn+/v40NTUVXRIAAFBCOr7UvMbGxlx33XUZHx/Pjh07ii4HAAAoMcEXYrkzAABUM8EXIvgCAEA1s8cXkvT29mbFihVpbGzMwMBAGhoaii4JAAAoER1fSNLW1parr746J06cyN69e4suBwAAKCHBF047s9x527ZtBVcCAACUkuALp9nnCwAA1ckeXzitp6cnl19+eVpbW3Ps2LHU1/u9EAAAVAM/2cNpXV1dWbVqVfr6+rJ///6iywEAAEpE8IXT6urqsnHjxiT2+QIAQDURfOFN7PMFAIDqI/jCmwi+AABQfRxuBW8yOjqa1tbWvPLKKzl06FDa29uLLgkAAJgnHV94kyVLluSGG25Ikmzfvr3gagAAgFIQfOFtHHAFAADVRfCFt7HPFwAAqos9vvA2Q0NDaWpqyqlTp9Lf35+mpqaiSwIAAOZBxxfeZvny5bnuuusyPj6enTt3Fl0OAAAwT4IvTOLMPl/LnQEAoPIJvjCJM/t8HXAFAACVzx5fmERvb29WrFiRxsbGDAwMpKGhoeiSAACAOdLxhUm0tbXlqquuyokTJ7J3796iywEAAOZB8IUpGGsEAADVQfCFKZw54Mo+XwAAqGz2+MIUenp6cvnll6e1tTXHjh1Lfb3fEwEAQCXykzxMoaurK6tWrUpfX1/2799fdDkAAMAcCb4whbq6Ovt8AQCgCgi+MA3BFwAAKp/gC9NwwBUAAFQ+h1vBNEZHR9Pa2ppXXnklhw4dSnt7e9ElAQAAs6TjC9NYsmRJbrjhhiTJ9u3bC64GAACYC8EXzsI+XwAAqGyCL5zFmeBrny8AAFQme3zhLIaGhtLU1JRTp06lv78/TU1NRZcEAADMgo4vnMXy5ctz3XXXZXx8PDt37iy6HAAAYJYEX5gB+3wBAKByCb4wA4IvAABULnt8YQZ6e3uzYsWKNDY2ZmBgIA0NDUWXBAAAzJCOL8xAW1tbrrrqqpw4cSJ79+4tuhwAAGAWBF+YIcudAQCgMgm+MEOCLwAAVCZ7fGGGnnvuubzrXe9KW1tbXnrppdTX+70RAABUAj+5wwx1d3dn1apV6e3tzf79+4suBwAAmCHBF2aorq7OcmcAAKhAgi/MguALAACVR/CFWRB8AQCg8jjcCmZhdHQ0ra2teeWVV3L48OGsWrWq6JIAAICz0PGFWViyZEluuOGGJLq+AABQKQRfmCXLnQEAoLIIvjBLgi8AAFQWe3xhll5//fU0NzdndHQ0fX19aWpqKrokAABgGjq+MEvnnntu1q5dm7GxsezcubPocgAAgLMQfGEONm7cmMRyZwAAqASCL8yBfb4AAFA57PGFOXj55Zdz0UUXpbGxMYODg1m2bFnRJQEAAFPQ8YU5WLFiRa688sqcOHEie/fuLbocAABgGoIvzNGZ5c7btm0ruBIAAGA6gi/MkQOuAACgMtjjC3P03HPP5V3velfa2try0ksvpb7e75EAAKAc+Ukd5qi7uzsrV65Mb29vnn322aLLAQAApiD4whzV1dXZ5wsAABVA8IV5MM8XAADKn+AL8+CAKwAAKH8Ot4J5GB0dTUtLS44fP57Dhw9n1apVRZcEAAC8jY4vzMOSJUtyww03JEm2b99ecDUAAMBkBF+YJwdcAQBAeRN8YZ7s8wUAgPJmjy/M0+uvv57m5uaMjo6mr68vTU1NRZcEAAC8iY4vzNO5556btWvXZmxsLI8++mjR5QAAAG8j+EIJmOcLAADlS/CFEnDAFQAAlC97fKEEXn755Vx00UVpbGzM4OBgli1bVnRJAADAaTq+UAIrVqzIlVdemRMnTmTv3r1FlwMAALyJ4AslYp8vAACUJ8EXSsQ+XwAAKE/2+EKJ/OIXv8i73/3utLW15aWXXkp9vd8rAQBAOfCTOZTI5ZdfnpUrV6a3tzfPPvts0eUAAACnCb5QInV1dfb5AgBAGRJ8oYQEXwAAKD+CL5SQA64AAKD8ONwKSmh0dDQtLS05fvx4Dh8+nFWrVhVdEgAA1DwdXyihJUuW5IYbbkiSbN++veBqAACARPCFkrPPFwAAyovgCyUm+AIAQHmxxxdK7PXXX09zc3NGR0fT39+fCy+8sOiSAACgpun4Qomde+65Wbt2bcbGxrJz586iywEAgJon+MICsNwZAADKh+ALC0DwBQCA8mGPLyyAY8eO5eKLL05jY2MGBwezbNmyoksCAICapeMLC+Ciiy7K6tWrc+LEiezdu7focgAAoKYJvrBANm7cmMRyZwAAKJrgCwvEPl8AACgP9vjCAvnFL36Rd7/73Wlra8uxY8dSV1dXdEkAAFCTdHxhgVx++eW57LLL0tvbm/379xddDgAA1CzBFxZIXV2d5c4AAFAGBF9YQA64AgCA4gm+sIB0fAEAoHgOt4IFdOrUqbS2tub48eN5/vnns3LlyqJLAgCAmqPjCwvonHPOyfr165Po+gIAQFEEX1hgljsDAECxBF9YYA64AgCAYtnjCwvs9ddfT1NTU8bGxtLf358LL7yw6JIAAKCm6PjCAjv33HOzdu3ajI2NZefOnUWXAwAANUfwhUVgny8AABRH8IVFIPgCAEBx7PGFRXDs2LFcfPHFWb58eQYGBrJs2bKiSwIAgJqh4wuL4KKLLsrq1aszNDSUffv2FV0OAADUFMEXFsmZ5c7btm0ruBIAAKgtgi8sEvt8AQCgGPb4wiL5xS9+kXe/+91pa2vLsWPHUldXV3RJAABQE3R8YZFcfvnlueyyy9Lb25tnn3226HIAAKBmCL6wSOrq6uzzBQCAAgi+sIjs8wUAgMV3TtEFQC258cYb05Xk/L/5m+Suu5J9+5K+vmRkJFm2LGltTa69Nlm7NrnuuqS7u+iSAQCg4jncChbD0FDy0EMZ/+pXU7d798zvW7cuueOO5GMfS5YvX7j6AACgigm+sJBGR5N77knuvnuis5tkPMmsz3NubU02b04+97lkyZJSVwkAAFVN8IWFsn9/csstyaOPlu6Z73tf8sADyerVpXsmAABUOYdbwUJ48MFkzZrSht5k4nlr1kw8HwAAmBHBF0pt69bk4x9PhocX5vnDw8knPjHxHgAA4KwsdYZSevDBidC7GOrqkm9/O7n55sV5HwAAVCjBF0pl//6JZcgL1emdTEND8vjj9vwCAMA0LHWGUhgdnTjIagah92CSe5K8P0lnkoYkFyT5lSRfSHJkNu8dHk4++cmJ9wMAAJPS8YVS+Iu/SP7wD8962aEkXZkYaXTGhUleS3ImurYk+V6S/3U27//KV5I775zNHQAAUDMEX5ivoaGkvf2NOb3T6UnyriT/IMnvJfm1TATdkSR/m+SOJM9lIgw/m+TSmdbQ2pocPpwsXz7L4gEAoPpZ6gzz9dBDMwq9yUTI3ZfkPyX56Om/J8myJP9bkv+cpDHJK0m+Ppsa+vqShx+ezR0AAFAzBF+Yry1bZnxpUyb28k5ldZL3nf58zwLWAQAAtUTwhfno6Ul27SrpI9tOf5z1cVWPPTZRDwAA8BaCL8zH7t0lfdypJNtPf37NXB6wZ9Z9YgAAqHqCL8xHiYPmV5MczcR/mP+oDOoBAIBqIPjCfOzbV7JH/fckm09//pkkV8/lIXv3lqweAACoFoIvzMcMT3M+myNJPpjk9SRrk3x5rg/q7y9JPQAAUE0EX5iPkZF5P6Ivyd/PxPzeX0ryf2dipNGcDA/Pux4AAKg2gi/Mx7Jl87p9MMmvJ3kySWeS/5rkkvk8sKFhXvUAAEA1EnxhPlpb53zra0n+QZLdSS7NROjtnG89LS3zfQIAAFQdwRfm49pr53TbUJL3J9mRibm9/zUTy5zn7b3vLcVTAACgqgi+MB9r1876lpEkH07y35I0J/kvmeMJziWqBwAAqp3gC/Nx3XWzunw0ye8k+ZskFyT56yQl7dEKvgAA8A514+Pj40UXARXt+uuTXbtmdOlPkvwvpz9vTNI0zbUdSWb21DfV8dOfzuYOAACoCTq+MF+f/vSMLx170+cnkrw4zZ9jC1gHAADUEh1fmK+hoaS9PenrK66G1tbk+eeTxjlPAAYAgKql4wvztXx5snlzoSW89gd/kJF6/zkDAMBkdHyhFEZHkxtvTB59dNFf/XxnZzoPHsxYkra2tnR0dGTlypVZtWrVWz7+0i/9Ut7znvcsen0AAFA0wRdKZf/+ZM2aZHh48d7Z0JAf/st/mQ9+/vMzuvxHP/pR3v/+9y9wUQAAUF6sjYRSWb06+eY3k7q6xXlfXV3yzW/mN//oj2YUZuvr69PZ2bkIhQEAQHkRfKGUbr45ue++hQ+/dXUT77n55iTJli1bct555017y+///u/nV37lVxa2LgAAKEOWOsNCePDB5FOfWphlz42NyTe+8UboPePP//zP80d/9EeT3nLppZfm5z//ec4///zS1wMAAGVOxxcWws03J48/nrzvfaV97vr1E899W+hNkj/4gz/IlVdeOeltR48ezZ133pmBgYHS1gMAABVA8IWFsnp18sgjyVe+MjFndz5aWyees21bcsUVk16ybNmy3Hvvve/4+jXXXJOlS5dm69atueqqq/K9730vFnoAAFBLBF9YSEuWJHfemRw+nHwMRJSRAAAbFUlEQVTrW8n118/u/uuvT/7Df5i4/847J543jV/91V/Nb//2b7/x99bW1vzt3/5t9u3bl/Xr1+fIkSP56Ec/mg996EN5/vnn5/ANAQBA5bHHFxZbT0+yZ8/En717k/7+ib3ADQ1JS0vy3vcma9dO/OnunvXjDx8+nNWrV+e1117LAw88kN/7vd9LkoyNjeW+++7LF77whRw/fjwXXHBBvvSlL+X2229Pfb3fgQEAUL0EX6hCf/d3f5dnn302mzZtSt3bTpg+fPhwPvOZz+SHP/xhkuSGG27I1q1bc/XVVxdRKgAALDjBF2rQ+Ph4vv/97+czn/lMjh49mqVLl+YLX/hCvvjFL6ahoaHo8gAAoKQEX6hhAwMD+fznP5+tW7cmSa644orcf//92bhxY8GVAQBA6djYBzWsubk5X//61/PjH/84V1xxRZ599tncdNNNue2224w+AgCgagi+QG666aY88cQT+eM//mOjjwAAqDqWOgNv8dRTT+XWW2/Nzp07kyS/+Zu/ma9+9atZtWpVwZUBAMDc6PgCb3H11VfnkUceyVe/+tVccMEF+eEPf5grr7wyW7ZsydjYWNHlAQDArOn4AlMy+ggAgGqg4wtMqb29PX/5l3+Z7373u7n00kuzY8eOXHvttfnjP/7jDA8PF10eAADMiI4vMCNGHwEAUKl0fIEZMfoIAIBKJfgCs2L0EQAAlcZSZ2DOjD4CAKAS6PgCc2b0EQAAlUDHFyiJyUYf3X///bnqqqsKrgwAgFqn4wuUxGSjj9asWZM/+ZM/MfoIAIBC6fgCJWf0EQAA5UTHFyg5o48AACgngi+wYG666aY8/vjj7xh99P3vf7/o0gAAqCGWOgOL4u2jjz74wQ/m3nvvNfoIAIAFp+MLLIq3jz76wQ9+YPQRAACLQscXWHRGHwEAsJh0fIFFZ/QRAACLSccXKJTRRwAALDQdX6BQRh8BALDQBF+gLBh9BADAQrHUGSg7Rh8BAFBKOr5A2TH6CACAUtLxBcqa0UcAAMyXji9Q1ow+AgBgvnR8gYrx9tFHq1evztatW40+AgBgWoIvUHF+8pOfZNOmTXn22WeTJJs2bcqXv/zlNDc3F1wZAADlyFJnoOKcGX30z//5Pzf6CACAs9LxBSqa0UcAAJyNji9Q0Yw+AgDgbHR8gaph9BEAAJPR8QWqhtFHAABMRscXqEpGHwEAcIbgC1Q1o48AALDUGahqRh8BAKDjC9QMo48AAGqTji9QM86MPrr33nuNPgIAqCE6vkBNMvoIAKB26PgCNcnoIwCA2qHjC9S8yUYf3X///bnxxhsLrgwAgFLQ8QVqXnNzc77+9a/nxz/+ca644ors378/GzduzO23356BgYGiywMAYJ4EX4DT3j766Otf/7rRRwAAVcBSZ4BJGH0EAFA9dHwBJjHZ6KOrrroqX/va14w+AgCoMDq+AGdh9BEAQGXT8QU4C6OPAAAqm44vwCwYfQQAUHl0fAFmYbrRR4ODg0WXBwDAJARfgDmYbPTRlVdeafQRAEAZstQZYJ6MPgIAKG86vgDzZPQRAEB50/EFKKHDhw/njjvuyI9+9KMkRh8BAJQDHV+AEmpvb88PfvADo48AAMqIji/AAjH6CACgPOj4AiwQo48AAMqD4AuwwIw+AgAolqXOAIvI6CMAgMWn4wuwiIw+AgBYfDq+AAV5++ijDRs2ZOvWrUYfAQCUmI4vQEHePvpo+/btWbNmTf70T//U6CMAgBLS8QUoA0YfAQAsHMEXoIz85Cc/ya233pqf/exnSZLbbrstX/7yl9PU1FRwZQAAlctSZ4AyctNNN+WJJ54w+ggAoIR0fAHKlNFHAACloeMLUKaMPgIAKA0dX4AKYPQRAMDc6fgCVIAzo4++853vGH0EADBLOr4AFcboIwCA2RF8ASqU0UcAADNjqTNAhTL6CABgZnR8AaqA0UcAAFPT8QWoAkYfAQBMTccXoMoYfQQAZaanJ9m9O9mzJ9m3L+nrS0ZGkmXLktbW5Nprk7Vrk+uuS7q7i662Kgm+AFVofHw83/ve9/LZz342R48ezdKlS7N58+bcddddaWhoKLo8AKh+Q0PJQw8lW7Yku3bN/L5165I77kg+9rFk+fKFq6/GCL4AVczoIwBYZKOjyT33JHffPdHZnavW1mTz5uRzn0uWLCldfTVK8AWoAUYfAcAi2L8/ueWW5NFHS/fM970veeCBZPXq0j2zBjncCqAGnBl99M/+2T/LOeecY/QRAJTagw8ma9aUNvQmE89bs2bi+cyZji9AjXnyySezadMmo48AoFS2bk1uu21h31FXl9x3X7Jp08K+p0rp+ALUmGuuucboIwAolQcfXPjQmyTj48ntt+v8zpGOL0ANM/oIAOZh//6JZcjDwzO6/GiSf5PkPyV5PklTkuuTfC7Jr830nQ0NyeOP2/M7S4IvQI0z+ggA5mB0NLnxxhnv6f3vSX41Se/pv1+Y5NUkY0nqktyd5Aszfff69cm2bU57ngVLnQFqXF1dXT760Y/mmWeeyaZNm3Ly5Mn8i3/xL7JmzZo88sgjRZcHAOXpnntmHHqHknwgE6H32iRPJhlM0p/kziTjSe5K8l9m+u6dOyfez4zp+ALwFkYfAcBZDA0l7e0zntN7T5J/nOT8JPuTvP04yQ8l+UGS9ybZM9MaWluTw4eT5ctnekdN0/EF4C2MPgKAs3jooRmH3iQ5cxzV7+SdoTdJ/unpj3szEYxnpK8vefjhGddQ6wRfAN6hsbExf/Znf5Z9+/Zl/fr1OXLkSD7ykY/kQx/6UJ5//vmiywOAYm3ZMuNLj+d/dnF/fYpr3peJg66S5P9doDpqneALwJSMPgKAt+npSXbtmvHlz2RiD2+SXD3FNfVJrjj9+dOzqeWxxybq4awEXwCmVV9fnzvuuCNPP/10PvCBD+SVV17Jpz/96dx00015+ulZ/d8zAFS+3btndfmRN32+cprrzvzbkWmumdSeGe8KrmmCLwAz0t7enh/84Af5zne+k0svvTTbt2/PmjVr8qd/+qcZnuH8QgCoeLMMmq+96fPpjqE69/THVxe4nlol+AIwY2dGHz399NO59dZbjT4CoPbs2zeryxd8hM7evQv9hqog+AIway0tLdm6dWt+/OMf5z3veU/279+fjRs35vbbb8/g4GDR5QHAwpnFac7JxAijM4amue71Sa6fkf7+2d5RkwRfAObM6CMAas7IyKwuf/O+3hemue7Mv10223psN5qRuvHx8QXvvgNQ/Z588sls2rQpO3fuTJJ88IMfzL333ptVqyabWAgA5WtoaCgHDx7MgQMH0tPT85aP9z72WNacPDnjZx3PxKii8STfS/LhSa4ZS9KaZDDJV5N8ejbFXn998tOfzuaOmiT4AlAyY2Nj+drXvpa77rorx48fz4UXXpgvfelLue2221Jfb5ERAOXhtddemzTUnvl49OjRKe/96yS/Mcv3XZ9kV5Lbk3xtkn/fmeSG05/vz/8cbTQjv/7ryd/8zSwrqj2CLwAld/jw4dxxxx350Y9+lCTZsGFDtm7dmquuuqrgygCoBa+88sqUobanpycvv/zytPefc8456ejoSHd3d7q6utLd3f3G52sefjjNX5ssvk7tniT/OMkFSZ7NO5czfyTJ95OsTTK7YUlJ7rorufvu2d5VcwRfABbE+Ph4vve97+Wzn/1sjh49mqVLl2bz5s2566670tDQUHR5AFSo8fHx9Pf3Txlqe3p6MjAwMO0zli1blq6urneE2jMfV65cmSVLlkx+83e/m/zWb82q5qEkVyY5kOS9Sb6d5KpMLIP+syR/fvq6/yfJ35/Vk0/X85GPzPaumiP4ArCg+vv78/nPfz73339/kuTKK6/M1q1bc+ONNxZcGQDlaHx8PC+//PKUofbAgQM5fvz4tM9Yvnz5lKG2u7s7l1xyydy34PT0JJdfPuvbnkjya0l6T//9wkzM7B1LUpfk7iRfmEs9zz2XdHfP5c6aIvgCsCh+8pOf5NZbb83PfvazJMntt9+eL33pS2lqaiq4MgAW09jYWF588cUpQ+2BAwfy+uuvT/uM888/f8pQ29XVlYsuuih1dXUL901cf32ya9esbzua5N8k+U9Jns9E+L0+E8ugf22udTjYakYEXwAWzYkTJ/Kv//W/zpe+9KWcOnUql112We699958+MOTnXEJQCUaHR3NkSNHJg21PT09OXjwYIbPMoKnubl5ylDb3d2dlpaWhQ22Z/OtbyW33FLc+8/41reS3/3doquoCIIvAIvuySefzK233ppHH300idFHAJXk1KlTOXz48KSh9sCBAzl48GBOnTo17TNWrFgxZajt6uoq/9VAQ0NJe3vS11dcDa2tyfPPJ42NxdVQQQRfAAoxOjqa++67z+gjgDIzMjKSQ4cOTRpqe3p68vzzz2d0dHTaZ1xyySVThtqurq6cf/75i/TdLKC/+IvkD/+wuPd/5SvJnXcW9/4KI/gCUCijjwAW19DQUA4ePDhlx/aFF17IdBGhrq4uK1eunLJj29nZmeXLly/id1SQ0dHkxhuT06uXFtX69cm2bclUJ0/zDoIvAIUz+gigdF599dU3DomarGP74osvTnt/fX192tvbJw213d3daW9v97/NZ+zfn6xZk5xlz3JJNTQkTzyRXHHF4r2zCgi+AJQNo48Azm5wcHDKUHvgwIG8/PLL095/zjnnpLOzc9JQ29XVlVWrVmXp0qWL9N1UgQcfTD7xiWQxYlVdXfLtbyc337zw76oygi8AZcfoI6BWjY+Pp7+/f8pQ29PTk4GBgWmf0dDQkM7OzklDbXd3dy677LIssUS2tLZuTW6/fWHDb11dct99yaZNC/eOKib4AlCWjD4CqtH4+HiOHTs2Zajt6enJq6++Ou0zli9fPuUy5K6urlxyySUOCSzCgw8mn/rUwix7bmxMvvENnd55EHwBKGtGHwGVZGxsLC+++OK0HduhoaFpn3H++ee/o0v75s9XrFhR7AxbprZ//8R831IeeLV+ffLAA/b0zpPgC0DZM/oIKBejo6N54YUXpt1jOzIyMu0zmpub3xFm3/yxpaVFsK1ko6PJPfckd989vzm/ra3J5s3J5z7n9OYSEHwBqBhGHwEL7dSpUzl8+PCUy5APHTqUU6dOTfuMFStWTDvD1nkFNWJoKHn44WTLluSxx2Z+3/XXJ3fckfzWbyW1MBZqkQi+AFQUo4+A+RgeHs6hQ4emnGF7+PDhjI2NTfuMSy65ZNqO7XnnnbdI3w0Vo6cn2bNn4s/evUl//8Re4IaGpKUlee97k7VrJ/50dxddbVUSfAGoSEYfAZMZGhrKwYMH39GpPfP5kSNHMt2Pv3V1dVm5cuWUobazszPLdeGg4gi+AFS0H//4x9m0aZPRR1AjXn311Rw4cGDKju2LL7447f319fXp6OiYNNR2d3eno6Mjy5YtW6TvBlgsgi8AFc/oI6geg4ODU4banp6e9Pb2Tnv/0qVL09HRMWXHdtWqVVm6dOkifTdAuRB8AagaRh9BeRsfH09/f/+UofbAgQMZGBiY9hkNDQ1vHBI1Wbi97LLLssQJuMDbCL4AVBWjj6A44+PjOXbs2LQzbF999dVpn3Huuee+Jdi+fZbtxRdf7L9lYNYEXwCqktFHUHpjY2M5evTopGN+zuy7HRoamvYZF1xwwTvC7Ju7titWrDDDFig5wReAqmX0EczO6OhoXnjhhSlPRD548GBGRkamfUZLS8uUoba7uzvNzc2CLbDoBF8Aqp7RRzDh5MmTOXz48JSHRx06dCinTp2a9hkrVqyYdobthRdeuEjfDcDMCb4A1Ayjj6h2w8PDOXTo0JSHRz3//PMZGxub9hmXXnrplKG2q6sr55133iJ9NwClI/gCUFPePvpo5cqVuffee/OhD32o6NLgrIaGhqY8NOrAgQM5cuRIpvvRrq6uLqtWrZryROTOzs40NjYu4ncEsDgEXwBqktFHlKPjx4+/cUjUZOH2pZdemvb+JUuWpL29fdJQ293dnfb29ixbtmyRvhuA8iH4AlCzRkdH87WvfS133XVXXn311YUZfdTTk+zenezZk+zbl/T1JSMjybJlSWtrcu21ydq1yXXXJd3dpXknZWtgYGDKUNvT05O+vr5p71+6dGk6OzunPDxq1apVOeeccxbpuwGoHIIvADXv0KFD+cxnPlO60UdDQ8lDDyVbtiS7ds38vnXrkjvuSD72sWT58rm9m8KMj4+nr69vyhORDxw4kMHBwWmf0dDQMO2JyJdeemmWLFmySN8RQPUQfAEgJRp9NDqa3HNPcvfdE53duWptTTZvTj73uUTIKRvj4+N56aWXpgy1PT09ee2116Z9xrnnnjvticgXX3xx6VYbAPAGwRcA3mTOo4/2709uuSU5vWe4JN73vuSBB5LVq0v3TKY0NjaWo0ePThlqDxw4kBMnTkz7jAsvvHDKUNvd3Z22tjYzbAEKIPgCwCRmNfrowQeTT30qGR4ufSENDck3v5ncfHPpn11jTp06lRdeeGHKUHvw4MGMjIxM+4zW1tYpQ213d3eam5sX6bsBYDYEXwCYwoxGH23dmtx228IWUleX3HdfsmnTwr6nwp08eTKHDh2a8vCoQ4cOZXR0dNpnXHTRRVOG2q6urlxwwQWL9N0AUEqCLwCcxZSjj/7u75KPf3xxiqirS7797Zru/A4PD+fgwYNTnoj8wgsvZGxsbNpnXHbZZVMeHtXZ2Znzzjtvkb4bABaT4AsAM/D20Udrzzsvjw4P55xTp6a973iS/5ZkV5Ldpz/2nv63Z5LMavduQ0Py+ONVu+f39ddff8sM27cH3CNHjkx7f11dXVatWjXl4VEdHR1pbGxcpO8GgHIi+ALALBw6dCi/f8cd+aO/+qusn8H1P0jyoSn+bdbBN0nWr0+2bavI056PHz8+7YnIx44dm/b+JUuWpKOjY8rDo9rb27Ns2bJF+m4AqCQmnAPALHR0dOT7N92Uur/6q4wnmcn5vBcnuS7JuiSrksxrp+7OnRMjk+68c9rLxsbGct9992Xfvn259957Zz6SaR4GBgamPRG57ywjnpYuXZqurq4pD49auXJlzjnHjy4AzJ6OLwDMxtBQ0t4+4zm9o0ne3JvtSXL56c/n1PFNJub8Hj6cLF8+6T///Oc/zyc/+ck88sgjSZK//uu/zm/8xm/M5U1vGB8fT29v75ShtqenJ6+88sq0z2hsbJz2RORLL73UDFsAFoRfmwLAbDz00IxDb/LW0FsyfX3Jww8nv/u7b/ny6Oho/v2///fZvHlzhoaG3vh6T0/PWR85Pj6eF198ccpQ29PTk9dff33aZ5x33nnTnoh88cUXm2ELQCEEXwCYjS1biq5gwpYtbwm+P/vZz/LJT34y27dvf8elPT09GRsby5EjR6YMtQcPHsyJEyemfeWFF174RpCdLOC2trYKtgCUJUudAWCmenqSyy8/62XTPiIlWOp8xnPPZbSjI//u3/27fPGLX5wyuJ5//vkZHh7OyZMnp31cW1vblEuRu7q60tzcPJ9qAaAwOr4AMFO7dxddwVsMbd+e7n/yT/LSSy9Ne92rr76aJLn44ov///buXzWqPIzj8HcUTRQMZCCVgmNlSk0wEFjIJaRKlUpEC72DXIO1qChWNlZewkAsRIhil85gEAsXs+hCiCDZYmAx7ro7kz9zkjfPAweG5Jz5vV345PzmzC+j9uLFizl37twwxgaAoRO+ANCvlZWmJ9jhz273f6M3SSYmJrK2tpazZ88OYSoAOHw8OhEA+vXmTdMT7DCxvp5ut5ubN2/m/Pnzvzzv06dPnpYMwLHmryAA9GuApzkPxcZG5ubm8vDhw7x//z7dbje3bt3K+Pj4P05dX19vYEAAOByELwD069u3pifYaWvr75cnTpzI3NxcHjx4kI8fP+b58+dZWFjI6OhoTp06ldOnTzc4KAA0y2d8AaBfhy0eR0Z+8eORzM/PZ35+Pl++fMnXr1//cys0AFQnfAGgX+120xPs9C9bmn82NjaWsbGxIQwDAIeXrc4A0K+rV5ueYKepqaYnAIAjwR1fAOjX9PSuLvv9h9cbP7z+46fftTPgf6R3OQ8AHDet7e3t7aaHAIAjYW0tuXRp4MtafZ73LklnkDd+9y7pDHQFABxLtjoDQL86neTataan6JmZEb0A0CfhCwCDuH174Eu2+zw6BzwHABxXtjoDwCA2N5MLF5LPn5ubod1OPnxIRkebmwEAjhB3fAFgEGfOJEtLzc6wtCR6AWAA7vgCwKC+f09++y15+XL4a8/OJsvLycmTw18bAI4o4QsAu7G6mly5kmxtDW/NkZHk7dvk8uXhrQkABdjqDAC7MTmZPH6ctPr9sqI9arV664leABiY8AWA3VpcTO7fP/j4bbV66ywuHuw6AFCUrc4AsFdPnyY3bhzMtufR0eTRI9ELAHsgfAFgP6yuJtev7+8Dr2ZnkydPbG8GgD2y1RkA9sPkZPLiRXL3bu97dvei3e69z/Ky6AWAfeCOLwDst83N5Nmz5N695NWr/q+bmUnu3EkWFnrfFwwA7AvhCwAHaW0tWVnpHa9fJxsbvc8Cj4wk4+PJ1FQyPd07Op2mpwWAkoQvAAAApfmMLwAAAKUJXwAAAEoTvgAAAJQmfAEAAChN+AIAAFCa8AUAAKA04QsAAEBpwhcAAIDShC8AAAClCV8AAABKE74AAACUJnwBAAAoTfgCAABQmvAFAACgNOELAABAacIXAACA0oQvAAAApQlfAAAAShO+AAAAlCZ8AQAAKE34AgAAUJrwBQAAoDThCwAAQGnCFwAAgNKELwAAAKUJXwAAAEoTvgAAAJQmfAEAAChN+AIAAFCa8AUAAKA04QsAAEBpwhcAAIDShC8AAAClCV8AAABKE74AAACUJnwBAAAoTfgCAABQmvAFAACgNOELAABAacIXAACA0oQvAAAApQlfAAAAShO+AAAAlCZ8AQAAKE34AgAAUJrwBQAAoDThCwAAQGnCFwAAgNKELwAAAKUJXwAAAEoTvgAAAJQmfAEAAChN+AIAAFCa8AUAAKA04QsAAEBpwhcAAIDShC8AAAClCV8AAABKE74AAACUJnwBAAAoTfgCAABQmvAFAACgNOELAABAacIXAACA0oQvAAAApQlfAAAAShO+AAAAlCZ8AQAAKE34AgAAUJrwBQAAoDThCwAAQGnCFwAAgNKELwAAAKUJXwAAAEoTvgAAAJQmfAEAAChN+AIAAFDaXz77x+ner5DmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 479
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G2, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have a message that begins at node 0, and it is only passed to its neighbors, then node 1 is the next one that possess the message. Node 1 then passes it to node 2, and so on, until it reaches node 3.\n",
    "\n",
    "There are two key ideas to introduce here. Firstly, there is the notion of the **\"wavefront\"** of message passing: at the first time step, node 0 is the wavefront, and as time progresses, node 1, 2 and 3 progressively become the wavefront.\n",
    "\n",
    "Secondly, as the message gets passed, the number of nodes that have seen the message progressively increases. \n",
    "\n",
    "Let's see how this gets implemented in matrix form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Message Passing\n",
    "\n",
    "To represent the data, we start with a vertical array of messages of shape `(1, 4)`. Let's use the following conventions:\n",
    "\n",
    "- `1` indicates that a node currently has the message.\n",
    "- `0` indicates that a node currently does not have the message.\n",
    "\n",
    "Since the message starts at node 0, let's put a `1` in that cell of the array, and `0`s elsewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg = np.array([1, 0, 0, 0]).reshape(1, 4)\n",
    "msg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to simulate one round of message passing, we matrix multiply the message with the adjacency matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg2 = msg @ A2\n",
    "msg2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpretation now is that the message is currently at node 1.\n",
    "\n",
    "To simulate a second round, we take that result and matrix multiply it against the adjacency matrix again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 1., 0.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg3 = msg2 @ A2\n",
    "msg3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpretation now is that the message is currently at node 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's make an animation of this. I have pre-written the animation functions for you; your task is to implement the message passing function `propagate()` to precompute at each time step the message status."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fig, ax = plt.subplots()\n",
    "\n",
    "def propagate(G, msg, n_frames):\n",
    "    \"\"\"\n",
    "    Computes the node values based on propagation.\n",
    "    \n",
    "    Intended to be used before or when being passed into the \n",
    "    anim() function (defined below).\n",
    "    \n",
    "    :param G: A NetworkX Graph.\n",
    "    :param msg: The initial state of the message.\n",
    "    :returns: A list of 1/0 representing message status at \n",
    "        each node.\n",
    "    \"\"\"\n",
    "    # Initialize a list to store message states at each timestep.\n",
    "    msg_states = []\n",
    "    \n",
    "    # Set a variable `new_msg` to be the initial message state.\n",
    "    new_msg = msg\n",
    "    \n",
    "    # Get the adjacency matrix of the graph G.\n",
    "    A = nx.to_numpy_array(G)\n",
    "    \n",
    "    # Perform message passing at each time step\n",
    "    for i in range(n_frames):\n",
    "        msg_states.append(new_msg)\n",
    "        new_msg = new_msg @ A\n",
    "        \n",
    "    # Return the message states.\n",
    "    return msg_states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the `matplotlib` animation functions are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
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     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 382
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def update_func(step, nodes, colors):\n",
    "    \"\"\"\n",
    "    The update function for each animation time step.\n",
    "    \n",
    "    :param step: Passed in from matplotlib's FuncAnimation. Must\n",
    "        be present in the function signature.\n",
    "    :param nodes: Returned from nx.draw_networkx_edges(). Is an\n",
    "        array of colors.\n",
    "    :param colors: A list of pre-computed colors.\n",
    "    \"\"\"\n",
    "    nodes.set_array(colors[step].ravel())\n",
    "    return nodes\n",
    "\n",
    "def anim(G, initial_state, n_frames=4):\n",
    "    colors = propagate(G, initial_state, n_frames)\n",
    "    fig = plt.figure()\n",
    "    pos = {i:(i, i) for i in range(len(G))}\n",
    "    adj = nx.to_numpy_array(G)\n",
    "    pos = nx.kamada_kawai_layout(G)\n",
    "    nodes = nx.draw_networkx_nodes(G, pos=pos, node_color=colors[0].ravel(), node_size=20)\n",
    "    ax = nx.draw_networkx_edges(G, pos)\n",
    "    return animation.FuncAnimation(fig, update_func, frames=range(n_frames), fargs=(nodes, colors))\n",
    "\n",
    "\n",
    "# Initialize the message\n",
    "msg = np.zeros(len(G2))\n",
    "msg[0] = 1\n",
    "\n",
    "# Animate the graph with message propagation.\n",
    "HTML(anim(G2, msg, n_frames=4).to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Visualize how a rumour would spread in the university dorm network. You can initialize the message on any node of your choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 388
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "msg = np.zeros(len(G))\n",
    "msg[0] = 1\n",
    "HTML(anim(G, msg, n_frames=4).to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bipartite Graph Matrices\n",
    "\n",
    "The section on message passing above assumed unipartite graphs, or at least graphs for which messages can be meaningfully passed between nodes. \n",
    "\n",
    "In this section, we will look at bipartite graphs. \n",
    "\n",
    "Recall from before the definition of a bipartite graph:\n",
    "\n",
    "- Nodes are separated into two partitions (hence 'bi'-'partite').\n",
    "- Edges can only occur between nodes of different partitions.\n",
    "\n",
    "Bipartite graphs have a natural matrix representation, known as the **biadjacency matrix**. Nodes on one partition are the rows, and nodes on the other partition are the columns.\n",
    "\n",
    "NetworkX's `bipartite` module provides a function for computing the biadjacency matrix of a bipartite graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by looking at a toy bipartite graph, a \"customer-product\" purchase record graph, with 4 products and 3 customers. The matrix representation might be as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# Rows = customers, columns = products, 1 = customer purchased product, 0 = customer did not purchase product.\n",
    "cp_mat = np.array([[0, 1, 0, 0],\n",
    "                   [1, 0, 1, 0],\n",
    "                   [1, 1, 1, 1]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this \"bi-adjacency\" matrix, one can compute the projection onto the customers, matrix multiplying the matrix with its transpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 1],\n",
       "       [0, 2, 2],\n",
       "       [1, 2, 4]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_mat = cp_mat @ cp_mat.T  # c_mat means \"customer matrix\"\n",
    "c_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Pause here and read carefully!**\n",
    "\n",
    "What we get is the connectivity matrix of the customers, based on shared purchases. The diagonals are the degree of the customers in the original graph, i.e. the number of purchases they originally made, and the off-diagonals are the connectivity matrix, based on shared products."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the products matrix, we make the transposed matrix the left side of the matrix multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 2, 1],\n",
       "       [1, 2, 1, 1],\n",
       "       [2, 1, 2, 1],\n",
       "       [1, 1, 1, 1]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_mat = cp_mat.T @ cp_mat  # p_mat means \"product matrix\"\n",
    "p_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may now try to convince yourself that the diagonals are the number of times a customer purchased that product, and the off-diagonals are the connectivity matrix of the products, weighted by how similar two customers are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises \n",
    "\n",
    "In the following exercises, you will now play with a customer-product graph from Amazon. This dataset was downloaded from [UCSD's Julian McAuley's website](http://jmcauley.ucsd.edu/data/amazon/), and corresponds to the digital music dataset.\n",
    "\n",
    "This is a bipartite graph. The two partitions are:\n",
    "\n",
    "- `customers`: The customers that were doing the reviews.\n",
    "- `products`: The music that was being reviewed.\n",
    "\n",
    "In the original dataset (see the original JSON in the `datasets/` directory), they are referred to as:\n",
    "\n",
    "- `customers`: `reviewerID`\n",
    "- `products`: `asin`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 64706/64706 [00:01<00:00, 40221.29it/s]\n",
      "100%|██████████| 64706/64706 [00:00<00:00, 353064.29it/s]\n",
      "100%|██████████| 64706/64706 [00:00<00:00, 279224.12it/s]\n"
     ]
    }
   ],
   "source": [
    "G_amzn = load_amazon_reviews()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NetworkX provides [`nx.bipartite.matrix.biadjacency_matrix()`](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.matrix.biadjacency_matrix.html#networkx.algorithms.bipartite.matrix.biadjacency_matrix) function that lets you get the biadjacency matrix of a graph object. This returns a `scipy.sparse` matrix. Sparse matrices are commonly used to represent graphs, especially large ones, as they take up much less memory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Read the [docs](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.matrix.biadjacency_matrix.html#networkx.algorithms.bipartite.matrix.biadjacency_matrix) on how to use the `biadjacency_matrix()` function. \n",
    "\n",
    "You probably would want to first define a function that gets all nodes from a partition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_partition_nodes(G, partition):\n",
    "    \"\"\"\n",
    "    A function that returns nodes from one partition.\n",
    "    \n",
    "    Assumes that the attribute key that stores the partition information\n",
    "    is 'bipartite'.\n",
    "    \"\"\"\n",
    "    return [n for n, d in G.nodes(data=True) if d['bipartite'] == partition]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Now, use the `get_partition_nodes()` function to get the `row_order` and `column_order` nodes from the Amazon music review graph, then get the biadjacency matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "customer_nodes = get_partition_nodes(G_amzn, 'customer')\n",
    "mat = nx.bipartite.biadjacency_matrix(G_amzn, customer_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's find out which customers reviewed the most number of music items.\n",
    "\n",
    "To do so, you can break the problem into a few steps.\n",
    "\n",
    "First off, compute the customer projection using matrix operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "customer_mat = mat @ mat.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, get the diagonals of the customer-customer matrix. Recall here that in `customer_mat`, the diagonals correspond to the degree of the customer nodes in the bipartite matrix.\n",
    "\n",
    "**Hint:** SciPy sparse matrices provide a `.diagonal()` method that returns the diagonal elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the diagonal.\n",
    "degrees = customer_mat.diagonal()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, find the index of the customer that has the highest degree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "294"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cust_idx = np.argmax(degrees)\n",
    "cust_idx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be customer 294 in the `customer_nodes` list.\n",
    "\n",
    "### Exercise\n",
    "\n",
    "Verify that this holds when looking at the degrees of each customer in `customer_nodes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "294"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cust_degrees = [G_amzn.degree(n) for n in customer_nodes]\n",
    "np.argmax(cust_degrees)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's now also compute which two customers are similar, based on shared reviews. To do so involves the following steps:\n",
    "\n",
    "1. We construct a sparse matrix consisting of only the diagonals. `scipy.sparse.diags(elements)` will construct a sparse diagonal matrix based on the elements inside `elements`.\n",
    "1. Subtract the diagonals from the customer matrix projection. This yields the customer-customer similarity matrix, which should only consist of the off-diagonal elements of the customer matrix projection.\n",
    "1. Finally, get the indices where the weight (shared number of between the customers is highest. (*This code is provided for you.*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.sparse as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(294, 86)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Construct diagonal elements.\n",
    "customer_diags = sp.diags(degrees)\n",
    "# Subtract off-diagonals.\n",
    "off_diagonals = customer_mat - customer_diags\n",
    "# Compute index of most similar individuals.\n",
    "np.unravel_index(np.argmax(off_diagonals), customer_mat.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance: Object vs. Matrices\n",
    "\n",
    "Finally, to motivate why you might want to use matrices rather than graph objects to compute some of these statistics, let's time the two ways of getting to the same answer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "24.465 seconds\n",
      "Most similar customers: ('A3HU0B9XUEVHIM', 'A9Q28YTLYREO7', {'weight': 154})\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "\n",
    "start = time()\n",
    "\n",
    "# Compute the projection\n",
    "G_cust = nx.bipartite.weighted_projected_graph(G_amzn, customer_nodes)\n",
    "\n",
    "# Identify the most similar customers\n",
    "most_similar_customers = sorted(G_cust.edges(data=True), key=lambda x: x[2]['weight'], reverse=True)[0]\n",
    "\n",
    "end = time()\n",
    "print(f'{end - start:.3f} seconds')\n",
    "print(f'Most similar customers: {most_similar_customers}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.884 seconds\n",
      "Most similar customers: A9Q28YTLYREO7, A3HU0B9XUEVHIM, 154\n"
     ]
    }
   ],
   "source": [
    "start = time()\n",
    "\n",
    "# Compute the projection using matrices\n",
    "mat = nx.bipartite.matrix.biadjacency_matrix(G_amzn, customer_nodes)\n",
    "cust_mat = mat @ mat.T\n",
    "\n",
    "# Identify the most similar customers\n",
    "degrees = customer_mat.diagonal()\n",
    "customer_diags = sp.diags(degrees)\n",
    "off_diagonals = customer_mat - customer_diags\n",
    "c1, c2 = np.unravel_index(np.argmax(off_diagonals), customer_mat.shape)\n",
    "\n",
    "end = time()\n",
    "print(f'{end - start:.3f} seconds')\n",
    "print(f'Most similar customers: {customer_nodes[c1]}, {customer_nodes[c2]}, {cust_mat[c1, c2]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may notice that it's much easier to read the \"objects\" code, but the matrix code way outperforms the object code. This then becomes a great reason to use matrices (even better, sparse matrices)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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