{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine learning and graph embeddings\n",
    "\n",
    "<div style=\"display: flex; align-items: center;\">\n",
    "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/yy/netsci-course/blob/master/docs/m11-ml/lab11.ipynb\">\n",
    "        <img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" style=\"vertical-align: -8px; margin-right: 10px;\" />\n",
    "        Open this notebook in Google Colab\n",
    "    </a>\n",
    "</div>\n",
    "\n",
    "\n",
    "<div style=\"display: flex; align-items: center;\">\n",
    "    <a href=\"https://raw.githubusercontent.com/yy/netsci-course/master/docs/m11-ml/lab11.ipynb\" download>\n",
    "        <img src=\"http://yyahn.com/netsci-course/images/download_icon.png\" style=\"vertical-align: -8px; margin-right: 10px;\" />\n",
    "        Download this notebook (File -> Save As)\n",
    "    </a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A simple illustration\n",
    "\n",
    "Let's first conceptually think about the two main graph machine learning tasks: node classification and link prediction. \n",
    "\n",
    "First, let me create a very simple, stylized network. The network has two distinct community structure, which is completely correlated with the colors (the classes) of the nodes (red or lightblue). Most edges are within the same community. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "\n",
    "G = nx.barbell_graph(6, 0)\n",
    "\n",
    "for i in range(6):\n",
    "    G.nodes[i]['color'] = 'red'\n",
    "for i in range(6, 12):\n",
    "    G.nodes[i]['color'] = 'lightblue'\n",
    "\n",
    "nx.draw(G, with_labels=True, node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Node classification\n",
    "\n",
    "Now, let's think about the node classification problem. Given this network, let's assume that we don't know the node class (color) of node 3 (pretend that you don't know the color of node 3!). \n",
    "\n",
    "What would be your strategy to predict the color of node 3? (Again, pretend that you don't know the color...)\n",
    "\n",
    "One obvious strategy that you can think of is just to look at the immediate neighbors of node 3. If most of the neighbors are red, then maybe it's safe to guess that node 3 is also red. If most of the neighbors are lightblue, then you can guess that node 3 is lightblue. This is more or less same as the K-nearest neighbors algorithm, one of the simplest yet powerful machine learning algorithms. \n",
    "\n",
    "Why is this strategy viable? Which property of the real-world networks does this strategy rely on? \n",
    "\n",
    "Yes! This works thanks to the _homophily_, which is the tendency of nodes to connect to similar nodes. Whenever homophily exists, we also expect that the network has a community structure and a node's properties can be inferred from its neighbors! Let's try this. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Node id: 0\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 1\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 2\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 3\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 4\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 5\n",
      "predicted by neighbors: red\n",
      "actual color:           red\n",
      "\n",
      "Node id: 6\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n",
      "Node id: 7\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n",
      "Node id: 8\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n",
      "Node id: 9\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n",
      "Node id: 10\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n",
      "Node id: 11\n",
      "predicted by neighbors: lightblue\n",
      "actual color:           lightblue\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "for node in G.nodes:\n",
    "    # YOUR SOLUTION HERE\n",
    "    \n",
    "    print(\"Node id:\", node)\n",
    "    print(f\"predicted by neighbors: {most_common_color}\")\n",
    "    print(f\"actual color:           {G.nodes[node]['color']}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A perfect prediction! \n",
    "\n",
    "As you can imagine, this strategy will become too simplistic as the network becomes more complex and noisy. But remember that what we just did is essentially the core idea of many, much fancier, machine learning algorithms including graph neural networks (GNNs). GNNs aggregate the information from the neighbors and combine with the node features to produce a new vector, which in turn can be used for more processing or prediction. \n",
    "\n",
    "Because of the usage of neural networks, GNNs are much more flexible than just counting the number of neighbors with a certain property. They can also utilize many features of the nodes and edges, not just the class labels. Still the idea is not that far!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Link prediction\n",
    "\n",
    "How about link prediction? Let's start with the same network. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, with_labels=True, node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, mark some edges to _pretend_ that they are missing. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 4), (2, 4), (9, 10), (8, 11), (10, 11)]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mark some edges to be missing. Set the edge attribute 'missing' to True\n",
    "import random \n",
    "\n",
    "missing_edges = random.sample(list(G.edges), 5)\n",
    "missing_edges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also sample \"negative\" edges, which are not present in the network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, 7), (8, 2), (9, 1), (10, 5), (11, 2)}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sample negative edges\n",
    "negative_edges = set()\n",
    "while len(negative_edges) < 5:\n",
    "    edge = tuple(random.sample(list(G.nodes), 2))\n",
    "    if edge not in G.edges:\n",
    "        negative_edges.add(edge)\n",
    "negative_edges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw these two see where they are located."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x1152c0f90>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "edge_colors = []\n",
    "for edge in G.edges:\n",
    "    if edge in missing_edges:\n",
    "        edge_colors.append('blue')\n",
    "    else:\n",
    "        edge_colors.append('black')\n",
    "\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "nx.draw(G, with_labels=True, pos=pos, \n",
    "        node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8, edge_color=edge_colors)\n",
    "nx.draw_networkx_edges(G, pos=pos, edgelist=negative_edges, edge_color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do you see?\n",
    "\n",
    "Yes! The missing edges are mostly between the nodes of the same color and the negative edges are mostly between the nodes of different colors. This is again due to the strong community structure that arises from the homophily. Because there are more edges within the same community, it's more likely that the missing edges are also within the same community; because there are fewer edges between the different communities, it's more likely that the negative edges are between the different communities.\n",
    "\n",
    "Then, what would be simple strategies to predict the missing edges correctly, or distinguish missing edges from the negative edges?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Link prediction is often about defining the similarity between the nodes\n",
    "\n",
    "One general idea is to think about the _similarity_ between the nodes. If two nodes are similar, or \"close\", then they are more likely to be connected. Then how should we think about the similarity?\n",
    "\n",
    "#### Link prediction with community membership, and SBM\n",
    "\n",
    "A super simple idea is simply use the community membership as the most informative feature of the nodes. If two nodes are in the same community, then they are \"similar\". If they are in different communities, then they are \"dissimilar\". You may think that this is too simple because we are not considering any other properties once the communities are found. But, do you remember the stochastic block models (SBM)? In the most basic SBM, the probability of connection between two nodes is determined solely by the community membership of the nodes. So, this simple idea may be not that bad!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adamic-Adar index\n",
    "\n",
    "Another simple idea is to think about similarity between nodes based on the number of common neighbors they share. If two people have many shared friends, then they are very likely to be friends. This is the idea behind the Adamic-Adar index and similar. Rather than counting the shared neighbors, Adamic-Adar index gives more weight to the shared neighbors with fewer neighbors. In doing so, the index discounts the shared neighbors that are too popular and thus less informative.  \n",
    "\n",
    "$$ \\text{Adamic-Adar}(u, v) = \\sum_{w \\in N(u) \\cap N(v)} \\frac{1}{\\log |N(w)|} $$\n",
    "\n",
    "where $N(u)$ is the set of neighbors of node $u$. Shall we try this? Let's first remove the missing edges from the network first. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for edge in missing_edges:\n",
    "    if G.has_edge(*edge):\n",
    "        G.remove_edge(*edge)\n",
    "\n",
    "nx.draw(G, with_labels=True, pos=pos, \n",
    "        node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, for every pair of disconnected nodes, we calculate the Adamic-Adar index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((8, 11), 1.6933439034806097),\n",
       " ((9, 10), 1.6933439034806097),\n",
       " ((0, 4), 1.6301195954722452),\n",
       " ((2, 4), 1.6301195954722452),\n",
       " ((10, 11), 1.072008968920998),\n",
       " ((0, 6), 0.5138983423697507),\n",
       " ((1, 6), 0.5138983423697507),\n",
       " ((2, 6), 0.5138983423697507),\n",
       " ((3, 6), 0.5138983423697507),\n",
       " ((4, 6), 0.5138983423697507),\n",
       " ((5, 7), 0.5138983423697507),\n",
       " ((5, 8), 0.5138983423697507),\n",
       " ((5, 9), 0.5138983423697507),\n",
       " ((5, 10), 0.5138983423697507),\n",
       " ((5, 11), 0.5138983423697507)]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate adamic-adar index for every pair of disconnected nodes\n",
    "import numpy as np\n",
    "from itertools import combinations\n",
    "\n",
    "aa_index = {}\n",
    "for u, v in combinations(G.nodes, 2):\n",
    "    if G.has_edge(u, v):\n",
    "        continue\n",
    "    # YOUR SOLUTION HERE\n",
    "\n",
    "    # let's only keep the non-zero ones\n",
    "    if adamic_adar_index > 0:\n",
    "        aa_index[(u, v)] = adamic_adar_index\n",
    "\n",
    "sorted(aa_index.items(), key=lambda x: x[1], reverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's draw them on top of the network. Draw them with ligh grey color and use the thickness of the line to represent the value of the Adamic-Adar index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x11537e550>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, with_labels=True, pos=pos, \n",
    "        node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)\n",
    "\n",
    "edge_width = [aa_index[edge] * 2 for edge in aa_index]\n",
    "\n",
    "nx.draw(G, with_labels=True, pos=pos,\n",
    "        node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)\n",
    "\n",
    "# draw potential edges based on adamic-adar index\n",
    "nx.draw_networkx_edges(G, pos=pos, edgelist=aa_index.keys(), width=edge_width, edge_color='lightgrey')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool! It seems like all the top predictions (large Adamic-Adar index) are located within the same community while those with small Adamic-Adar index are located between the different communities. We can compare this with the actual missing edges (positive) and negative edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>edge</th>\n",
       "      <th>adamic_adar_index</th>\n",
       "      <th>missing</th>\n",
       "      <th>negative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(8, 11)</td>\n",
       "      <td>1.693344</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(9, 10)</td>\n",
       "      <td>1.693344</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(0, 4)</td>\n",
       "      <td>1.630120</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(2, 4)</td>\n",
       "      <td>1.630120</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(10, 11)</td>\n",
       "      <td>1.072009</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(0, 6)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(1, 6)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(2, 6)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(3, 6)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(4, 6)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>(5, 7)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>(5, 8)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>(5, 9)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>(5, 10)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>(5, 11)</td>\n",
       "      <td>0.513898</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        edge  adamic_adar_index  missing  negative\n",
       "0    (8, 11)           1.693344     True     False\n",
       "1    (9, 10)           1.693344     True     False\n",
       "2     (0, 4)           1.630120     True     False\n",
       "3     (2, 4)           1.630120     True     False\n",
       "4   (10, 11)           1.072009     True     False\n",
       "5     (0, 6)           0.513898    False     False\n",
       "6     (1, 6)           0.513898    False     False\n",
       "7     (2, 6)           0.513898    False     False\n",
       "8     (3, 6)           0.513898    False     False\n",
       "9     (4, 6)           0.513898    False     False\n",
       "10    (5, 7)           0.513898    False     False\n",
       "11    (5, 8)           0.513898    False     False\n",
       "12    (5, 9)           0.513898    False     False\n",
       "13   (5, 10)           0.513898    False     False\n",
       "14   (5, 11)           0.513898    False     False"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# YOUR SOLUTION HERE\n",
    "\n",
    "aa_index_df\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This table shows that the top 5 edges with the largest Adamic-Adar index are all positive edges, while none of the node pairs with non-zero Adamic-Adar index are negative edges. This confirms that the Adamic-Adar index is pretty good at capturing the similarity between the nodes. \n",
    "\n",
    "Although Adamic-Adar index is a very good heuristic, there may be numerous other measures that may work similarly. This is how the machine learning problems were tackled before the deep learning era. Many new methods were about new hand-crafted features, new similarity measures, and new ways to combine them. However, the deep learning era has changed this landscape and ushered the era of end-to-end learning that focuses on good representations. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph embeddings\n",
    "\n",
    "Some of the most important lessons from deep learning are:\n",
    "\n",
    "1. Good representations are crucial for good performance.\n",
    "2. Usually it is hard to design good representations by hand.\n",
    "3. By letting the neural network learn the representations, we can achieve better performance.\n",
    "\n",
    "In a more classical approach, one may construct hand-crafted features and use them as input to the machine learning algorithms. For instance, in the link prediction problem, one may use the Adamic-Adar index as a feature of each pair of nodes. You can also add more features such as the number of common neighbors, the Jaccard index, the distance, etc. Each of these number captures some aspect of the similarity between the nodes and then the machine learning algorithm (e.g., logistic regression) learns how to use these features to predict the link based on examples (training data). \n",
    "\n",
    "However, our intuition is never perfect! We may miss some important features, or we may include some irrelevant features. By contrast, neural network methods tend to be end-to-end, meaning that they learn the representations and the prediction model simultaneously. This leads to much better representations (features) that are optimized for the task at hand. \n",
    "\n",
    "But, another interesting lesson has been that we can \"pre-train\" the neural networks using lots of data that captures the structure of the data. Once we have a good pre-trained model (and good representations), we can reuse the model for other tasks quite successfully. Word embeddings, LLMs, and graph embeddings are all examples of this idea."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Word2vec\n",
    "\n",
    "Word2vec is a famous example of learning embeddings. The idea is to learn the embeddings of the words simply by trying to predict words that appear in the context of the target word. This originates from the idea of \"language model\". \n",
    "\n",
    "A language model is just a statistical model (probability distribution) that capture the structure of the language. In the simplest sense, a language model is a model that can estimate the joint probability of a sequence of words.\n",
    "\n",
    "$$ \\tilde{P}_{LM}(w_1, w_2, \\ldots, w_T) \\approx P(w_1, w_2, \\ldots, w_T) $$\n",
    "\n",
    "This conditional probability can be factorized into the product of the conditional probabilities of each word given the previous words.\n",
    "\n",
    "$$ P(w_1, w_2, \\ldots, w_T) = P(w_1) P(w_2 | w_1) P(w_3 | w_1, w_2) \\ldots P(w_T | w_1, w_2, \\ldots, w_{T-1}) $$\n",
    "\n",
    "In other words, if you can simply predict the next word (token) given the previous words, then you have a language model. Sounds familiar? This is exactly what the ChatGPT and other LLMs are doing! \n",
    "\n",
    "The core idea behind these complex LLMs originated from the simple idea of word2vec -- learn the vector representations (embeddings) of the words that allow us to predict the next (or previous) word. \n",
    "\n",
    "From the conditional probability formulation of the language model, word2vec has another simplification. Instead of thinking about many previous token, it says \"let's just use a single token to predict another\". In other words,\n",
    "\n",
    "$$ P(w_t | w_{t-1}, w_{t-2}, \\ldots, w_{t-n}) \\approx P(w_t | w_{t-\\tau}) $$\n",
    "\n",
    "where $\\tau$ is a small number (window size). This is called the \"skip-gram\" model because we are skipping all the words in between. Given a large corpus (a collection of sentences), word2vec keeps trying to predict the words around a focal word and use the result to update the embeddings. \n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### word2vec to node2vec\n",
    "\n",
    "The input to the word2vec model is just sentences, many of them. From this, we get the embeddings of the words. A really cool thing about this model is that the input \"sentences\" don't have to be real sentences. *Any* sequence of tokens can be used as the input and word2vec will happily produce the embeddings. The \"tokens\" that consist the input sentences can be anything -- words, characters, or even nodes in a graph!\n",
    "\n",
    "That's the idea behind many graph embedding methods. Instead of learning the embeddings of the words, why don't we learn the embeddings of the nodes in a graph? We just need to feed many sequences of nodes to the word2vec model.\n",
    "\n",
    "But, what should be the reasonable sequences of nodes? These sentences should be able to capture the structure of the graph. When a node follows another, they should be somehow related. How can we do that?\n",
    "\n",
    "One super simple, yet extremely powerful idea is to use the random walks. A random walk is a sequence of nodes that starts from a node and moves to a randomly selected neighbor. By repeating this process many times, we can generate many sequences of nodes that capture the structure of the graph. Because random walks follow edges, it organically captures the structure of the graph. The more two nodes are connected (via different paths), the more likely they will appear in the same random walk. Thus they are more likely to be close in the embedding space!\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try this. There are many variations, but let's keep it simple and use the word2vec algorithm. We're reusing the graph with the missing edges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, with_labels=True, pos=pos, \n",
    "        node_color=[G.nodes[i]['color'] for i in G.nodes], node_size=200, font_size=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first step is to generate the random walks. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[5, 1, 2, 0, 1, 0, 3, 0, 2],\n",
       " [1, 2, 5, 1, 0, 5, 1, 4, 3],\n",
       " [3, 4, 5, 0, 2, 0, 1, 2, 5]]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def generate_random_walks(G, walk_length, num_walks):\n",
    "    \"\"\" Generate random walks on the graph G.\n",
    "    \"\"\"\n",
    "    for _ in range(num_walks):\n",
    "        # YOUR SOLUTION HERE\n",
    "        yield walk\n",
    "\n",
    "list(generate_random_walks(G, 8, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then feed these random walks to the word2vec model. For word2vec model, we can use the `gensim` library. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: gensim in ./.venv/lib/python3.11/site-packages (4.3.2)\n",
      "Requirement already satisfied: numpy>=1.18.5 in ./.venv/lib/python3.11/site-packages (from gensim) (1.26.3)\n",
      "Requirement already satisfied: scipy>=1.7.0 in ./.venv/lib/python3.11/site-packages (from gensim) (1.11.4)\n",
      "Requirement already satisfied: smart-open>=1.8.1 in ./.venv/lib/python3.11/site-packages (from gensim) (6.4.0)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m23.2.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.0\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# install gensim library \n",
    "!pip install gensim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Refer to the [official documentation](https://radimrehurek.com/gensim/models/word2vec.html) to train a model from the random walks. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<gensim.models.word2vec.Word2Vec at 0x173ebec10>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# gensim word2vec model using our random walk generator\n",
    "from gensim.models import Word2Vec\n",
    "\n",
    "\n",
    "rws = list(generate_random_walks(G, 10, 1000))\n",
    "\n",
    "# YOUR SOLUTION HERE\n",
    "\n",
    "model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once we have a model, we can plot the embedding. Maybe we can use the PCA to reduce the dimensionality of the embeddings to 2D. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# YOUR SOLUTION HERE\n",
    "\n",
    "words = list(model.wv.index_to_key)\n",
    "for i, word in enumerate(words):\n",
    "    plt.annotate(word, xy=(result[i, 0], result[i, 1]))\n",
    "\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the first principal component separates the two communities quite well. In other words, by simplying observing many random walk trajectories on this network, the word2vec model was able to learn that there are two clusters of nodes in the data. \n",
    "\n",
    "Can we use this embedding for the node classification or link prediction?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Node classification with node embeddings\n",
    "\n",
    "Let's try the node classification first. Instead of looking at the network neighbors, we are going to use the node embeddings. Let's look at the three nearest neighbors of each node in the embedding space. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Node id: 0\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 1\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 2\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 3\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 4\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 5\n",
      "actual: red\n",
      "predicted: red\n",
      "\n",
      "Node id: 6\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n",
      "Node id: 7\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n",
      "Node id: 8\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n",
      "Node id: 9\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n",
      "Node id: 10\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n",
      "Node id: 11\n",
      "actual: lightblue\n",
      "predicted: lightblue\n",
      "\n"
     ]
    }
   ],
   "source": [
    "for node in G.nodes:\n",
    "    print(\"Node id:\", node)\n",
    "    print(\"actual:\", G.nodes[node]['color'])\n",
    "    \n",
    "    # find the 3-nearest neighbors in the embedding space and \n",
    "    # use their majority class as the prediction\n",
    "    # YOUR SOLUTION HERE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yay! A perfect prediction! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Link prediction with node embeddings\n",
    "\n",
    "Let's try the link prediction next. The similarity between two nodes is simply the distance in the embedding space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[((9, 10), 0.99832845),\n",
       " ((8, 11), 0.9982137),\n",
       " ((10, 11), 0.9981303),\n",
       " ((2, 4), 0.99602705),\n",
       " ((0, 4), 0.9918693),\n",
       " ((4, 6), 0.51385474),\n",
       " ((4, 8), 0.4770486),\n",
       " ((4, 11), 0.45507237),\n",
       " ((2, 6), 0.45084545),\n",
       " ((5, 8), 0.44465238),\n",
       " ((4, 10), 0.44050527),\n",
       " ((4, 9), 0.43067354),\n",
       " ((5, 11), 0.4222979),\n",
       " ((3, 6), 0.4199267),\n",
       " ((4, 7), 0.41550887),\n",
       " ((2, 8), 0.41253433),\n",
       " ((0, 6), 0.41068062),\n",
       " ((5, 10), 0.40792263),\n",
       " ((1, 6), 0.40312147),\n",
       " ((5, 9), 0.39760047),\n",
       " ((2, 11), 0.38934413),\n",
       " ((5, 7), 0.38227364),\n",
       " ((3, 8), 0.38113827),\n",
       " ((2, 10), 0.3747149),\n",
       " ((0, 8), 0.37161374),\n",
       " ((2, 9), 0.36459893),\n",
       " ((1, 8), 0.36389732),\n",
       " ((3, 11), 0.3577143),\n",
       " ((2, 7), 0.34931344),\n",
       " ((0, 11), 0.34853363),\n",
       " ((3, 10), 0.34225166),\n",
       " ((1, 11), 0.340205),\n",
       " ((0, 10), 0.33327013),\n",
       " ((3, 9), 0.33221066),\n",
       " ((1, 10), 0.32469416),\n",
       " ((0, 9), 0.32284117),\n",
       " ((3, 7), 0.316696),\n",
       " ((1, 9), 0.3148909),\n",
       " ((0, 7), 0.3072211),\n",
       " ((1, 7), 0.29900423)]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "similarities = {}\n",
    "\n",
    "for u, v in combinations(G.nodes, 2):\n",
    "    if G.has_edge(u, v):\n",
    "        continue\n",
    "    # YOUR SOLUTION HERE\n",
    "\n",
    "sorted(similarities.items(), key=lambda x: x[1], reverse=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can again make a table. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>edge</th>\n",
       "      <th>similarity</th>\n",
       "      <th>missing</th>\n",
       "      <th>negative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(9, 10)</td>\n",
       "      <td>0.998328</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(8, 11)</td>\n",
       "      <td>0.998214</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(10, 11)</td>\n",
       "      <td>0.998130</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(2, 4)</td>\n",
       "      <td>0.996027</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(0, 4)</td>\n",
       "      <td>0.991869</td>\n",
       "      <td>True</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(4, 6)</td>\n",
       "      <td>0.513855</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(4, 8)</td>\n",
       "      <td>0.477049</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(4, 11)</td>\n",
       "      <td>0.455072</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(2, 6)</td>\n",
       "      <td>0.450845</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(5, 8)</td>\n",
       "      <td>0.444652</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>(4, 10)</td>\n",
       "      <td>0.440505</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>(4, 9)</td>\n",
       "      <td>0.430674</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>(5, 11)</td>\n",
       "      <td>0.422298</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>(3, 6)</td>\n",
       "      <td>0.419927</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>(4, 7)</td>\n",
       "      <td>0.415509</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>(2, 8)</td>\n",
       "      <td>0.412534</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>(0, 6)</td>\n",
       "      <td>0.410681</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>(5, 10)</td>\n",
       "      <td>0.407923</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>(1, 6)</td>\n",
       "      <td>0.403121</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>(5, 9)</td>\n",
       "      <td>0.397600</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>(2, 11)</td>\n",
       "      <td>0.389344</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>(5, 7)</td>\n",
       "      <td>0.382274</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>(3, 8)</td>\n",
       "      <td>0.381138</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>(2, 10)</td>\n",
       "      <td>0.374715</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>(0, 8)</td>\n",
       "      <td>0.371614</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>(2, 9)</td>\n",
       "      <td>0.364599</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>(1, 8)</td>\n",
       "      <td>0.363897</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>(3, 11)</td>\n",
       "      <td>0.357714</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>(2, 7)</td>\n",
       "      <td>0.349313</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>(0, 11)</td>\n",
       "      <td>0.348534</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>(3, 10)</td>\n",
       "      <td>0.342252</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>(1, 11)</td>\n",
       "      <td>0.340205</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>(0, 10)</td>\n",
       "      <td>0.333270</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>(3, 9)</td>\n",
       "      <td>0.332211</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>(1, 10)</td>\n",
       "      <td>0.324694</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>(0, 9)</td>\n",
       "      <td>0.322841</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>(3, 7)</td>\n",
       "      <td>0.316696</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>(1, 9)</td>\n",
       "      <td>0.314891</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>(0, 7)</td>\n",
       "      <td>0.307221</td>\n",
       "      <td>False</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>(1, 7)</td>\n",
       "      <td>0.299004</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        edge  similarity  missing  negative\n",
       "0    (9, 10)    0.998328     True     False\n",
       "1    (8, 11)    0.998214     True     False\n",
       "2   (10, 11)    0.998130     True     False\n",
       "3     (2, 4)    0.996027     True     False\n",
       "4     (0, 4)    0.991869     True     False\n",
       "5     (4, 6)    0.513855    False     False\n",
       "6     (4, 8)    0.477049    False     False\n",
       "7    (4, 11)    0.455072    False     False\n",
       "8     (2, 6)    0.450845    False     False\n",
       "9     (5, 8)    0.444652    False     False\n",
       "10   (4, 10)    0.440505    False     False\n",
       "11    (4, 9)    0.430674    False     False\n",
       "12   (5, 11)    0.422298    False     False\n",
       "13    (3, 6)    0.419927    False     False\n",
       "14    (4, 7)    0.415509    False     False\n",
       "15    (2, 8)    0.412534    False     False\n",
       "16    (0, 6)    0.410681    False     False\n",
       "17   (5, 10)    0.407923    False     False\n",
       "18    (1, 6)    0.403121    False     False\n",
       "19    (5, 9)    0.397600    False     False\n",
       "20   (2, 11)    0.389344    False     False\n",
       "21    (5, 7)    0.382274    False     False\n",
       "22    (3, 8)    0.381138    False     False\n",
       "23   (2, 10)    0.374715    False     False\n",
       "24    (0, 8)    0.371614    False     False\n",
       "25    (2, 9)    0.364599    False     False\n",
       "26    (1, 8)    0.363897    False     False\n",
       "27   (3, 11)    0.357714    False     False\n",
       "28    (2, 7)    0.349313    False     False\n",
       "29   (0, 11)    0.348534    False     False\n",
       "30   (3, 10)    0.342252    False     False\n",
       "31   (1, 11)    0.340205    False     False\n",
       "32   (0, 10)    0.333270    False     False\n",
       "33    (3, 9)    0.332211    False     False\n",
       "34   (1, 10)    0.324694    False     False\n",
       "35    (0, 9)    0.322841    False     False\n",
       "36    (3, 7)    0.316696    False     False\n",
       "37    (1, 9)    0.314891    False     False\n",
       "38    (0, 7)    0.307221    False      True\n",
       "39    (1, 7)    0.299004    False     False"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# YOUR SOLUTION HERE\n",
    "\n",
    "similarity_df\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, all the missing edges (positive set) have similarity value larger than 0.99 while all other pairs have similarity value at most about 0.5. This is pretty good!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Q: as the final exercise, pick a small-ish real-world network, learn the node embeddings, and make both traditional network visualization (node-link diagram) and the embedding visualization. You can try PCA or UMAP.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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