graph_analyze.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from graph_tool.all import *\n",
    "import networkx as nx\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import functools\n",
    "import torch\n",
    "import pickle\n",
    "from multiprocessing import Process, Value, Array\n",
    "from pyvis.network import Network\n",
    "import graph_tool as gt\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Graph object, directed, with 1000000 vertices and 100000000 edges, at 0x7f505e6875e0>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "adjs = np.fromfile('output.bin', dtype=np.uint32).reshape(-1, K)\n",
    "adj_dic = {}\n",
    "g = gt.Graph()\n",
    "for i, adj in zip(range(adjs.shape[0]), adjs):\n",
    "    for x in adj:\n",
    "        g.add_edge(i, x)\n",
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# with open('output_graph_iter2.pkl', 'wb') as f:\n",
    "#     pickle.dump(g, f)\n",
    "#     f.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Open the file in binary read mode\n",
    "with open('output_graph.pkl', 'rb') as f:\n",
    "    \n",
    "    # Load the object from the file\n",
    "    g = pickle.load(f)\n",
    "    \n",
    "    # Close the file\n",
    "    f.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Graph object, directed, with 1000000 vertices and 100000000 edges, at 0x7f505e582b20>"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>104</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>73</td>\n",
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       "      <th>3</th>\n",
       "      <td>55</td>\n",
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       "      <th>4</th>\n",
       "      <td>22</td>\n",
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       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>999995</th>\n",
       "      <td>30</td>\n",
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       "      <td>128</td>\n",
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       "    <tr>\n",
       "      <th>999999</th>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000000 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          0\n",
       "0       104\n",
       "1        64\n",
       "2        73\n",
       "3        55\n",
       "4        22\n",
       "...     ...\n",
       "999995   30\n",
       "999996  128\n",
       "999997   43\n",
       "999998  110\n",
       "999999   10\n",
       "\n",
       "[1000000 rows x 1 columns]"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vid = np.arange(0, g.num_vertices()).tolist()\n",
    "all_ind = g.get_in_degrees(vid)\n",
    "ind_df = pd.DataFrame(all_ind)\n",
    "ind_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>171.873161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>29.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>57.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>109.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10658.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    0\n",
       "count  1000000.000000\n",
       "mean       100.000000\n",
       "std        171.873161\n",
       "min          0.000000\n",
       "25%         29.000000\n",
       "50%         57.000000\n",
       "75%        109.000000\n",
       "max      10658.000000"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_gt = open('../evaluation-code/contest-data-release-gt-1m.ibin', 'rb')\n",
    "f_gt.seek(4)\n",
    "gt_ids = np.empty((1000000, K), dtype=np.uint32)\n",
    "for i in range(1000000):\n",
    "    cur_id = np.fromfile(f_gt, dtype=np.uint32, count=1)[0]\n",
    "    gt_ids[cur_id] = np.fromfile(f_gt, dtype=np.uint32, count=K)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "gt_graph = gt.Graph()\n",
    "for i in range(gt_ids.shape[0]):\n",
    "    for x in gt_ids[0]:\n",
    "        gt_graph.add_edge(i, x)\n",
    "gt_graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# with open('output_graph_iter2.pkl', 'wb') as f:\n",
    "#     pickle.dump(g, f)\n",
    "#     f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "f_res = open('output.bin', 'rb')\n",
    "graph_res = np.fromfile(f_res, dtype=np.uint32).reshape(-1, K)\n",
    "f_res.close()\n",
    "\n",
    "for i in range(graph_res.shape[0]):\n",
    "    unique_vals = np.unique(graph_res[i])\n",
    "    if len(unique_vals) == graph_res.shape[1]:\n",
    "        pass\n",
    "        # print(\"All elements in graph_res[{}] are unique\".format(i))\n",
    "    else:\n",
    "        print(\"There are duplicate elements in graph_res[{}]: {}\".format(i, unique_vals))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[513548, 964580, 510954, ..., 450783, 703797, 368286],\n",
       "       [182423, 555328, 481001, ..., 244628,  46471, 552387],\n",
       "       [654596, 319311, 115908, ..., 702534, 416532, 429405],\n",
       "       ...,\n",
       "       [259154, 542208, 864029, ..., 366741, 878759, 802517],\n",
       "       [616694, 916714, 838316, ..., 771087, 233660, 186672],\n",
       "       [ 65364, 769904, 391230, ..., 528604, 294449, 582554]],\n",
       "      dtype=uint32)"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "graph_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        187863, 491194, 257503, 190437, 909537, 774366, 597076, 839464,\n",
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       "        566492, 244628,  46471, 552387], dtype=uint32),\n",
       " array([182423, 555328, 481001, 870285, 105516, 379912, 767419, 234646,\n",
       "         14593, 611263, 823224, 800336, 375059, 116483, 176962, 287145,\n",
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       "        524707, 449789, 879774, 945364, 314083, 445653, 387173, 913225,\n",
       "        860499, 499465, 481872, 116577,  56237, 836803, 662816, 757656,\n",
       "        319471, 891329, 900657, 769486, 187863, 491194, 257503, 190437,\n",
       "        909537, 774366, 830083, 597076, 839464, 495226, 292169, 977571,\n",
       "        578385, 421420, 132079, 728161, 759135, 532606, 604573, 480445,\n",
       "        873091, 747105, 665991, 554666], dtype=uint32))"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph_res[1], gt_ids[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True, False,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True, False,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True, False, False,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True, False,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True, False,  True,  True,  True,  True,\n",
       "        True])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.isin(gt_ids[1], graph_res[1])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocessing as mp\n",
    "\n",
    "def process_chunk(start_idx, end_idx):\n",
    "    chunk_hit_mx = np.zeros((end_idx-start_idx, K), dtype=np.uint32)\n",
    "    for i in range(start_idx, end_idx):\n",
    "        mask = np.isin(gt_ids[i], graph_res[i])\n",
    "        hit_indices = np.where(mask)[0]\n",
    "        gt_indices = np.where(mask == True)[0]\n",
    "        chunk_hit_mx[i-start_idx, gt_indices] = 1\n",
    "    return chunk_hit_mx\n",
    "\n",
    "# number of worker processes\n",
    "num_procs = mp.cpu_count()\n",
    "\n",
    "# chunk size\n",
    "chunk_size = 10**4\n",
    "\n",
    "# create pool of worker processes\n",
    "pool = mp.Pool(processes=num_procs)\n",
    "\n",
    "# submit jobs to pool\n",
    "results = []\n",
    "for i in range(0, 10**6, chunk_size):\n",
    "    results.append(pool.apply_async(process_chunk, args=(i, min(i+chunk_size, 10**6))))\n",
    "\n",
    "# collect results and combine into final hit_mx array\n",
    "hit_mx = np.concatenate([r.get() for r in results], axis=0)\n",
    "\n",
    "# close pool\n",
    "pool.close()\n",
    "pool.join()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "import multiprocessing as mp\n",
    "\n",
    "def process_chunk(start_idx, end_idx):\n",
    "    chunk_in_gt_mx = np.zeros((end_idx-start_idx, K), dtype=np.uint32)\n",
    "    for i in range(start_idx, end_idx):\n",
    "        mask = np.isin(graph_res[i], gt_ids[i])\n",
    "        hit_indices = np.where(mask == True)[0]\n",
    "        # gt_indices = np.where(mask == True)[0]\n",
    "        chunk_in_gt_mx[i-start_idx, hit_indices] = 1\n",
    "    return chunk_in_gt_mx\n",
    "\n",
    "# number of worker processes\n",
    "num_procs = mp.cpu_count()\n",
    "\n",
    "# chunk size\n",
    "chunk_size = 10**4\n",
    "\n",
    "# create pool of worker processes\n",
    "pool = mp.Pool(processes=num_procs)\n",
    "\n",
    "# submit jobs to pool\n",
    "results = []\n",
    "for i in range(0, 10**6, chunk_size):\n",
    "    results.append(pool.apply_async(process_chunk, args=(i, min(i+chunk_size, 10**6))))\n",
    "\n",
    "# collect results and combine into final hit_mx array\n",
    "res_in_gt_mx = np.concatenate([r.get() for r in results], axis=0)\n",
    "\n",
    "# close pool\n",
    "pool.close()\n",
    "pool.join()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
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       "      <th>99</th>\n",
       "      <th>recall</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000000.0</td>\n",
       "      <td>1000000.0</td>\n",
       "      <td>1000000.0</td>\n",
       "      <td>1000000.0</td>\n",
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       "      <td>1000000.0</td>\n",
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       "      <td>1000000.0</td>\n",
       "      <td>1000000.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.976283</td>\n",
       "      <td>0.964373</td>\n",
       "      <td>0.947329</td>\n",
       "      <td>0.923445</td>\n",
       "      <td>0.890018</td>\n",
       "      <td>0.843602</td>\n",
       "      <td>0.777756</td>\n",
       "      <td>0.679643</td>\n",
       "      <td>0.511206</td>\n",
       "      <td>0.984735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.152166</td>\n",
       "      <td>0.185358</td>\n",
       "      <td>0.223376</td>\n",
       "      <td>0.265884</td>\n",
       "      <td>0.312867</td>\n",
       "      <td>0.363232</td>\n",
       "      <td>0.415754</td>\n",
       "      <td>0.466614</td>\n",
       "      <td>0.499875</td>\n",
       "      <td>0.023803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.700000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.950000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.970000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.980000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.990000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 101 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               0          1          2          3          4          5  \\\n",
       "count  1000000.0  1000000.0  1000000.0  1000000.0  1000000.0  1000000.0   \n",
       "mean         1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "std          0.0        0.0        0.0        0.0        0.0        0.0   \n",
       "min          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "0%           1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "10%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "20%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "30%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "40%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "50%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "60%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "70%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "80%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "90%          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "max          1.0        1.0        1.0        1.0        1.0        1.0   \n",
       "\n",
       "               6          7          8          9  ...              91  \\\n",
       "count  1000000.0  1000000.0  1000000.0  1000000.0  ...  1000000.000000   \n",
       "mean         1.0        1.0        1.0        1.0  ...        0.976283   \n",
       "std          0.0        0.0        0.0        0.0  ...        0.152166   \n",
       "min          1.0        1.0        1.0        1.0  ...        0.000000   \n",
       "0%           1.0        1.0        1.0        1.0  ...        0.000000   \n",
       "10%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "20%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "30%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "40%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "50%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "60%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "70%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "80%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "90%          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "max          1.0        1.0        1.0        1.0  ...        1.000000   \n",
       "\n",
       "                   92              93              94              95  \\\n",
       "count  1000000.000000  1000000.000000  1000000.000000  1000000.000000   \n",
       "mean         0.964373        0.947329        0.923445        0.890018   \n",
       "std          0.185358        0.223376        0.265884        0.312867   \n",
       "min          0.000000        0.000000        0.000000        0.000000   \n",
       "0%           0.000000        0.000000        0.000000        0.000000   \n",
       "10%          1.000000        1.000000        1.000000        0.000000   \n",
       "20%          1.000000        1.000000        1.000000        1.000000   \n",
       "30%          1.000000        1.000000        1.000000        1.000000   \n",
       "40%          1.000000        1.000000        1.000000        1.000000   \n",
       "50%          1.000000        1.000000        1.000000        1.000000   \n",
       "60%          1.000000        1.000000        1.000000        1.000000   \n",
       "70%          1.000000        1.000000        1.000000        1.000000   \n",
       "80%          1.000000        1.000000        1.000000        1.000000   \n",
       "90%          1.000000        1.000000        1.000000        1.000000   \n",
       "max          1.000000        1.000000        1.000000        1.000000   \n",
       "\n",
       "                   96              97              98              99  \\\n",
       "count  1000000.000000  1000000.000000  1000000.000000  1000000.000000   \n",
       "mean         0.843602        0.777756        0.679643        0.511206   \n",
       "std          0.363232        0.415754        0.466614        0.499875   \n",
       "min          0.000000        0.000000        0.000000        0.000000   \n",
       "0%           0.000000        0.000000        0.000000        0.000000   \n",
       "10%          0.000000        0.000000        0.000000        0.000000   \n",
       "20%          1.000000        0.000000        0.000000        0.000000   \n",
       "30%          1.000000        1.000000        0.000000        0.000000   \n",
       "40%          1.000000        1.000000        1.000000        0.000000   \n",
       "50%          1.000000        1.000000        1.000000        1.000000   \n",
       "60%          1.000000        1.000000        1.000000        1.000000   \n",
       "70%          1.000000        1.000000        1.000000        1.000000   \n",
       "80%          1.000000        1.000000        1.000000        1.000000   \n",
       "90%          1.000000        1.000000        1.000000        1.000000   \n",
       "max          1.000000        1.000000        1.000000        1.000000   \n",
       "\n",
       "               recall  \n",
       "count  1000000.000000  \n",
       "mean         0.984735  \n",
       "std          0.023803  \n",
       "min          0.700000  \n",
       "0%           0.700000  \n",
       "10%          0.950000  \n",
       "20%          0.970000  \n",
       "30%          0.980000  \n",
       "40%          0.990000  \n",
       "50%          1.000000  \n",
       "60%          1.000000  \n",
       "70%          1.000000  \n",
       "80%          1.000000  \n",
       "90%          1.000000  \n",
       "max          1.000000  \n",
       "\n",
       "[15 rows x 101 columns]"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_in_gt_df = pd.DataFrame(res_in_gt_mx)\n",
    "res_in_gt_df['recall'] = res_in_gt_df.sum(axis=1) / K\n",
    "res_in_gt_df.describe(percentiles=np.arange(0, 1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [],
   "source": [
    "res_in_gt_dgree_df = pd.DataFrame({'recall': res_in_gt_df['recall'], 'indegree': all_ind})\n",
    "check_low_degree_ids = res_in_gt_dgree_df[res_in_gt_dgree_df['indegree'] < 30].index.tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>259760.000000</td>\n",
       "      <td>259760.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.966249</td>\n",
       "      <td>16.806460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.031738</td>\n",
       "      <td>7.613237</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.700000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.950000</td>\n",
       "      <td>11.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.970000</td>\n",
       "      <td>17.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.990000</td>\n",
       "      <td>23.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>29.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              recall       indegree\n",
       "count  259760.000000  259760.000000\n",
       "mean        0.966249      16.806460\n",
       "std         0.031738       7.613237\n",
       "min         0.700000       0.000000\n",
       "25%         0.950000      11.000000\n",
       "50%         0.970000      17.000000\n",
       "75%         0.990000      23.000000\n",
       "max         1.000000      29.000000"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# res_in_gt_dgree_df[res_in_gt_dgree_df['indegree'] < 30].describe(percentiles=np.arange(0, 1, 0.1))\n",
    "res_in_gt_dgree_df.loc[check_low_degree_ids].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[126736, 822158,  86291, ..., 788157, 170660, 831658],\n",
       "       [852650, 575158, 978794, ..., 890248, 249781, 968516],\n",
       "       [139478, 888771, 878955, ..., 221272, 680823, 806732],\n",
       "       ...,\n",
       "       [396207, 102840, 539300, ..., 699379,  20698, 466189],\n",
       "       [878743,  23340, 527434, ..., 731936, 583239, 718855],\n",
       "       [ 65364, 769904, 391230, ..., 820345, 370596, 528604]],\n",
       "      dtype=uint32)"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp_gt = gt_ids[check_low_degree_ids,:]\n",
    "temp_gt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "hit_df = pd.DataFrame(hit_mx)\n",
    "hit_df['recall'] = hit_df.sum(axis=1) / K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.89</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.51</td>\n",
       "      <td>46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.65</td>\n",
       "      <td>53</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.77</td>\n",
       "      <td>44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.73</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999995</th>\n",
       "      <td>0.72</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999996</th>\n",
       "      <td>0.87</td>\n",
       "      <td>139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999997</th>\n",
       "      <td>0.61</td>\n",
       "      <td>52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999998</th>\n",
       "      <td>0.80</td>\n",
       "      <td>101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999999</th>\n",
       "      <td>0.75</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000000 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        recall  indegree\n",
       "0         0.89       100\n",
       "1         0.51        46\n",
       "2         0.65        53\n",
       "3         0.77        44\n",
       "4         0.73        20\n",
       "...        ...       ...\n",
       "999995    0.72        28\n",
       "999996    0.87       139\n",
       "999997    0.61        52\n",
       "999998    0.80       101\n",
       "999999    0.75         8\n",
       "\n",
       "[1000000 rows x 2 columns]"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_ind_df = pd.DataFrame({'recall': hit_df['recall'], 'indegree': all_ind})\n",
    "recall_ind_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='indegree', ylabel='recall'>"
      ]
     },
     "execution_count": 118,
     "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": [
    "sorted_df = recall_ind_df.sort_values(by='indegree')\n",
    "sorted_df.plot(x='indegree', y='recall', kind='scatter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1000000.000000</td>\n",
       "      <td>1000000.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.759159</td>\n",
       "      <td>100.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.163924</td>\n",
       "      <td>195.63499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.170000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>0.170000</td>\n",
       "      <td>0.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>0.520000</td>\n",
       "      <td>11.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>0.610000</td>\n",
       "      <td>19.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>0.680000</td>\n",
       "      <td>28.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>0.740000</td>\n",
       "      <td>37.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.780000</td>\n",
       "      <td>49.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>0.830000</td>\n",
       "      <td>65.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>0.870000</td>\n",
       "      <td>87.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>0.910000</td>\n",
       "      <td>124.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>0.960000</td>\n",
       "      <td>210.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>14600.00000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               recall       indegree\n",
       "count  1000000.000000  1000000.00000\n",
       "mean         0.759159      100.00000\n",
       "std          0.163924      195.63499\n",
       "min          0.170000        0.00000\n",
       "0%           0.170000        0.00000\n",
       "10%          0.520000       11.00000\n",
       "20%          0.610000       19.00000\n",
       "30%          0.680000       28.00000\n",
       "40%          0.740000       37.00000\n",
       "50%          0.780000       49.00000\n",
       "60%          0.830000       65.00000\n",
       "70%          0.870000       87.00000\n",
       "80%          0.910000      124.00000\n",
       "90%          0.960000      210.00000\n",
       "max          1.000000    14600.00000"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df.describe(percentiles=np.arange(0, 1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1677, 100)"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "low_recall_ids = sorted_df[sorted_df['indegree'] > 2000].index.tolist()\n",
    "low_recall_gt = gt_ids[low_recall_ids, :]\n",
    "low_recall_gt.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1677.000000</td>\n",
       "      <td>1677.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.998986</td>\n",
       "      <td>2893.134168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.004496</td>\n",
       "      <td>945.952572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.950000</td>\n",
       "      <td>2001.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>0.950000</td>\n",
       "      <td>2001.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>4976.120000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>5358.720000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>5620.240000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>6288.680000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>14600.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>105 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            recall      indegree\n",
       "count  1677.000000   1677.000000\n",
       "mean      0.998986   2893.134168\n",
       "std       0.004496    945.952572\n",
       "min       0.950000   2001.000000\n",
       "0%        0.950000   2001.000000\n",
       "...            ...           ...\n",
       "96%       1.000000   4976.120000\n",
       "97%       1.000000   5358.720000\n",
       "98%       1.000000   5620.240000\n",
       "99%       1.000000   6288.680000\n",
       "max       1.000000  14600.000000\n",
       "\n",
       "[105 rows x 2 columns]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df.loc[low_recall_ids, :].describe(percentiles=np.arange(0, 1, 0.01))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>334500.000000</td>\n",
       "      <td>334500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.980234</td>\n",
       "      <td>1327.882410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.056636</td>\n",
       "      <td>1177.780395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.320000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>0.320000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>0.940000</td>\n",
       "      <td>177.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>0.990000</td>\n",
       "      <td>345.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>540.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>754.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1004.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1305.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1667.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2147.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2908.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>14600.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              recall       indegree\n",
       "count  334500.000000  334500.000000\n",
       "mean        0.980234    1327.882410\n",
       "std         0.056636    1177.780395\n",
       "min         0.320000       2.000000\n",
       "0%          0.320000       2.000000\n",
       "10%         0.940000     177.000000\n",
       "20%         0.990000     345.000000\n",
       "30%         1.000000     540.000000\n",
       "40%         1.000000     754.000000\n",
       "50%         1.000000    1004.000000\n",
       "60%         1.000000    1305.000000\n",
       "70%         1.000000    1667.300000\n",
       "80%         1.000000    2147.000000\n",
       "90%         1.000000    2908.000000\n",
       "max         1.000000   14600.000000"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df.loc[low_recall_gt.flatten()].describe(percentiles=np.arange(0, 1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "low_recall_hit_mx = hit_mx[low_recall_ids, :]\n",
    "loc_1_ij = np.where(low_recall_hit_mx == 1)\n",
    "loc_0_ij = np.where(low_recall_hit_mx == 0)\n",
    "low_recall_hit = []\n",
    "low_recall_miss = []\n",
    "for i, j in zip(loc_1_ij[0], loc_1_ij[1]):\n",
    "    low_recall_hit.append(low_recall_gt[i][j])\n",
    "    \n",
    "for i, j in zip(loc_0_ij[0], loc_0_ij[1]):\n",
    "    low_recall_miss.append(low_recall_gt[i][j])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10311091, 14143009)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(low_recall_miss), len(low_recall_hit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.414301e+07</td>\n",
       "      <td>1.414301e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.575216e-01</td>\n",
       "      <td>3.106310e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.376442e-01</td>\n",
       "      <td>5.596071e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5%</th>\n",
       "      <td>5.700000e-01</td>\n",
       "      <td>2.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>6.500000e-01</td>\n",
       "      <td>3.300000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15%</th>\n",
       "      <td>7.000000e-01</td>\n",
       "      <td>4.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>7.400000e-01</td>\n",
       "      <td>5.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>7.800000e-01</td>\n",
       "      <td>6.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>8.100000e-01</td>\n",
       "      <td>7.300000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35%</th>\n",
       "      <td>8.300000e-01</td>\n",
       "      <td>8.500000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>8.600000e-01</td>\n",
       "      <td>9.800000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45%</th>\n",
       "      <td>8.800000e-01</td>\n",
       "      <td>1.140000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>9.000000e-01</td>\n",
       "      <td>1.330000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55%</th>\n",
       "      <td>9.200000e-01</td>\n",
       "      <td>1.550000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>9.300000e-01</td>\n",
       "      <td>1.830000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65%</th>\n",
       "      <td>9.500000e-01</td>\n",
       "      <td>2.180000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>9.600000e-01</td>\n",
       "      <td>2.630000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>9.700000e-01</td>\n",
       "      <td>3.240000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>9.800000e-01</td>\n",
       "      <td>4.060000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85%</th>\n",
       "      <td>9.900000e-01</td>\n",
       "      <td>5.290000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>7.360000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95%</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.181000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.396500e+04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             recall      indegree\n",
       "count  1.414301e+07  1.414301e+07\n",
       "mean   8.575216e-01  3.106310e+02\n",
       "std    1.376442e-01  5.596071e+02\n",
       "min    2.000000e-01  1.000000e+00\n",
       "0%     2.000000e-01  1.000000e+00\n",
       "5%     5.700000e-01  2.200000e+01\n",
       "10%    6.500000e-01  3.300000e+01\n",
       "15%    7.000000e-01  4.200000e+01\n",
       "20%    7.400000e-01  5.200000e+01\n",
       "25%    7.800000e-01  6.200000e+01\n",
       "30%    8.100000e-01  7.300000e+01\n",
       "35%    8.300000e-01  8.500000e+01\n",
       "40%    8.600000e-01  9.800000e+01\n",
       "45%    8.800000e-01  1.140000e+02\n",
       "50%    9.000000e-01  1.330000e+02\n",
       "55%    9.200000e-01  1.550000e+02\n",
       "60%    9.300000e-01  1.830000e+02\n",
       "65%    9.500000e-01  2.180000e+02\n",
       "70%    9.600000e-01  2.630000e+02\n",
       "75%    9.700000e-01  3.240000e+02\n",
       "80%    9.800000e-01  4.060000e+02\n",
       "85%    9.900000e-01  5.290000e+02\n",
       "90%    1.000000e+00  7.360000e+02\n",
       "95%    1.000000e+00  1.181000e+03\n",
       "max    1.000000e+00  1.396500e+04"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df.loc[low_recall_hit].describe(percentiles=np.arange(0, 1, 0.05))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1.031109e+07</td>\n",
       "      <td>1.031109e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>8.075388e-01</td>\n",
       "      <td>1.714015e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.507752e-01</td>\n",
       "      <td>2.831267e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>0.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>5.800000e-01</td>\n",
       "      <td>2.400000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>6.700000e-01</td>\n",
       "      <td>3.800000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>7.400000e-01</td>\n",
       "      <td>5.200000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>7.900000e-01</td>\n",
       "      <td>6.800000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>8.400000e-01</td>\n",
       "      <td>8.800000e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>8.800000e-01</td>\n",
       "      <td>1.150000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>9.200000e-01</td>\n",
       "      <td>1.540000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>9.500000e-01</td>\n",
       "      <td>2.230000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>9.800000e-01</td>\n",
       "      <td>3.800000e+02</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>1.396500e+04</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             recall      indegree\n",
       "count  1.031109e+07  1.031109e+07\n",
       "mean   8.075388e-01  1.714015e+02\n",
       "std    1.507752e-01  2.831267e+02\n",
       "min    2.000000e-01  0.000000e+00\n",
       "0%     2.000000e-01  0.000000e+00\n",
       "10%    5.800000e-01  2.400000e+01\n",
       "20%    6.700000e-01  3.800000e+01\n",
       "30%    7.400000e-01  5.200000e+01\n",
       "40%    7.900000e-01  6.800000e+01\n",
       "50%    8.400000e-01  8.800000e+01\n",
       "60%    8.800000e-01  1.150000e+02\n",
       "70%    9.200000e-01  1.540000e+02\n",
       "80%    9.500000e-01  2.230000e+02\n",
       "90%    9.800000e-01  3.800000e+02\n",
       "max    1.000000e+00  1.396500e+04"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df.loc[low_recall_miss].describe(percentiles=np.arange(0, 1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\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>recall</th>\n",
       "      <th>indegree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>981083.000000</td>\n",
       "      <td>981083.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.792813</td>\n",
       "      <td>80.457897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.150215</td>\n",
       "      <td>91.424250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0%</th>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10%</th>\n",
       "      <td>0.570000</td>\n",
       "      <td>12.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20%</th>\n",
       "      <td>0.660000</td>\n",
       "      <td>19.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30%</th>\n",
       "      <td>0.730000</td>\n",
       "      <td>28.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40%</th>\n",
       "      <td>0.780000</td>\n",
       "      <td>38.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.820000</td>\n",
       "      <td>49.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60%</th>\n",
       "      <td>0.860000</td>\n",
       "      <td>64.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70%</th>\n",
       "      <td>0.900000</td>\n",
       "      <td>85.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80%</th>\n",
       "      <td>0.930000</td>\n",
       "      <td>118.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90%</th>\n",
       "      <td>0.970000</td>\n",
       "      <td>187.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>599.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              recall       indegree\n",
       "count  981083.000000  981083.000000\n",
       "mean        0.792813      80.457897\n",
       "std         0.150215      91.424250\n",
       "min         0.200000       0.000000\n",
       "0%          0.200000       0.000000\n",
       "10%         0.570000      12.000000\n",
       "20%         0.660000      19.000000\n",
       "30%         0.730000      28.000000\n",
       "40%         0.780000      38.000000\n",
       "50%         0.820000      49.000000\n",
       "60%         0.860000      64.000000\n",
       "70%         0.900000      85.000000\n",
       "80%         0.930000     118.000000\n",
       "90%         0.970000     187.000000\n",
       "max         1.000000     599.000000"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_df[sorted_df['indegree'] < 600].describe(percentiles=np.arange(0, 1, 0.1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "hit_loc_mean_df = pd.DataFrame(hit_df.describe().loc['mean'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# pd.set_option('display.max_rows', None)\n",
    "hit_loc_mean_df['id'] = hit_loc_mean_df.index.tolist()\n",
    "hit_loc_mean_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to find reverse k-nearest neighbors\n",
    "def reverse_knn(adj_list, k):\n",
    "    # Initialize empty dictionary to store rKNN counts\n",
    "    rknn_counts = {}\n",
    "    # Iterate over every vertex in the graph\n",
    "    for i, vertex in enumerate(adj_list):\n",
    "        # Initialize count of rKNNs to 0\n",
    "        count_rknn = 0\n",
    "        # Iterate over every other vertex in the graph\n",
    "        for j, other_vertex in enumerate(adj_list):\n",
    "            # Skip the current vertex\n",
    "            if i == j:\n",
    "                continue\n",
    "            # If the current vertex is one of the K nearest neighbors of the other vertex,\n",
    "            # increment the rKNN count of the current vertex\n",
    "            if i in other_vertex[:k]:\n",
    "                count_rknn += 1\n",
    "        # Store the rKNN count of the current vertex in the dictionary\n",
    "        rknn_counts[i] = count_rknn\n",
    "    # Return the dictionary of rKNN counts\n",
    "    return rknn_counts\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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