_Reachability_queries_in_large_graphs.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'pandas' from '/usr/local/lib/python3.6/dist-packages/pandas/__init__.py'>"
      ]
     },
     "execution_count": null,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Imports SciPy modules\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FELINE index\n",
    "\n",
    "\"Reachability Queries in Very Large Graphs: A Fast Refined Online Search Approach\" (2014)  \n",
    "<http://openprocedings.org/EDBT/2014/paper_166.pdf>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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>vertices</th>\n",
       "      <th>edges</th>\n",
       "      <th>edges[% V^2]</th>\n",
       "      <th>edges/vertices</th>\n",
       "      <th>Cluster coeff.</th>\n",
       "      <th>Eff. diameter</th>\n",
       "      <th>roots</th>\n",
       "      <th>leafs</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Graph</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>arXiv</th>\n",
       "      <td>6000</td>\n",
       "      <td>66707</td>\n",
       "      <td>0.185297</td>\n",
       "      <td>11.117833</td>\n",
       "      <td>0.35</td>\n",
       "      <td>5.48</td>\n",
       "      <td>961</td>\n",
       "      <td>624</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yago</th>\n",
       "      <td>6642</td>\n",
       "      <td>42392</td>\n",
       "      <td>0.096092</td>\n",
       "      <td>6.382415</td>\n",
       "      <td>0.24</td>\n",
       "      <td>6.57</td>\n",
       "      <td>5176</td>\n",
       "      <td>263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go</th>\n",
       "      <td>6793</td>\n",
       "      <td>13361</td>\n",
       "      <td>0.028954</td>\n",
       "      <td>1.966878</td>\n",
       "      <td>0.07</td>\n",
       "      <td>10.92</td>\n",
       "      <td>64</td>\n",
       "      <td>3087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pubmed</th>\n",
       "      <td>9000</td>\n",
       "      <td>40028</td>\n",
       "      <td>0.049417</td>\n",
       "      <td>4.447556</td>\n",
       "      <td>0.10</td>\n",
       "      <td>6.32</td>\n",
       "      <td>2609</td>\n",
       "      <td>4702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseer</th>\n",
       "      <td>10720</td>\n",
       "      <td>44258</td>\n",
       "      <td>0.038513</td>\n",
       "      <td>4.128545</td>\n",
       "      <td>0.28</td>\n",
       "      <td>8.36</td>\n",
       "      <td>4572</td>\n",
       "      <td>1868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot22m</th>\n",
       "      <td>1595444</td>\n",
       "      <td>1595442</td>\n",
       "      <td>0.000063</td>\n",
       "      <td>0.999999</td>\n",
       "      <td>0.00</td>\n",
       "      <td>3.30</td>\n",
       "      <td>1556157</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cit-patents</th>\n",
       "      <td>3774768</td>\n",
       "      <td>16518047</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>4.375911</td>\n",
       "      <td>0.09</td>\n",
       "      <td>10.50</td>\n",
       "      <td>515785</td>\n",
       "      <td>1685423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseerx</th>\n",
       "      <td>6540401</td>\n",
       "      <td>15011260</td>\n",
       "      <td>0.000035</td>\n",
       "      <td>2.295159</td>\n",
       "      <td>0.06</td>\n",
       "      <td>8.40</td>\n",
       "      <td>567149</td>\n",
       "      <td>5740710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go-uniprot</th>\n",
       "      <td>6967956</td>\n",
       "      <td>34770235</td>\n",
       "      <td>0.000072</td>\n",
       "      <td>4.990019</td>\n",
       "      <td>0.00</td>\n",
       "      <td>4.80</td>\n",
       "      <td>6945721</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot100m</th>\n",
       "      <td>16087295</td>\n",
       "      <td>16087293</td>\n",
       "      <td>0.000006</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>4.10</td>\n",
       "      <td>14598959</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot150m</th>\n",
       "      <td>25037600</td>\n",
       "      <td>25037598</td>\n",
       "      <td>0.000004</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.00</td>\n",
       "      <td>4.40</td>\n",
       "      <td>21650056</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             vertices     edges  edges[% V^2]  ...  Eff. diameter     roots    leafs\n",
       "Graph                                          ...                                  \n",
       "arXiv            6000     66707      0.185297  ...           5.48       961      624\n",
       "Yago             6642     42392      0.096092  ...           6.57      5176      263\n",
       "Go               6793     13361      0.028954  ...          10.92        64     3087\n",
       "Pubmed           9000     40028      0.049417  ...           6.32      2609     4702\n",
       "citeseer        10720     44258      0.038513  ...           8.36      4572     1868\n",
       "Uniprot22m    1595444   1595442      0.000063  ...           3.30   1556157        1\n",
       "Cit-patents   3774768  16518047      0.000116  ...          10.50    515785  1685423\n",
       "citeseerx     6540401  15011260      0.000035  ...           8.40    567149  5740710\n",
       "Go-uniprot    6967956  34770235      0.000072  ...           4.80   6945721        4\n",
       "Uniprot100m  16087295  16087293      0.000006  ...           4.10  14598959        1\n",
       "Uniprot150m  25037600  25037598      0.000004  ...           4.40  21650056        1\n",
       "\n",
       "[11 rows x 8 columns]"
      ]
     },
     "execution_count": null,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Table 1: Datasets from FELINE (table_fel) { form-width: \"25%\" }\n",
    "\n",
    "import io\n",
    "\n",
    "csv=u\"\"\"Graph;vertices;edges;Cluster coeff.;Eff. diameter;roots;leafs\n",
    "arXiv;6000;66707;0.35;5.48;961;624\n",
    "Yago;6642;42392;0.24;6.57;5176;263\n",
    "Go;6793;13361;0.07;10.92;64;3087\n",
    "Pubmed;9000;40028;0.10;6.32;2609;4702\n",
    "citeseer;10720;44258;0.28;8.36;4572;1868\n",
    "Uniprot22m;1595444;1595442;0.00;3.3;1556157;1\n",
    "Cit-patents;3774768;16518047;0.09;10.5;515785;1685423\n",
    "citeseerx;6540401;15011260;0.06;8.4;567149;5740710\n",
    "Go-uniprot;6967956;34770235;0.00;4.8;6945721;4\n",
    "Uniprot100m;16087295;16087293;0.00;4.1;14598959;1\n",
    "Uniprot150m;25037600;25037598;0.00;4.4;21650056;1\n",
    "\"\"\"\n",
    "csv_stream = io.StringIO(csv)\n",
    "\n",
    "table_fel=pd.read_csv(csv_stream,sep=';',index_col=0)\n",
    "table_fel.insert(loc=2,column='edges[% V^2]',\n",
    "               value=100.0*(table_fel['edges']/(table_fel['vertices']**2)))\n",
    "table_fel.insert(loc=3,column='edges/vertices',\n",
    "               value=table_fel['edges']/table_fel['vertices'])\n",
    "table_fel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0MiYs7FxAaGhjYE1AaGgg4AlcKLJNKuBh/t0QExZ2b0Bo6BhMiSoIaA+8Atw8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\nEhGRUPt/XAMc4aAoo5EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ee=np.geomspace(5000,25000000,num=10)\n",
    "ax=table_fel[table_fel['vertices'] < 100000].plot.scatter(x='vertices',y='edges',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,label='small',\n",
    "                          title='Graphs from FELINE paper, Table 1')\n",
    "ax=table_fel[table_fel['vertices'] >= 100000].plot.scatter(ax=ax,x='vertices',y='edges',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,c='red',label='large',\n",
    "                          title='Graphs from FELINE paper, Table 1')\n",
    "ax.plot(ee,2*ee,'-',label='dense vs sparse',c='gray')\n",
    "for row in table_fel.itertuples():\n",
    "    ax.annotate(row[0], xy=(row.vertices,row.edges),\n",
    "                xytext=(3,-3), textcoords='offset points',horizontalalignment='left',\n",
    "                family='sans-serif', fontsize=9, color='darkslategrey')\n",
    "ax.set_xlim(left  =2e3)\n",
    "ax.set_ylim(bottom=5e3)\n",
    "plt.legend(loc='upper left')\n",
    "plt.savefig('feline_graphs_vertices_vs_edges.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tet91F/OmTAHgscmTufyiizivTRtycnMZ9fzzbNq2jXPOOIPB/fvzx9atvPPI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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax=table_fel[table_fel['vertices'] < 100000].plot.scatter(x='roots',y='leafs',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,label='small',\n",
    "                          title='Graphs from FELINE paper, Table 1')\n",
    "ax=table_fel[table_fel['vertices'] >= 100000].plot.scatter(ax=ax,x='roots',y='leafs',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,c='red',label='large',\n",
    "                          title='Graphs from FELINE paper, Table 1')\n",
    "for row in table_fel.itertuples():\n",
    "    ax.annotate(row[0], xy=(row.roots,row.leafs),\n",
    "                xytext=(-3,-3), textcoords='offset points',horizontalalignment='right',\n",
    "                family='sans-serif', fontsize=9, color='darkslategrey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    ""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"FERRARI: Flexible and Efficient Reachability Range Assignment for Graph Indexing\" (2013)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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>type</th>\n",
       "      <th>vertices</th>\n",
       "      <th>edges</th>\n",
       "      <th>edges/vertices</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Graph</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>arXiv</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>6000</td>\n",
       "      <td>66707</td>\n",
       "      <td>11.117833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>6793</td>\n",
       "      <td>13361</td>\n",
       "      <td>1.966878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pubmed</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>9000</td>\n",
       "      <td>40028</td>\n",
       "      <td>4.447556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Human</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>38811</td>\n",
       "      <td>39816</td>\n",
       "      <td>1.025895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseer</th>\n",
       "      <td>large</td>\n",
       "      <td>693947</td>\n",
       "      <td>312383</td>\n",
       "      <td>0.450154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cit-patents</th>\n",
       "      <td>large</td>\n",
       "      <td>3774768</td>\n",
       "      <td>16518047</td>\n",
       "      <td>4.375911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseerx</th>\n",
       "      <td>large</td>\n",
       "      <td>6540401</td>\n",
       "      <td>15011260</td>\n",
       "      <td>2.295159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go-uniprot</th>\n",
       "      <td>large</td>\n",
       "      <td>6967956</td>\n",
       "      <td>34770235</td>\n",
       "      <td>4.990019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GovWild</th>\n",
       "      <td>RDF</td>\n",
       "      <td>80222880</td>\n",
       "      <td>23652610</td>\n",
       "      <td>0.294836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yago2</th>\n",
       "      <td>RDF</td>\n",
       "      <td>16375503</td>\n",
       "      <td>25908132</td>\n",
       "      <td>1.582127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Twitter</th>\n",
       "      <td>social network</td>\n",
       "      <td>18121168</td>\n",
       "      <td>18359487</td>\n",
       "      <td>1.013151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Web-UK</th>\n",
       "      <td>web graph</td>\n",
       "      <td>22753644</td>\n",
       "      <td>38184039</td>\n",
       "      <td>1.678150</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                       type  vertices     edges  edges/vertices\n",
       "Graph                                                          \n",
       "arXiv          small, dense      6000     66707       11.117833\n",
       "Go             small, dense      6793     13361        1.966878\n",
       "Pubmed         small, dense      9000     40028        4.447556\n",
       "Human         small, sparse     38811     39816        1.025895\n",
       "citeseer              large    693947    312383        0.450154\n",
       "Cit-patents           large   3774768  16518047        4.375911\n",
       "citeseerx             large   6540401  15011260        2.295159\n",
       "Go-uniprot            large   6967956  34770235        4.990019\n",
       "GovWild                 RDF  80222880  23652610        0.294836\n",
       "Yago2                   RDF  16375503  25908132        1.582127\n",
       "Twitter      social network  18121168  18359487        1.013151\n",
       "Web-UK            web graph  22753644  38184039        1.678150"
      ]
     },
     "execution_count": null,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Table 1: Datasets Used from FERRARI (table_fer) { form-width: \"25%\" }\n",
    "\n",
    "import io\n",
    "\n",
    "csv=u\"\"\"Graph;type;vertices;edges\n",
    "arXiv;small, dense;6000;66707\n",
    "Go;small, dense;6793;13361\n",
    "Pubmed;small, dense;9000;40028\n",
    "Human;small, sparse;38811;39816\n",
    "citeseer;large;693947;312383\n",
    "Cit-patents;large;3774768;16518047\n",
    "citeseerx;large;6540401;15011260\n",
    "Go-uniprot;large;6967956;34770235\n",
    "GovWild;RDF;80222880;23652610\n",
    "Yago2;RDF;16375503;25908132\n",
    "Twitter;social network;18121168;18359487\n",
    "Web-UK;web graph;22753644;38184039\n",
    "\"\"\"\n",
    "csv_stream = io.StringIO(csv)\n",
    "\n",
    "table_fer=pd.read_csv(csv_stream,sep=';',index_col=0)\n",
    "table_fer.insert(loc=3,column='edges/vertices',\n",
    "               value=table_fer['edges']/table_fer['vertices'])\n",
    "table_fer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v1/P1119z4cKFypPAx8IJzoqiAoSiWKEqbm7MmTyZNz77jKzsbBwdHKjh7c2w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\niIj4pQIhIiJ+qUCIiIhf/wdJaNQrx5YPWgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ee=np.geomspace(5000,80000000,num=10)\n",
    "ax=table_fer[table_fer['vertices'] < 100000].plot.scatter(x='vertices',y='edges',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,label='small',\n",
    "                          title='Graphs from FERRARI paper, Table 1(a)(b)')\n",
    "ax=table_fer[table_fer['vertices'] >= 100000].plot.scatter(ax=ax,x='vertices',y='edges',\n",
    "                          logx=True,logy=True,\n",
    "                          grid=True,c='red',label='large',\n",
    "                          title='Graphs from FERRARI paper, Table 1(a)(b)')\n",
    "ax.plot(ee,ee,'--',ee,2*ee,'-',label='dense vs sparse',c='gray')\n",
    "for row in table_fer[table_fer['vertices'] < 100000].itertuples():\n",
    "    ax.annotate(row[0], xy=(row.vertices,row.edges),\n",
    "                xytext=(3,-3), textcoords='offset points',horizontalalignment='left',\n",
    "                family='sans-serif', fontsize=9, color='darkslategrey')\n",
    "    #print(row)\n",
    "for row in table_fer[table_fer['vertices'] >= 100000].itertuples():\n",
    "    ax.annotate(row[0], xy=(row.vertices,row.edges),\n",
    "                xytext=(-3,-8), textcoords='offset points',horizontalalignment='right',\n",
    "                family='sans-serif', fontsize=9, color='darkslategrey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "other pruning mechanisms with min-post / pre-max DFS spanning-tree interval labeling\n",
    "\n",
    "\"PReaCH: A Fast Lightweight Reachability Index using Pruning and Contraction Hierarchies\" (2014)  \n",
    "<https://arxiv.org/abs/1404.4465>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['small, dense' 'small, sparse' 'large' 'stanford']\n"
     ]
    },
    {
     "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>type</th>\n",
       "      <th>vertices</th>\n",
       "      <th>edges</th>\n",
       "      <th>edges/vertices</th>\n",
       "      <th>maxlevel</th>\n",
       "      <th>r-score</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Graph</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>arXiv</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>6000</td>\n",
       "      <td>66707</td>\n",
       "      <td>11.12</td>\n",
       "      <td>167</td>\n",
       "      <td>0.150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseer-sub</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>11000</td>\n",
       "      <td>44000</td>\n",
       "      <td>4.13</td>\n",
       "      <td>36</td>\n",
       "      <td>0.004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>6793</td>\n",
       "      <td>13361</td>\n",
       "      <td>1.97</td>\n",
       "      <td>16</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pubmed</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>9000</td>\n",
       "      <td>40028</td>\n",
       "      <td>4.45</td>\n",
       "      <td>19</td>\n",
       "      <td>0.007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yago</th>\n",
       "      <td>small, dense</td>\n",
       "      <td>6642</td>\n",
       "      <td>42392</td>\n",
       "      <td>6.38</td>\n",
       "      <td>13</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>agrocyc</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>13000</td>\n",
       "      <td>14000</td>\n",
       "      <td>1.07</td>\n",
       "      <td>16</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>amaze</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>3710</td>\n",
       "      <td>3947</td>\n",
       "      <td>1.06</td>\n",
       "      <td>16</td>\n",
       "      <td>0.170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>anthra</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>12000</td>\n",
       "      <td>13000</td>\n",
       "      <td>1.07</td>\n",
       "      <td>16</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ecoo</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>13000</td>\n",
       "      <td>14000</td>\n",
       "      <td>1.08</td>\n",
       "      <td>22</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Human</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>38811</td>\n",
       "      <td>39816</td>\n",
       "      <td>1.01</td>\n",
       "      <td>18</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>kegg</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>3617</td>\n",
       "      <td>4395</td>\n",
       "      <td>1.22</td>\n",
       "      <td>26</td>\n",
       "      <td>0.200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mtbrv</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>9602</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.09</td>\n",
       "      <td>22</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>nasa</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>5605</td>\n",
       "      <td>6538</td>\n",
       "      <td>1.17</td>\n",
       "      <td>35</td>\n",
       "      <td>0.006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>vchocyc</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>9491</td>\n",
       "      <td>10000</td>\n",
       "      <td>1.09</td>\n",
       "      <td>21</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>xmark</th>\n",
       "      <td>small, sparse</td>\n",
       "      <td>6080</td>\n",
       "      <td>7051</td>\n",
       "      <td>1.16</td>\n",
       "      <td>38</td>\n",
       "      <td>0.014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseer</th>\n",
       "      <td>large</td>\n",
       "      <td>693947</td>\n",
       "      <td>312383</td>\n",
       "      <td>0.45</td>\n",
       "      <td>13</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>citeseerx</th>\n",
       "      <td>large</td>\n",
       "      <td>6540401</td>\n",
       "      <td>15011260</td>\n",
       "      <td>2.30</td>\n",
       "      <td>59</td>\n",
       "      <td>0.002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cit-patents</th>\n",
       "      <td>large</td>\n",
       "      <td>3774768</td>\n",
       "      <td>16518047</td>\n",
       "      <td>4.38</td>\n",
       "      <td>32</td>\n",
       "      <td>0.001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Go-uniprot</th>\n",
       "      <td>large</td>\n",
       "      <td>6967956</td>\n",
       "      <td>34770235</td>\n",
       "      <td>4.99</td>\n",
       "      <td>21</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot22m</th>\n",
       "      <td>large</td>\n",
       "      <td>1595444</td>\n",
       "      <td>1595442</td>\n",
       "      <td>1.00</td>\n",
       "      <td>4</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot100m</th>\n",
       "      <td>large</td>\n",
       "      <td>16087295</td>\n",
       "      <td>16087293</td>\n",
       "      <td>1.00</td>\n",
       "      <td>9</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Uniprot150m</th>\n",
       "      <td>large</td>\n",
       "      <td>25037600</td>\n",
       "      <td>25037598</td>\n",
       "      <td>1.00</td>\n",
       "      <td>10</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>email-EuAll</th>\n",
       "      <td>stanford</td>\n",
       "      <td>231000</td>\n",
       "      <td>223000</td>\n",
       "      <td>0.97</td>\n",
       "      <td>7</td>\n",
       "      <td>0.050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>p2p-Gnutella31</th>\n",
       "      <td>stanford</td>\n",
       "      <td>48000</td>\n",
       "      <td>55000</td>\n",
       "      <td>1.15</td>\n",
       "      <td>14</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>soc-LiveJournal1</th>\n",
       "      <td>stanford</td>\n",
       "      <td>971000</td>\n",
       "      <td>1024000</td>\n",
       "      <td>1.05</td>\n",
       "      <td>24</td>\n",
       "      <td>0.210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>web-Google</th>\n",
       "      <td>stanford</td>\n",
       "      <td>372000</td>\n",
       "      <td>518000</td>\n",
       "      <td>1.39</td>\n",
       "      <td>34</td>\n",
       "      <td>0.150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wiki-Talk</th>\n",
       "      <td>stanford</td>\n",
       "      <td>2282000</td>\n",
       "      <td>2312000</td>\n",
       "      <td>1.01</td>\n",
       "      <td>8</td>\n",
       "      <td>0.008</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           type  vertices     edges  edges/vertices  maxlevel  \\\n",
       "Graph                                                                           \n",
       "arXiv              small, dense      6000     66707           11.12       167   \n",
       "citeseer-sub       small, dense     11000     44000            4.13        36   \n",
       "Go                 small, dense      6793     13361            1.97        16   \n",
       "Pubmed             small, dense      9000     40028            4.45        19   \n",
       "Yago               small, dense      6642     42392            6.38        13   \n",
       "agrocyc           small, sparse     13000     14000            1.07        16   \n",
       "amaze             small, sparse      3710      3947            1.06        16   \n",
       "anthra            small, sparse     12000     13000            1.07        16   \n",
       "ecoo              small, sparse     13000     14000            1.08        22   \n",
       "Human             small, sparse     38811     39816            1.01        18   \n",
       "kegg              small, sparse      3617      4395            1.22        26   \n",
       "mtbrv             small, sparse      9602     10000            1.09        22   \n",
       "nasa              small, sparse      5605      6538            1.17        35   \n",
       "vchocyc           small, sparse      9491     10000            1.09        21   \n",
       "xmark             small, sparse      6080      7051            1.16        38   \n",
       "citeseer                  large    693947    312383            0.45        13   \n",
       "citeseerx                 large   6540401  15011260            2.30        59   \n",
       "Cit-patents               large   3774768  16518047            4.38        32   \n",
       "Go-uniprot                large   6967956  34770235            4.99        21   \n",
       "Uniprot22m                large   1595444   1595442            1.00         4   \n",
       "Uniprot100m               large  16087295  16087293            1.00         9   \n",
       "Uniprot150m               large  25037600  25037598            1.00        10   \n",
       "email-EuAll            stanford    231000    223000            0.97         7   \n",
       "p2p-Gnutella31         stanford     48000     55000            1.15        14   \n",
       "soc-LiveJournal1       stanford    971000   1024000            1.05        24   \n",
       "web-Google             stanford    372000    518000            1.39        34   \n",
       "wiki-Talk              stanford   2282000   2312000            1.01         8   \n",
       "\n",
       "                  r-score  \n",
       "Graph                      \n",
       "arXiv               0.150  \n",
       "citeseer-sub        0.004  \n",
       "Go                  0.002  \n",
       "Pubmed              0.007  \n",
       "Yago                0.002  \n",
       "agrocyc             0.001  \n",
       "amaze               0.170  \n",
       "anthra              0.001  \n",
       "ecoo                0.001  \n",
       "Human               0.000  \n",
       "kegg                0.200  \n",
       "mtbrv               0.002  \n",
       "nasa                0.006  \n",
       "vchocyc             0.001  \n",
       "xmark               0.014  \n",
       "citeseer            0.000  \n",
       "citeseerx           0.002  \n",
       "Cit-patents         0.001  \n",
       "Go-uniprot          0.000  \n",
       "Uniprot22m          0.000  \n",
       "Uniprot100m         0.000  \n",
       "Uniprot150m         0.000  \n",
       "email-EuAll         0.050  \n",
       "p2p-Gnutella31      0.008  \n",
       "soc-LiveJournal1    0.210  \n",
       "web-Google          0.150  \n",
       "wiki-Talk           0.008  "
      ]
     },
     "execution_count": null,
     "metadata": {
      "tags": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Table 1: Instances used for experimets from PReaCH (table_rch) { form-width: \"25%\" }\n",
    "\n",
    "import io\n",
    "\n",
    "csv=u\"\"\"Graph;type;vertices;edges;edges/vertices;maxlevel;r-score\n",
    "arXiv;small, dense;6000;66707;11.12;167;0.15\n",
    "citeseer-sub;small, dense;11000;44000;4.13;36;0.004\n",
    "Go;small, dense;6793;13361;1.97;16;0.002\n",
    "Pubmed;small, dense;9000;40028;4.45;19;0.007\n",
    "Yago;small, dense;6642;42392;6.38;13;0.002\n",
    "agrocyc;small, sparse;13000;14000;1.07;16;0.001\n",
    "amaze;small, sparse;3710;3947;1.06;16;0.17\n",
    "anthra;small, sparse;12000;13000;1.07;16;0.001\n",
    "ecoo;small, sparse;13000;14000;1.08;22;0.001\n",
    "Human;small, sparse;38811;39816;1.01;18;0.000\n",
    "kegg;small, sparse;3617;4395;1.22;26;0.20\n",
    "mtbrv;small, sparse;9602;10000;1.09;22;0.002\n",
    "nasa;small, sparse;5605;6538;1.17;35;0.006\n",
    "vchocyc;small, sparse;9491;10000;1.09;21;0.001\n",
    "xmark;small, sparse;6080;7051;1.16;38;0.014\n",
    "citeseer;large;693947;312383;0.45;13;0.000\n",
    "citeseerx;large;6540401;15011260;2.30;59;0.002\n",
    "Cit-patents;large;3774768;16518047;4.38;32;0.001\n",
    "Go-uniprot;large;6967956;34770235;4.99;21;0.000\n",
    "Uniprot22m;large;1595444;1595442;1.00;4;0.000\n",
    "Uniprot100m;large;16087295;16087293;1.00;9;0.000\n",
    "Uniprot150m;large;25037600;25037598;1.00;10;0.000\n",
    "email-EuAll;stanford;231000;223000;0.97;7;0.05\n",
    "p2p-Gnutella31;stanford;48000;55000;1.15;14;0.008\n",
    "soc-LiveJournal1;stanford;971000;1024000;1.05;24;0.21\n",
    "web-Google;stanford;372000;518000;1.39;34;0.15\n",
    "wiki-Talk;stanford;2282000;2312000;1.01;8;0.008\n",
    "\"\"\"\n",
    "csv_stream = io.StringIO(csv)\n",
    "\n",
    "table_rch=pd.read_csv(csv_stream,sep=';',index_col=0)\n",
    "print(table_rch['type'].unique())\n",
    "table_rch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CQ0OZM2cOzzzzDE2aNCEwMJB169YZLTZFqTNpadofvadn9f/wjSAzM5PNmzeTkJCAi4sL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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ee=np.geomspace(4000,25000000,num=10)\n",
    "ax=plt.gca()\n",
    "types =table_rch['type'].unique()\n",
    "colors=('blue', 'cyan', 'red', 'orange')\n",
    "for i, t in enumerate(types):\n",
    "  ax=table_rch[table_rch['type'] == t].plot.scatter(x='vertices',y='edges',ax=ax,\n",
    "                                                    logx=True,logy=True,grid=True,\n",
    "                                                    label=t,c=colors[i],\n",
    "                                                    title='Graphs from PReaCH paper, Table 1')\n",
    "ax.plot(ee,ee,'--',ee,2*ee,'-',label='dense vs sparse',c='gray')\n",
    "ann=('Uniprot150m','soc-LiveJournal1','wiki-Talk','Go','amaze','arXiv','Human','citeseer','citeseerx')\n",
    "for g in ann:\n",
    "  row = table_rch.loc[g]\n",
    "  ax.annotate(g, xy=(row['vertices'],row['edges']),\n",
    "              xytext=(5,-3), textcoords='offset points',horizontalalignment='left',\n",
    "              family='sans-serif', fontsize=9, color='darkslategrey')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    ""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}