Analysis on BFS Output.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### In this notebook we analyze some of the data gathered in the BFS notebook file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part A:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import sqlite3 as sql\n",
    "\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "analysis = pd.read_csv('permutations.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we read in our saved data from the BFS on Wikipedia Graph notebook. Following we can begin to find some interesting metrics that give us an idea of how our graph is connected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.214846</td>\n",
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       "      <td>3</td>\n",
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       "      <td>1</td>\n",
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       "      <td>6</td>\n",
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       "      <td>4</td>\n",
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       "      <td>5</td>\n",
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       "            Combination                 Start Title  \\\n",
       "0  (34298991, 45522031)  Geological_history_of_Mars   \n",
       "1  (34298991, 54435140)  Geological_history_of_Mars   \n",
       "2  (34298991, 40983657)  Geological_history_of_Mars   \n",
       "3  (34298991, 45522031)  Geological_history_of_Mars   \n",
       "4  (34298991, 54435140)  Geological_history_of_Mars   \n",
       "\n",
       "                               Goal Title  Paths Found  \\\n",
       "0     Always_Near_-_A_Romantic_Collection            1   \n",
       "1  St_Faith\\'s_and_Aylsham_Rural_District            1   \n",
       "2                 Kojur_Industrial_Estate            5   \n",
       "3     Always_Near_-_A_Romantic_Collection            1   \n",
       "4  St_Faith\\'s_and_Aylsham_Rural_District            1   \n",
       "\n",
       "                                           All Paths  Shortest Path Length  \\\n",
       "0  [[34298991, 20257, 8786, 235828, 4014281, 4552...                     6   \n",
       "1      [[34298991, 26298, 349345, 449143, 54435140]]                     5   \n",
       "2  [[34298991, 21857752, 19653787, 2524494, 40983...                     5   \n",
       "3  [[34298991, 20257, 8786, 235828, 4014281, 4552...                     6   \n",
       "4      [[34298991, 26298, 349345, 449143, 54435140]]                     5   \n",
       "\n",
       "                                       Shortest Path  Time Taken  \n",
       "0  [34298991, 20257, 8786, 235828, 4014281, 45522...    0.247299  \n",
       "1        [34298991, 26298, 349345, 449143, 54435140]    0.337016  \n",
       "2  [34298991, 21857752, 19653787, 2524494, 40983657]    0.214846  \n",
       "3  [34298991, 20257, 8786, 235828, 4014281, 45522...    0.262307  \n",
       "4        [34298991, 26298, 349345, 449143, 54435140]    0.344064  "
      ]
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "analysis.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Lengths of Shortest Paths:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean and Standard Deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.9528175291156105"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Shortest Path Length'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6194481077525276"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Shortest Path Length'].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combinations of Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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       "      <td>1346</td>\n",
       "      <td>(28191801, 15087124)</td>\n",
       "      <td>Entäs_nyt,_Niskavuori?</td>\n",
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       "      <td>3538</td>\n",
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       "      <td>9</td>\n",
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       "      <td>0.466908</td>\n",
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       "    <tr>\n",
       "      <td>15382</td>\n",
       "      <td>(237214, 15087124)</td>\n",
       "      <td>AspectJ</td>\n",
       "      <td>Greenleaf_Township</td>\n",
       "      <td>652</td>\n",
       "      <td>[[237214, 10635, 118450, 27318, 1769262, 11169...</td>\n",
       "      <td>9</td>\n",
       "      <td>[237214, 10635, 118450, 27318, 1769262, 111695...</td>\n",
       "      <td>0.837989</td>\n",
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      ],
      "text/plain": [
       "                Combination             Start Title          Goal Title  \\\n",
       "1346   (28191801, 15087124)  Entäs_nyt,_Niskavuori?  Greenleaf_Township   \n",
       "3538    (1511826, 52514696)             Blind_Shaft  Stenoparmena_nigra   \n",
       "7686   (49109470, 52514696)           Mohamed_Ayech  Stenoparmena_nigra   \n",
       "8962     (471568, 52514696)                    USWA  Stenoparmena_nigra   \n",
       "15382    (237214, 15087124)                 AspectJ  Greenleaf_Township   \n",
       "\n",
       "       Paths Found                                          All Paths  \\\n",
       "1346           644  [[28191801, 8439, 11887, 4689264, 3517460, 111...   \n",
       "3538          1482  [[1511826, 5751, 100640, 2579000, 204182, 4507...   \n",
       "7686           591  [[49109470, 30188, 358, 49871, 518913, 1186631...   \n",
       "8962           127  [[471568, 1130008, 689, 159283, 45022184, 1186...   \n",
       "15382          652  [[237214, 10635, 118450, 27318, 1769262, 11169...   \n",
       "\n",
       "       Shortest Path Length  \\\n",
       "1346                      9   \n",
       "3538                      9   \n",
       "7686                      9   \n",
       "8962                      9   \n",
       "15382                     9   \n",
       "\n",
       "                                           Shortest Path  Time Taken  \n",
       "1346   [28191801, 8439, 11887, 4689264, 3517460, 1116...    1.119453  \n",
       "3538   [1511826, 5751, 100640, 2579000, 204182, 45079...    2.862116  \n",
       "7686   [49109470, 30188, 358, 49871, 518913, 11866314...    1.828297  \n",
       "8962   [471568, 1130008, 689, 159283, 45022184, 11866...    0.466908  \n",
       "15382  [237214, 10635, 118450, 27318, 1769262, 111695...    0.837989  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Shortest Path Length'].max()\n",
    "ans = analysis.loc[analysis['Shortest Path Length']==maxi]\n",
    "ans.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "      <td>9</td>\n",
       "      <td>(34298991, 28191801)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
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       "      <td>0.000608</td>\n",
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       "<p>7976 rows × 8 columns</p>\n",
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      ],
      "text/plain": [
       "                 Combination                 Start Title  \\\n",
       "9       (34298991, 28191801)  Geological_history_of_Mars   \n",
       "16      (34298991, 28191801)  Geological_history_of_Mars   \n",
       "40        (34298991, 471568)  Geological_history_of_Mars   \n",
       "61      (34298991, 16224284)  Geological_history_of_Mars   \n",
       "80       (34298991, 5789258)  Geological_history_of_Mars   \n",
       "...                      ...                         ...   \n",
       "102040  (32540089, 36572955)                  Terreplein   \n",
       "102041  (32540089, 40161542)                  Terreplein   \n",
       "102047  (32540089, 28589339)                  Terreplein   \n",
       "102066  (32540089, 35302964)                  Terreplein   \n",
       "102083  (32540089, 55488245)                  Terreplein   \n",
       "\n",
       "                    Goal Title  Paths Found All Paths  Shortest Path Length  \\\n",
       "9       Entäs_nyt,_Niskavuori?            0        []                     0   \n",
       "16      Entäs_nyt,_Niskavuori?            0        []                     0   \n",
       "40                        USWA            0        []                     0   \n",
       "61                Saiye,_Ghana            0        []                     0   \n",
       "80                    Benzonia            0        []                     0   \n",
       "...                        ...          ...       ...                   ...   \n",
       "102040          Geoffrey_Plitt            0        []                     0   \n",
       "102041                 Doruhan            0        []                     0   \n",
       "102047          Maria_Carrillo            0        []                     0   \n",
       "102066             Mir_Khavand            0        []                     0   \n",
       "102083   Jamalpur,_Sikandarpur            0        []                     0   \n",
       "\n",
       "       Shortest Path  Time Taken  \n",
       "9                 []    0.001773  \n",
       "16                []    0.000655  \n",
       "40                []    0.001082  \n",
       "61                []    0.001663  \n",
       "80                []    0.000876  \n",
       "...              ...         ...  \n",
       "102040            []    0.000576  \n",
       "102041            []    0.000522  \n",
       "102047            []    0.000542  \n",
       "102066            []    0.000588  \n",
       "102083            []    0.000608  \n",
       "\n",
       "[7976 rows x 8 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Shortest Path Length'].min()\n",
    "analysis.loc[analysis['Shortest Path Length']==mini]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Shortest Path Length'].plot.hist( alpha=1, bins=9)\n",
    "ax.set_xticks([1,2,3,4,5,6,7,8,9])\n",
    "\n",
    "ax.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Amounts of Time Taken:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4673503090241208"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Time Taken'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>66664</td>\n",
       "      <td>(53125642, 58867760)</td>\n",
       "      <td>Missing_(2016_film)</td>\n",
       "      <td>2008_Women\\'s_Australian_Hockey_League</td>\n",
       "      <td>152</td>\n",
       "      <td>[[53125642, 16756, 11884, 1148, 4501639, 58867...</td>\n",
       "      <td>6</td>\n",
       "      <td>[53125642, 16756, 11884, 1148, 4501639, 58867760]</td>\n",
       "      <td>17.885316</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Combination          Start Title  \\\n",
       "66664  (53125642, 58867760)  Missing_(2016_film)   \n",
       "\n",
       "                                   Goal Title  Paths Found  \\\n",
       "66664  2008_Women\\'s_Australian_Hockey_League          152   \n",
       "\n",
       "                                               All Paths  \\\n",
       "66664  [[53125642, 16756, 11884, 1148, 4501639, 58867...   \n",
       "\n",
       "       Shortest Path Length  \\\n",
       "66664                     6   \n",
       "\n",
       "                                           Shortest Path  Time Taken  \n",
       "66664  [53125642, 16756, 11884, 1148, 4501639, 58867760]   17.885316  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Time Taken'].max()\n",
    "analysis.loc[analysis['Time Taken']==maxi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>85694</td>\n",
       "      <td>(44633696, 37008297)</td>\n",
       "      <td>Frank_Sebaratnam</td>\n",
       "      <td>Velupillai</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000483</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Combination       Start Title  Goal Title  Paths Found  \\\n",
       "85694  (44633696, 37008297)  Frank_Sebaratnam  Velupillai            0   \n",
       "\n",
       "      All Paths  Shortest Path Length Shortest Path  Time Taken  \n",
       "85694        []                     0            []    0.000483  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Time Taken'].min()\n",
    "analysis.loc[analysis['Time Taken']==mini]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Time Taken'].plot.hist(bins=12, alpha=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Total Time Taken"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.253665305333211"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Time Taken'].sum()/60/60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data set took 13 hours to generate! This was only finding permutations of 350 data points. While we know these 350 points indepth, we can only assume the rest of the wikipedia graph behaves in the same way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Number of Paths Found"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "121.07728399173287"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Paths Found'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Combinations with Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>91404</td>\n",
       "      <td>(14457829, 57833267)</td>\n",
       "      <td>Succinyl-CoA_hydrolase</td>\n",
       "      <td>Kwon_Oh-hee</td>\n",
       "      <td>10984</td>\n",
       "      <td>[[14457829, 1645089, 25, 31717, 592311, 119003...</td>\n",
       "      <td>7</td>\n",
       "      <td>[14457829, 1645089, 25, 31717, 592311, 1190037...</td>\n",
       "      <td>11.423608</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Combination             Start Title   Goal Title  Paths Found  \\\n",
       "91404  (14457829, 57833267)  Succinyl-CoA_hydrolase  Kwon_Oh-hee        10984   \n",
       "\n",
       "                                               All Paths  \\\n",
       "91404  [[14457829, 1645089, 25, 31717, 592311, 119003...   \n",
       "\n",
       "       Shortest Path Length  \\\n",
       "91404                     7   \n",
       "\n",
       "                                           Shortest Path  Time Taken  \n",
       "91404  [14457829, 1645089, 25, 31717, 592311, 1190037...   11.423608  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Paths Found'].max()\n",
    "analysis.loc[analysis['Paths Found']==maxi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>(34298991, 28191801)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
       "      <td>Entäs_nyt,_Niskavuori?</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>(34298991, 28191801)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
       "      <td>Entäs_nyt,_Niskavuori?</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>40</td>\n",
       "      <td>(34298991, 471568)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
       "      <td>USWA</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>61</td>\n",
       "      <td>(34298991, 16224284)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
       "      <td>Saiye,_Ghana</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>80</td>\n",
       "      <td>(34298991, 5789258)</td>\n",
       "      <td>Geological_history_of_Mars</td>\n",
       "      <td>Benzonia</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102040</td>\n",
       "      <td>(32540089, 36572955)</td>\n",
       "      <td>Terreplein</td>\n",
       "      <td>Geoffrey_Plitt</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102041</td>\n",
       "      <td>(32540089, 40161542)</td>\n",
       "      <td>Terreplein</td>\n",
       "      <td>Doruhan</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102047</td>\n",
       "      <td>(32540089, 28589339)</td>\n",
       "      <td>Terreplein</td>\n",
       "      <td>Maria_Carrillo</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102066</td>\n",
       "      <td>(32540089, 35302964)</td>\n",
       "      <td>Terreplein</td>\n",
       "      <td>Mir_Khavand</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>102083</td>\n",
       "      <td>(32540089, 55488245)</td>\n",
       "      <td>Terreplein</td>\n",
       "      <td>Jamalpur,_Sikandarpur</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000608</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7976 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Combination                 Start Title  \\\n",
       "9       (34298991, 28191801)  Geological_history_of_Mars   \n",
       "16      (34298991, 28191801)  Geological_history_of_Mars   \n",
       "40        (34298991, 471568)  Geological_history_of_Mars   \n",
       "61      (34298991, 16224284)  Geological_history_of_Mars   \n",
       "80       (34298991, 5789258)  Geological_history_of_Mars   \n",
       "...                      ...                         ...   \n",
       "102040  (32540089, 36572955)                  Terreplein   \n",
       "102041  (32540089, 40161542)                  Terreplein   \n",
       "102047  (32540089, 28589339)                  Terreplein   \n",
       "102066  (32540089, 35302964)                  Terreplein   \n",
       "102083  (32540089, 55488245)                  Terreplein   \n",
       "\n",
       "                    Goal Title  Paths Found All Paths  Shortest Path Length  \\\n",
       "9       Entäs_nyt,_Niskavuori?            0        []                     0   \n",
       "16      Entäs_nyt,_Niskavuori?            0        []                     0   \n",
       "40                        USWA            0        []                     0   \n",
       "61                Saiye,_Ghana            0        []                     0   \n",
       "80                    Benzonia            0        []                     0   \n",
       "...                        ...          ...       ...                   ...   \n",
       "102040          Geoffrey_Plitt            0        []                     0   \n",
       "102041                 Doruhan            0        []                     0   \n",
       "102047          Maria_Carrillo            0        []                     0   \n",
       "102066             Mir_Khavand            0        []                     0   \n",
       "102083   Jamalpur,_Sikandarpur            0        []                     0   \n",
       "\n",
       "       Shortest Path  Time Taken  \n",
       "9                 []    0.001773  \n",
       "16                []    0.000655  \n",
       "40                []    0.001082  \n",
       "61                []    0.001663  \n",
       "80                []    0.000876  \n",
       "...              ...         ...  \n",
       "102040            []    0.000576  \n",
       "102041            []    0.000522  \n",
       "102047            []    0.000542  \n",
       "102066            []    0.000588  \n",
       "102083            []    0.000608  \n",
       "\n",
       "[7976 rows x 8 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Paths Found'].min()\n",
    "analysis.loc[analysis['Paths Found']==mini]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tny1JMt/jlKRD2UJcuewF/n1V/TKwHrggyQnAZuDGqloH3NjWAc4A1rXXJuA9MAgj4CLgZOAFwEUTgdTabBrab8M8jEuS1Mx7uFTVg1X1xbb8GHAXsBo4C7iiNbsCOLstnwVcWQNfAFYkOQY4HdheVXuq6mFgO7ChbTuyqj5fVQVcOfRekqR5sKDPXJKsBZ4P3AQ8q6oehEEAAc9szVYD9w/ttqvVpqvvmqI+1fE3JdmRZMfu3btnOxxJUrNg4ZLkZ4CPAW+sqkenazpFrQ6g/sRi1aVVNVZVY6tWrdpflyVJI1qQcEnyZAbB8sGq+ngrf7Pd0qL9fajVdwHHDu2+BnhgP/U1U9QlSfNkIWaLBbgMuKuq3jG0aSswMeNrI3DdUP28NmtsPfBIu222DTgtycr2IP80YFvb9liS9e1Y5w29lyRpHixfgGO+GPhXwO1JvtRqfwRcDFyT5HzgPuCctu164ExgHPge8FqAqtqT5C3ALa3dm6tqT1t+HfAB4HDghvaSJM2TeQ+XqvrfTP1cBODUKdoXcME+3uty4PIp6juA586im5KkWfAT+pKk7gwXSVJ3hoskqTvDRZLUneEiSerOcJEkdWe4SJK6M1wkSd0ZLpKk7gwXSVJ3hoskqTvDRZLUneEiSerOcJEkdWe4SJK6M1wkSd0ZLpKk7gwXSVJ3hoskqTvDRZLUneEiSerOcJEkdWe4SJK6M1wkSd0ZLpKk7gwXSVJ3hoskqTvDRZLUneEiSepu+UJ34FC3dvOnDnjfr1/8io49kaR+vHKRJHVnuEiSujNcJEndGS6SpO6W7AP9JBuAdwHLgPdX1cUL3KXuZjMZAJwQIGnuLMkrlyTLgHcDZwAnAK9OcsLC9kqSDh1L9crlBcB4Vd0DkORq4CzgKwvaq4PMbK98DpRXTNLSt1TDZTVw/9D6LuDkyY2SbAI2tdXvJLn7AI93NPCtA9x3MekyzrytQ0/mludz6TlUxroQ4/z5qYpLNVwyRa2eUKi6FLh01gdLdlTV2Gzf52DnOJeWQ2WccOiM9WAa55J85sLgSuXYofU1wAML1BdJOuQs1XC5BViX5LgkhwHnAlsXuE+SdMhYkrfFqmpvktcD2xhMRb68qu6cw0PO+tbaIuE4l5ZDZZxw6Iz1oBlnqp7wKEKSpFlZqrfFJEkLyHCRJHVnuMxSkg1J7k4ynmTzQvdnJpIcm+SzSe5KcmeSN7T6UUm2J9nZ/q5s9STZ0sb65SQnDr3XxtZ+Z5KNCzWm6SRZluS2JJ9s68cluan1+SNt8gdJntLWx9v2tUPvcWGr353k9IUZyfSSrEhybZKvtnP7wqV4TpP8fvvv9o4kH07y1KVwTpNcnuShJHcM1bqdvyQnJbm97bMlyVQf3Zi9qvJ1gC8GkwW+BhwPHAb8H+CEhe7XDPp/DHBiW/5Z4G8ZfF3OnwGbW30z8La2fCZwA4PPEa0Hbmr1o4B72t+VbXnlQo9vivH+AfAh4JNt/Rrg3Lb8XuB1bfl3gfe25XOBj7TlE9o5fgpwXDv3yxZ6XFOM8wrgt9vyYcCKpXZOGXxQ+l7g8KFz+a+XwjkFXgKcCNwxVOt2/oCbgRe2fW4AzpiTcSz0fySL+dVO0Lah9QuBCxe6X7MYz3XAy4G7gWNa7Rjg7rb8PuDVQ+3vbttfDbxvqP5T7Q6GF4PPOt0InAJ8sv0f1reA5ZPPJYNZhi9sy8tbu0w+v8PtDpYXcGT7H91Mqi+pc8pPvoXjqHaOPgmcvlTOKbB2Urh0OX9t21eH6j/VrufL22KzM9XXzKxeoL7MSrtN8HzgJuBZVfUgQPv7zNZsX+NdDP8O7wT+EPiHtv4M4NtVtbetD/f5x+Np2x9p7RfDOI8HdgN/2W4Bvj/J01hi57SqvgG8HbgPeJDBObqVpXlOod/5W92WJ9e7M1xmZ6SvmTnYJfkZ4GPAG6vq0emaTlGraeoHhSS/ATxUVbcOl6doWvvZdlCPs1nO4JbKe6rq+cB3GdxG2ZdFOdb2zOEsBreyfg54GoNvQZ9sKZzT6cx0XPM2XsNldhb918wkeTKDYPlgVX28lb+Z5Ji2/RjgoVbf13gP9n+HFwOvTPJ14GoGt8beCaxIMvFB4uE+/3g8bfvTgT0c/OOEQR93VdVNbf1aBmGz1M7py4B7q2p3Vf0Q+DjwIpbmOYV+529XW55c785wmZ1F/TUzbZbIZcBdVfWOoU1bgYnZJRsZPIuZqJ/XZqisBx5pl+jbgNOSrGz/H+VprXZQqKoLq2pNVa1lcI4+U1WvAT4LvKo1mzzOifG/qrWvVj+3zTw6DljH4OHoQaOq/g64P8lzWulUBj81saTOKYPbYeuTHNH+O54Y55I7p02X89e2PZZkfft3O2/ovfpa6AdXi/3FYLbG3zKYZfLHC92fGfb91xhcEn8Z+FJ7ncngXvSNwM7296jWPgx+hO1rwO3A2NB7/RtgvL1eu9Bjm2bML+Uns8WOZ/A/JOPAR4GntPpT2/p423780P5/3MZ/N3M0y6bDGP8JsKOd108wmC205M4p8F+ArwJ3AFcxmPG16M8p8GEGz5F+yOBK4/ye5w8Ya/9mXwP+nEmTP3q9/PoXSVJ33haTJHVnuEiSujNcJEndGS6SpO4MF0lSd4aLJKk7w0WS1N3/B1LaiDUWw2GWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Paths Found'].plot.hist(bins=20, alpha=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us consider that a short path between two articles in one direction does not mean a short path in the return direction. Below we show an example of this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(237214, 15087124)\tAspectJ\tGreenleaf_Township\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "new1 = analysis[(analysis['Start Title']=='AspectJ') & (analysis['Goal Title']=='Greenleaf_Township')]\n",
    "new2 = analysis[(analysis['Start Title']=='Greenleaf_Township') & (analysis['Goal Title']=='AspectJ')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>15382</td>\n",
       "      <td>(237214, 15087124)</td>\n",
       "      <td>AspectJ</td>\n",
       "      <td>Greenleaf_Township</td>\n",
       "      <td>652</td>\n",
       "      <td>[[237214, 10635, 118450, 27318, 1769262, 11169...</td>\n",
       "      <td>9</td>\n",
       "      <td>[237214, 10635, 118450, 27318, 1769262, 111695...</td>\n",
       "      <td>0.837989</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Combination Start Title          Goal Title  Paths Found  \\\n",
       "15382  (237214, 15087124)     AspectJ  Greenleaf_Township          652   \n",
       "\n",
       "                                               All Paths  \\\n",
       "15382  [[237214, 10635, 118450, 27318, 1769262, 11169...   \n",
       "\n",
       "       Shortest Path Length  \\\n",
       "15382                     9   \n",
       "\n",
       "                                           Shortest Path  Time Taken  \n",
       "15382  [237214, 10635, 118450, 27318, 1769262, 111695...    0.837989  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>18563</td>\n",
       "      <td>(15087124, 237214)</td>\n",
       "      <td>Greenleaf_Township</td>\n",
       "      <td>AspectJ</td>\n",
       "      <td>318</td>\n",
       "      <td>[[15087124, 91817, 2709, 6698, 34154, 237214],...</td>\n",
       "      <td>6</td>\n",
       "      <td>[15087124, 91817, 2709, 6698, 34154, 237214]</td>\n",
       "      <td>0.69792</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Combination         Start Title Goal Title  Paths Found  \\\n",
       "18563  (15087124, 237214)  Greenleaf_Township    AspectJ          318   \n",
       "\n",
       "                                               All Paths  \\\n",
       "18563  [[15087124, 91817, 2709, 6698, 34154, 237214],...   \n",
       "\n",
       "       Shortest Path Length                                 Shortest Path  \\\n",
       "18563                     6  [15087124, 91817, 2709, 6698, 34154, 237214]   \n",
       "\n",
       "       Time Taken  \n",
       "18563     0.69792  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part B:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us also consider our alternate  data. We perform similar analysis to see if we get similar results. An obvious flaw is that it is difficult to consider every article using these methods. However, if we find similar results across multiple article groupings, we can comfortably assume the graph as a whole is similar."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When generating this dataset we used 1000 articles and each article was used as a destination and beginning once. This is less in depth compared to using permutations, but we get access to more unique articles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "analysis = pd.read_csv('randompairs.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>[51385595, 20321524]</td>\n",
       "      <td>Ladbrooke_School</td>\n",
       "      <td>Favianna_Rodriguez</td>\n",
       "      <td>6</td>\n",
       "      <td>[[51385595, 1135131, 31056, 525428, 20321524],...</td>\n",
       "      <td>5</td>\n",
       "      <td>[51385595, 1135131, 31056, 525428, 20321524]</td>\n",
       "      <td>0.305049</td>\n",
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       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>[20321524, 52692366]</td>\n",
       "      <td>Favianna_Rodriguez</td>\n",
       "      <td>Miltogramma_punctata</td>\n",
       "      <td>9</td>\n",
       "      <td>[[20321524, 18987, 775859, 12206720, 48703134,...</td>\n",
       "      <td>6</td>\n",
       "      <td>[20321524, 18987, 775859, 12206720, 48703134, ...</td>\n",
       "      <td>0.216768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>[52692366, 21260623]</td>\n",
       "      <td>Miltogramma_punctata</td>\n",
       "      <td>Ministry_of_National_Defense_(Liberia)</td>\n",
       "      <td>1041</td>\n",
       "      <td>[[52692366, 9239, 10156432, 1516996, 1500005, ...</td>\n",
       "      <td>6</td>\n",
       "      <td>[52692366, 9239, 10156432, 1516996, 1500005, 2...</td>\n",
       "      <td>0.735166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>[21260623, 587847]</td>\n",
       "      <td>Ministry_of_National_Defense_(Liberia)</td>\n",
       "      <td>Amaral\\'s_Brazilian_gecko</td>\n",
       "      <td>9</td>\n",
       "      <td>[[21260623, 17791, 20611195, 323702, 587847], ...</td>\n",
       "      <td>5</td>\n",
       "      <td>[21260623, 17791, 20611195, 323702, 587847]</td>\n",
       "      <td>0.044975</td>\n",
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       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>[587847, 2147446]</td>\n",
       "      <td>Amaral\\'s_Brazilian_gecko</td>\n",
       "      <td>Division_of_Northern_Territory</td>\n",
       "      <td>5</td>\n",
       "      <td>[[587847, 3383, 4689264, 984203, 2147446], [58...</td>\n",
       "      <td>5</td>\n",
       "      <td>[587847, 3383, 4689264, 984203, 2147446]</td>\n",
       "      <td>0.668001</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Combination                             Start Title  \\\n",
       "0  [51385595, 20321524]                        Ladbrooke_School   \n",
       "1  [20321524, 52692366]                      Favianna_Rodriguez   \n",
       "2  [52692366, 21260623]                    Miltogramma_punctata   \n",
       "3    [21260623, 587847]  Ministry_of_National_Defense_(Liberia)   \n",
       "4     [587847, 2147446]               Amaral\\'s_Brazilian_gecko   \n",
       "\n",
       "                               Goal Title  Paths Found  \\\n",
       "0                      Favianna_Rodriguez            6   \n",
       "1                    Miltogramma_punctata            9   \n",
       "2  Ministry_of_National_Defense_(Liberia)         1041   \n",
       "3               Amaral\\'s_Brazilian_gecko            9   \n",
       "4          Division_of_Northern_Territory            5   \n",
       "\n",
       "                                           All Paths  Shortest Path Length  \\\n",
       "0  [[51385595, 1135131, 31056, 525428, 20321524],...                     5   \n",
       "1  [[20321524, 18987, 775859, 12206720, 48703134,...                     6   \n",
       "2  [[52692366, 9239, 10156432, 1516996, 1500005, ...                     6   \n",
       "3  [[21260623, 17791, 20611195, 323702, 587847], ...                     5   \n",
       "4  [[587847, 3383, 4689264, 984203, 2147446], [58...                     5   \n",
       "\n",
       "                                       Shortest Path  Time Taken  \n",
       "0       [51385595, 1135131, 31056, 525428, 20321524]    0.305049  \n",
       "1  [20321524, 18987, 775859, 12206720, 48703134, ...    0.216768  \n",
       "2  [52692366, 9239, 10156432, 1516996, 1500005, 2...    0.735166  \n",
       "3        [21260623, 17791, 20611195, 323702, 587847]    0.044975  \n",
       "4           [587847, 3383, 4689264, 984203, 2147446]    0.668001  "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Lengths of Shortest Paths:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.126"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Shortest Path Length'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random Pairs Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <td>114</td>\n",
       "      <td>[4689107, 39741984]</td>\n",
       "      <td>Fort_McPherson_National_Cemetery</td>\n",
       "      <td>Harpalus_indigens</td>\n",
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       "      <td>4.525727</td>\n",
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       "</div>"
      ],
      "text/plain": [
       "             Combination                       Start Title         Goal Title  \\\n",
       "114  [4689107, 39741984]  Fort_McPherson_National_Cemetery  Harpalus_indigens   \n",
       "\n",
       "     Paths Found                                          All Paths  \\\n",
       "114         1822  [[4689107, 29810, 10418624, 14208, 890203, 385...   \n",
       "\n",
       "     Shortest Path Length                                      Shortest Path  \\\n",
       "114                     9  [4689107, 29810, 10418624, 14208, 890203, 3858...   \n",
       "\n",
       "     Time Taken  \n",
       "114    4.525727  "
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Shortest Path Length'].max()\n",
    "ans = analysis.loc[analysis['Shortest Path Length']==mini]\n",
    "ans.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "74"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ans)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\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>Combination</th>\n",
       "      <th>Start Title</th>\n",
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       "      <th>All Paths</th>\n",
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       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>[517095, 34234410]</td>\n",
       "      <td>Reduced-gravity_aircraft</td>\n",
       "      <td>Siha_Mashariki</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50</td>\n",
       "      <td>[15178198, 60307883]</td>\n",
       "      <td>Istishhad</td>\n",
       "      <td>Christ_Is_Risen!_Christ_Is_Risen!</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>65</td>\n",
       "      <td>[7185151, 35943315]</td>\n",
       "      <td>Powered_roller_coaster</td>\n",
       "      <td>McCatty</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>82</td>\n",
       "      <td>[19986355, 37576611]</td>\n",
       "      <td>Zuan_Francesco_Venier</td>\n",
       "      <td>Irish_heath</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>126</td>\n",
       "      <td>[21494511, 62032496]</td>\n",
       "      <td>Olympic-Wallowa_Lineament</td>\n",
       "      <td>List_of_Za_sklom_(TV_series)_episodes</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>137</td>\n",
       "      <td>[43317723, 20358901]</td>\n",
       "      <td>Sebastián_Salem</td>\n",
       "      <td>Tigerville</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>[11055223, 41285185]</td>\n",
       "      <td>Soleto_Map</td>\n",
       "      <td>Darreh_Panbehdan</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>[19589870, 24021338]</td>\n",
       "      <td>Bilbarin,_Western_Australia</td>\n",
       "      <td>Shumbi,_Papua_New_Guinea</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>153</td>\n",
       "      <td>[60888293, 742593]</td>\n",
       "      <td>Waiheke_Local_Board</td>\n",
       "      <td>Guyuk</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>170</td>\n",
       "      <td>[4961443, 13972839]</td>\n",
       "      <td>List_of_rasa\\'il_in_the_Encyclopedia_of_the_Br...</td>\n",
       "      <td>Macroglossinae</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>202</td>\n",
       "      <td>[16655285, 30933497]</td>\n",
       "      <td>Sydney–Melbourne_rail_corridor</td>\n",
       "      <td>Heavy_Rocks</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>237</td>\n",
       "      <td>[58467944, 44144112]</td>\n",
       "      <td>CS_Rapid_București_(men\\'s_basketball)</td>\n",
       "      <td>Korean_Oriental_Pharmacist</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>253</td>\n",
       "      <td>[25154381, 56806373]</td>\n",
       "      <td>Villalba_v_Merrill_Lynch_&amp;_Co_Inc</td>\n",
       "      <td>Lists_of_governors</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>261</td>\n",
       "      <td>[25292957, 48611457]</td>\n",
       "      <td>Edzard_I,_Count_of_East_Frisia</td>\n",
       "      <td>2015_Bharuch_riots</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>267</td>\n",
       "      <td>[30958480, 14436302]</td>\n",
       "      <td>Voorschoten_\\'97</td>\n",
       "      <td>Mimulus_nudatus</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>274</td>\n",
       "      <td>[12923840, 42047110]</td>\n",
       "      <td>Uvariodendron_occidentale</td>\n",
       "      <td>CA1P</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>281</td>\n",
       "      <td>[4378601, 24510484]</td>\n",
       "      <td>Cutthroat_eel</td>\n",
       "      <td>Freshwater_smelt</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>289</td>\n",
       "      <td>[55685427, 51517532]</td>\n",
       "      <td>Ana_Maria_Savu</td>\n",
       "      <td>Muñoz_West,_Roxas,_Isabela</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>306</td>\n",
       "      <td>[53119993, 61809749]</td>\n",
       "      <td>Nicolle_Galyon</td>\n",
       "      <td>Mzamane</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>359</td>\n",
       "      <td>[35791427, 55071247]</td>\n",
       "      <td>Aba_Airport</td>\n",
       "      <td>Christopher_Mends</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>374</td>\n",
       "      <td>[55280446, 56850631]</td>\n",
       "      <td>Cylindrocopturus</td>\n",
       "      <td>Driving_in_Mexico</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>381</td>\n",
       "      <td>[7685415, 23799215]</td>\n",
       "      <td>Australian_Aboriginal_culture</td>\n",
       "      <td>Mary_Vincent</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>388</td>\n",
       "      <td>[13642850, 51146352]</td>\n",
       "      <td>Basti</td>\n",
       "      <td>S.P._Bansal</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>404</td>\n",
       "      <td>[37686490, 37961211]</td>\n",
       "      <td>Tea:_A_Mirror_of_Soul</td>\n",
       "      <td>V._echinata</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>422</td>\n",
       "      <td>[34975852, 21557785]</td>\n",
       "      <td>Quest_Pistols_Show</td>\n",
       "      <td>Madeleine_Taylor</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>428</td>\n",
       "      <td>[15922685, 44975523]</td>\n",
       "      <td>Avrainville,_Vosges</td>\n",
       "      <td>Juan_Manuel_Ferreira</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>467</td>\n",
       "      <td>[47305372, 4066404]</td>\n",
       "      <td>Chionodes_cusor</td>\n",
       "      <td>Chicken_Ranch</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>476</td>\n",
       "      <td>[60260220, 12249813]</td>\n",
       "      <td>2000/01_NTFL_season</td>\n",
       "      <td>Handelsman</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>486</td>\n",
       "      <td>[2206457, 35570338]</td>\n",
       "      <td>1912_North_Mount_Lyell_disaster</td>\n",
       "      <td>Jankov</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>499</td>\n",
       "      <td>[59548795, 2922225]</td>\n",
       "      <td>Abraham_L._Artz</td>\n",
       "      <td>Khibiny</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>545</td>\n",
       "      <td>[30473086, 51548170]</td>\n",
       "      <td>Dawn_(1985_film)</td>\n",
       "      <td>Business_Trading_Company</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>563</td>\n",
       "      <td>[14446998, 61743502]</td>\n",
       "      <td>Gui_d\\'Ussel</td>\n",
       "      <td>Makudi_railway_station</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>575</td>\n",
       "      <td>[22777772, 40983809]</td>\n",
       "      <td>Coolie_itch</td>\n",
       "      <td>Khushal</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>579</td>\n",
       "      <td>[8589718, 57724727]</td>\n",
       "      <td>The_Wizard_of_Oz_on_television</td>\n",
       "      <td>Bouabdellah</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>583</td>\n",
       "      <td>[45423007, 53108129]</td>\n",
       "      <td>Alastair_Willis</td>\n",
       "      <td>Külhanlı</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>600</td>\n",
       "      <td>[30710463, 29176103]</td>\n",
       "      <td>Andrew_D._Morgan</td>\n",
       "      <td>Outsourced</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>603</td>\n",
       "      <td>[5917746, 50353646]</td>\n",
       "      <td>Soft-body_dynamics</td>\n",
       "      <td>A._agrestis</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>627</td>\n",
       "      <td>[36130371, 42353313]</td>\n",
       "      <td>Razi,_Golestan</td>\n",
       "      <td>Scharfenberg_Castle</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>667</td>\n",
       "      <td>[5629957, 41254519]</td>\n",
       "      <td>Franck_Atsou</td>\n",
       "      <td>Tazehabad-e_Amin</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>675</td>\n",
       "      <td>[36643389, 51061922]</td>\n",
       "      <td>Julianne_Schultz</td>\n",
       "      <td>Three_Principles</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>680</td>\n",
       "      <td>[37736113, 29893650]</td>\n",
       "      <td>Porcellio_auritus</td>\n",
       "      <td>Edes</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>687</td>\n",
       "      <td>[53967096, 10835657]</td>\n",
       "      <td>2010_Southern_Nevada_Coyotes_baseball_team</td>\n",
       "      <td>What_I_Want</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>752</td>\n",
       "      <td>[37270499, 478692]</td>\n",
       "      <td>William_Crawford_(Canadian_politician)</td>\n",
       "      <td>UCAR</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>785</td>\n",
       "      <td>[57712729, 42003063]</td>\n",
       "      <td>White_Ring_(band)</td>\n",
       "      <td>Inconceivable</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>787</td>\n",
       "      <td>[39141749, 55033763]</td>\n",
       "      <td>Puzeh-ye_Lakhar</td>\n",
       "      <td>Lee_Shing_Chak</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>806</td>\n",
       "      <td>[36614216, 36379534]</td>\n",
       "      <td>Caldron_Linn_(Idaho)</td>\n",
       "      <td>Naimabad</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>807</td>\n",
       "      <td>[36379534, 1252529]</td>\n",
       "      <td>Naimabad</td>\n",
       "      <td>HHP</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>848</td>\n",
       "      <td>[24578055, 37429295]</td>\n",
       "      <td>Tormé_(album)</td>\n",
       "      <td>Kunihiro</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>891</td>\n",
       "      <td>[34087159, 30208451]</td>\n",
       "      <td>Tommie_Ginn</td>\n",
       "      <td>Institute_for_Practical_Research_and_Training</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>900</td>\n",
       "      <td>[35841612, 20398311]</td>\n",
       "      <td>Galina_Inzhuvatova</td>\n",
       "      <td>Caseworker</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>912</td>\n",
       "      <td>[50887542, 26526258]</td>\n",
       "      <td>Jambhavali</td>\n",
       "      <td>Claudio_Cavalieri</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>923</td>\n",
       "      <td>[46629574, 61395520]</td>\n",
       "      <td>All_Saints\\'_Church,_Pavement,_York</td>\n",
       "      <td>Hell_(novel)</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>924</td>\n",
       "      <td>[61395520, 5280173]</td>\n",
       "      <td>Hell_(novel)</td>\n",
       "      <td>Egvad</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>951</td>\n",
       "      <td>[43523718, 29665332]</td>\n",
       "      <td>The_Feather_and_Father_Gang</td>\n",
       "      <td>Girma</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>991</td>\n",
       "      <td>[14248609, 47584767]</td>\n",
       "      <td>A._E._Backus_Gallery_&amp;_Museum</td>\n",
       "      <td>Martin_Creek_(Larabee_Creek_tributary)</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001488</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Combination                                        Start Title  \\\n",
       "13     [517095, 34234410]                           Reduced-gravity_aircraft   \n",
       "50   [15178198, 60307883]                                          Istishhad   \n",
       "65    [7185151, 35943315]                             Powered_roller_coaster   \n",
       "82   [19986355, 37576611]                              Zuan_Francesco_Venier   \n",
       "126  [21494511, 62032496]                          Olympic-Wallowa_Lineament   \n",
       "137  [43317723, 20358901]                                    Sebastián_Salem   \n",
       "145  [11055223, 41285185]                                         Soleto_Map   \n",
       "149  [19589870, 24021338]                        Bilbarin,_Western_Australia   \n",
       "153    [60888293, 742593]                                Waiheke_Local_Board   \n",
       "170   [4961443, 13972839]  List_of_rasa\\'il_in_the_Encyclopedia_of_the_Br...   \n",
       "202  [16655285, 30933497]                     Sydney–Melbourne_rail_corridor   \n",
       "237  [58467944, 44144112]             CS_Rapid_București_(men\\'s_basketball)   \n",
       "253  [25154381, 56806373]                  Villalba_v_Merrill_Lynch_&_Co_Inc   \n",
       "261  [25292957, 48611457]                     Edzard_I,_Count_of_East_Frisia   \n",
       "267  [30958480, 14436302]                                   Voorschoten_\\'97   \n",
       "274  [12923840, 42047110]                          Uvariodendron_occidentale   \n",
       "281   [4378601, 24510484]                                      Cutthroat_eel   \n",
       "289  [55685427, 51517532]                                     Ana_Maria_Savu   \n",
       "306  [53119993, 61809749]                                     Nicolle_Galyon   \n",
       "359  [35791427, 55071247]                                        Aba_Airport   \n",
       "374  [55280446, 56850631]                                   Cylindrocopturus   \n",
       "381   [7685415, 23799215]                      Australian_Aboriginal_culture   \n",
       "388  [13642850, 51146352]                                              Basti   \n",
       "404  [37686490, 37961211]                              Tea:_A_Mirror_of_Soul   \n",
       "422  [34975852, 21557785]                                 Quest_Pistols_Show   \n",
       "428  [15922685, 44975523]                                Avrainville,_Vosges   \n",
       "467   [47305372, 4066404]                                    Chionodes_cusor   \n",
       "476  [60260220, 12249813]                                2000/01_NTFL_season   \n",
       "486   [2206457, 35570338]                    1912_North_Mount_Lyell_disaster   \n",
       "499   [59548795, 2922225]                                    Abraham_L._Artz   \n",
       "545  [30473086, 51548170]                                   Dawn_(1985_film)   \n",
       "563  [14446998, 61743502]                                       Gui_d\\'Ussel   \n",
       "575  [22777772, 40983809]                                        Coolie_itch   \n",
       "579   [8589718, 57724727]                     The_Wizard_of_Oz_on_television   \n",
       "583  [45423007, 53108129]                                    Alastair_Willis   \n",
       "600  [30710463, 29176103]                                   Andrew_D._Morgan   \n",
       "603   [5917746, 50353646]                                 Soft-body_dynamics   \n",
       "627  [36130371, 42353313]                                     Razi,_Golestan   \n",
       "667   [5629957, 41254519]                                       Franck_Atsou   \n",
       "675  [36643389, 51061922]                                   Julianne_Schultz   \n",
       "680  [37736113, 29893650]                                  Porcellio_auritus   \n",
       "687  [53967096, 10835657]         2010_Southern_Nevada_Coyotes_baseball_team   \n",
       "752    [37270499, 478692]             William_Crawford_(Canadian_politician)   \n",
       "785  [57712729, 42003063]                                  White_Ring_(band)   \n",
       "787  [39141749, 55033763]                                    Puzeh-ye_Lakhar   \n",
       "806  [36614216, 36379534]                               Caldron_Linn_(Idaho)   \n",
       "807   [36379534, 1252529]                                           Naimabad   \n",
       "848  [24578055, 37429295]                                      Tormé_(album)   \n",
       "891  [34087159, 30208451]                                        Tommie_Ginn   \n",
       "900  [35841612, 20398311]                                 Galina_Inzhuvatova   \n",
       "912  [50887542, 26526258]                                         Jambhavali   \n",
       "923  [46629574, 61395520]                All_Saints\\'_Church,_Pavement,_York   \n",
       "924   [61395520, 5280173]                                       Hell_(novel)   \n",
       "951  [43523718, 29665332]                        The_Feather_and_Father_Gang   \n",
       "991  [14248609, 47584767]                      A._E._Backus_Gallery_&_Museum   \n",
       "\n",
       "                                        Goal Title  Paths Found All Paths  \\\n",
       "13                                  Siha_Mashariki            0        []   \n",
       "50               Christ_Is_Risen!_Christ_Is_Risen!            0        []   \n",
       "65                                         McCatty            0        []   \n",
       "82                                     Irish_heath            0        []   \n",
       "126          List_of_Za_sklom_(TV_series)_episodes            0        []   \n",
       "137                                     Tigerville            0        []   \n",
       "145                               Darreh_Panbehdan            0        []   \n",
       "149                       Shumbi,_Papua_New_Guinea            0        []   \n",
       "153                                          Guyuk            0        []   \n",
       "170                                 Macroglossinae            0        []   \n",
       "202                                    Heavy_Rocks            0        []   \n",
       "237                     Korean_Oriental_Pharmacist            0        []   \n",
       "253                             Lists_of_governors            0        []   \n",
       "261                             2015_Bharuch_riots            0        []   \n",
       "267                                Mimulus_nudatus            0        []   \n",
       "274                                           CA1P            0        []   \n",
       "281                               Freshwater_smelt            0        []   \n",
       "289                     Muñoz_West,_Roxas,_Isabela            0        []   \n",
       "306                                        Mzamane            0        []   \n",
       "359                              Christopher_Mends            0        []   \n",
       "374                              Driving_in_Mexico            0        []   \n",
       "381                                   Mary_Vincent            0        []   \n",
       "388                                    S.P._Bansal            0        []   \n",
       "404                                    V._echinata            0        []   \n",
       "422                               Madeleine_Taylor            0        []   \n",
       "428                           Juan_Manuel_Ferreira            0        []   \n",
       "467                                  Chicken_Ranch            0        []   \n",
       "476                                     Handelsman            0        []   \n",
       "486                                         Jankov            0        []   \n",
       "499                                        Khibiny            0        []   \n",
       "545                       Business_Trading_Company            0        []   \n",
       "563                         Makudi_railway_station            0        []   \n",
       "575                                        Khushal            0        []   \n",
       "579                                    Bouabdellah            0        []   \n",
       "583                                       Külhanlı            0        []   \n",
       "600                                     Outsourced            0        []   \n",
       "603                                    A._agrestis            0        []   \n",
       "627                            Scharfenberg_Castle            0        []   \n",
       "667                               Tazehabad-e_Amin            0        []   \n",
       "675                               Three_Principles            0        []   \n",
       "680                                           Edes            0        []   \n",
       "687                                    What_I_Want            0        []   \n",
       "752                                           UCAR            0        []   \n",
       "785                                  Inconceivable            0        []   \n",
       "787                                 Lee_Shing_Chak            0        []   \n",
       "806                                       Naimabad            0        []   \n",
       "807                                            HHP            0        []   \n",
       "848                                       Kunihiro            0        []   \n",
       "891  Institute_for_Practical_Research_and_Training            0        []   \n",
       "900                                     Caseworker            0        []   \n",
       "912                              Claudio_Cavalieri            0        []   \n",
       "923                                   Hell_(novel)            0        []   \n",
       "924                                          Egvad            0        []   \n",
       "951                                          Girma            0        []   \n",
       "991         Martin_Creek_(Larabee_Creek_tributary)            0        []   \n",
       "\n",
       "     Shortest Path Length Shortest Path  Time Taken  \n",
       "13                      0            []    0.000863  \n",
       "50                      0            []    0.000867  \n",
       "65                      0            []    0.000827  \n",
       "82                      0            []    0.001000  \n",
       "126                     0            []    0.001468  \n",
       "137                     0            []    0.000939  \n",
       "145                     0            []    0.001066  \n",
       "149                     0            []    0.000874  \n",
       "153                     0            []    0.000870  \n",
       "170                     0            []    0.000759  \n",
       "202                     0            []    0.000587  \n",
       "237                     0            []    0.000809  \n",
       "253                     0            []    0.000809  \n",
       "261                     0            []    0.001552  \n",
       "267                     0            []    0.000788  \n",
       "274                     0            []    0.001048  \n",
       "281                     0            []    0.000536  \n",
       "289                     0            []    0.000652  \n",
       "306                     0            []    0.001137  \n",
       "359                     0            []    0.001590  \n",
       "374                     0            []    0.001935  \n",
       "381                     0            []    0.000809  \n",
       "388                     0            []    0.000731  \n",
       "404                     0            []    0.000607  \n",
       "422                     0            []    0.000571  \n",
       "428                     0            []    0.000979  \n",
       "467                     0            []    0.000825  \n",
       "476                     0            []    0.000605  \n",
       "486                     0            []    0.000827  \n",
       "499                     0            []    0.000914  \n",
       "545                     0            []    0.000939  \n",
       "563                     0            []    0.000588  \n",
       "575                     0            []    0.000860  \n",
       "579                     0            []    0.000625  \n",
       "583                     0            []    0.001354  \n",
       "600                     0            []    0.000878  \n",
       "603                     0            []    0.000808  \n",
       "627                     0            []    0.001580  \n",
       "667                     0            []    0.000955  \n",
       "675                     0            []    0.000856  \n",
       "680                     0            []    0.001469  \n",
       "687                     0            []    0.000798  \n",
       "752                     0            []    0.000836  \n",
       "785                     0            []    0.001353  \n",
       "787                     0            []    0.000604  \n",
       "806                     0            []    0.001006  \n",
       "807                     0            []    0.000775  \n",
       "848                     0            []    0.000861  \n",
       "891                     0            []    0.001355  \n",
       "900                     0            []    0.001140  \n",
       "912                     0            []    0.000844  \n",
       "923                     0            []    0.000561  \n",
       "924                     0            []    0.000552  \n",
       "951                     0            []    0.001265  \n",
       "991                     0            []    0.001488  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Shortest Path Length'].min()\n",
    "analysis.loc[analysis['Shortest Path Length']==mini]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MH1XVU0l+C/hzYBXwoaq6Z+BY07BcpsLM8XTLIcdyyADm2NsRnSNVz5i2lyStUMtp+kiSNDBLQZLUWQoDSfKhJHuS3D1ghpOTfCHJziT3JLl8oBxHJ/lykq+2HL8/RI5FeVYluSPJpwbM8ECSu5LcmWR2wBxrklyb5N725+SfDpDh5e33YeHnsSRvHyDHv21/Pu9O8rEkR087Q8txectwzyR+HzynMJAkrwMeB66uqlcNlGEdsK6qbk/yAmAHcGFVfX3KOQIcV1WPJzkK+Avg8qq6dZo5FuV5B7AJeGFVvWmgDA8Am6pq0A9JJdkG/J+q+mC7KvDYqvr2gHlWAd8AXltVfzPF/a5n9OfylVX1vSTXADdV1R9PK0PL8SpGd3s4HXgS+Azwm1V13+Hah0cKA6mqLwHfGjjDw1V1e1v+DrCT0SfLp52jqurxtnpU+xnkfytJNgDnAR8cYv/LSZIXAq8DtgJU1ZNDFkJzNvBX0yyERVYDxyRZDRzLMJ+jegVwa1U9UVVPAV8E3nw4d2ApCIAkM8CpwG0D7X9VkjuBPcD2qhokB/A+4HeBHw20/wUFfDbJjnZrlyG8DJgH/mebTvtgkuMGyrLgLcDHpr3TqvoG8AfAg8DDwKNV9dlp5wDuBl6X5PgkxwLn8vQP/R4yS0Ek+XHgOuDtVfXYEBmq6odV9RpGn2Q/vR0mT1WSNwF7qmrHtPe9hDOr6jRGdw2+rE03Tttq4DTgA1V1KvBdYLBb2rfpq/OBTwyw7xczukHnKcA/AI5L8q+mnaOqdgLvBbYzmjr6KvDU4dyHpbDCtTn864CPVNUnh87TpiduAd44wO7PBM5v8/kfB85K8icD5KCqdrfHPcD1jOaQp20OmFt01HYto5IYyjnA7VX1zQH2/Qbgr6tqvqp+AHwS+GcD5KCqtlbVaVX1OkZT0IftfAJYCitaO8G7FdhZVX84YI61Sda05WMY/QW8d9o5qupdVbWhqmYYTVN8vqqm/r/BJMe1E/+06ZqfYzRtMFVV9X+Bh5K8vA2dDUz1IoS9vJUBpo6aB4Ezkhzb/t6czegc3NQlObE9vhT4BQ7z78myuc3FSpPkY8DrgROSzAHvqaqtU45xJvCrwF1tPh/g3VV105RzrAO2tStLngdcU1WDXQ66DJwEXD/6t4fVwEer6jMDZflt4CNt6uZ+4JIhQrT5858FfmOI/VfVbUmuBW5nNF1zB8Pd7uK6JMcDPwAuq6pHDuebe0mqJKlz+kiS1FkKkqTOUpAkdZaCJKmzFCRJnaUgSeosBUlS9/8ANAnr3KOfaHYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Shortest Path Length'].plot.hist( alpha=1, bins=9)\n",
    "ax.set_xticks([1,2,3,4,5,6,7,8,9])\n",
    "ax.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Amounts of Time Taken:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6003973361000171"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Time Taken'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>978</td>\n",
       "      <td>[19072913, 6144714]</td>\n",
       "      <td>List_of_Top_25_albums_for_1970_in_Australia</td>\n",
       "      <td>Philadelphia_Freedoms</td>\n",
       "      <td>1243</td>\n",
       "      <td>[[19072913, 16095, 11388236, 23338, 6144714], ...</td>\n",
       "      <td>5</td>\n",
       "      <td>[19072913, 16095, 11388236, 23338, 6144714]</td>\n",
       "      <td>18.940672</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Combination                                  Start Title  \\\n",
       "978  [19072913, 6144714]  List_of_Top_25_albums_for_1970_in_Australia   \n",
       "\n",
       "                Goal Title  Paths Found  \\\n",
       "978  Philadelphia_Freedoms         1243   \n",
       "\n",
       "                                             All Paths  Shortest Path Length  \\\n",
       "978  [[19072913, 16095, 11388236, 23338, 6144714], ...                     5   \n",
       "\n",
       "                                   Shortest Path  Time Taken  \n",
       "978  [19072913, 16095, 11388236, 23338, 6144714]   18.940672  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Time Taken'].max()\n",
    "analysis.loc[analysis['Time Taken']==maxi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>281</td>\n",
       "      <td>[4378601, 24510484]</td>\n",
       "      <td>Cutthroat_eel</td>\n",
       "      <td>Freshwater_smelt</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Combination    Start Title        Goal Title  Paths Found  \\\n",
       "281  [4378601, 24510484]  Cutthroat_eel  Freshwater_smelt            0   \n",
       "\n",
       "    All Paths  Shortest Path Length Shortest Path  Time Taken  \n",
       "281        []                     0            []    0.000536  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Time Taken'].min()\n",
    "analysis.loc[analysis['Time Taken']==mini]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Time Taken'].plot.hist(bins=12, alpha=1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.006622268333619"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Time Taken'].sum()/60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It took us 10 minutes to generate all the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Number of Paths Found"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "129.007"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "analysis['Paths Found'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Random pairs with Max and Min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>402</td>\n",
       "      <td>[35633282, 7797146]</td>\n",
       "      <td>Ingestive_behaviors</td>\n",
       "      <td>USS_Witek_(DD-848)</td>\n",
       "      <td>2915</td>\n",
       "      <td>[[35633282, 13980, 39, 22153, 194856, 7797146]...</td>\n",
       "      <td>6</td>\n",
       "      <td>[35633282, 13980, 39, 22153, 194856, 7797146]</td>\n",
       "      <td>3.316532</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Combination          Start Title          Goal Title  \\\n",
       "402  [35633282, 7797146]  Ingestive_behaviors  USS_Witek_(DD-848)   \n",
       "\n",
       "     Paths Found                                          All Paths  \\\n",
       "402         2915  [[35633282, 13980, 39, 22153, 194856, 7797146]...   \n",
       "\n",
       "     Shortest Path Length                                  Shortest Path  \\\n",
       "402                     6  [35633282, 13980, 39, 22153, 194856, 7797146]   \n",
       "\n",
       "     Time Taken  \n",
       "402    3.316532  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "maxi = analysis['Paths Found'].max()\n",
    "analysis.loc[analysis['Paths Found']==maxi]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interestingly, we find many paths are impossible to complete. Perhaps we are seeing many pages with no in-links."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "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>Combination</th>\n",
       "      <th>Start Title</th>\n",
       "      <th>Goal Title</th>\n",
       "      <th>Paths Found</th>\n",
       "      <th>All Paths</th>\n",
       "      <th>Shortest Path Length</th>\n",
       "      <th>Shortest Path</th>\n",
       "      <th>Time Taken</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>[517095, 34234410]</td>\n",
       "      <td>Reduced-gravity_aircraft</td>\n",
       "      <td>Siha_Mashariki</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>50</td>\n",
       "      <td>[15178198, 60307883]</td>\n",
       "      <td>Istishhad</td>\n",
       "      <td>Christ_Is_Risen!_Christ_Is_Risen!</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>65</td>\n",
       "      <td>[7185151, 35943315]</td>\n",
       "      <td>Powered_roller_coaster</td>\n",
       "      <td>McCatty</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>82</td>\n",
       "      <td>[19986355, 37576611]</td>\n",
       "      <td>Zuan_Francesco_Venier</td>\n",
       "      <td>Irish_heath</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>126</td>\n",
       "      <td>[21494511, 62032496]</td>\n",
       "      <td>Olympic-Wallowa_Lineament</td>\n",
       "      <td>List_of_Za_sklom_(TV_series)_episodes</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001468</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>137</td>\n",
       "      <td>[43317723, 20358901]</td>\n",
       "      <td>Sebastián_Salem</td>\n",
       "      <td>Tigerville</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>145</td>\n",
       "      <td>[11055223, 41285185]</td>\n",
       "      <td>Soleto_Map</td>\n",
       "      <td>Darreh_Panbehdan</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>149</td>\n",
       "      <td>[19589870, 24021338]</td>\n",
       "      <td>Bilbarin,_Western_Australia</td>\n",
       "      <td>Shumbi,_Papua_New_Guinea</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>153</td>\n",
       "      <td>[60888293, 742593]</td>\n",
       "      <td>Waiheke_Local_Board</td>\n",
       "      <td>Guyuk</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>170</td>\n",
       "      <td>[4961443, 13972839]</td>\n",
       "      <td>List_of_rasa\\'il_in_the_Encyclopedia_of_the_Br...</td>\n",
       "      <td>Macroglossinae</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>202</td>\n",
       "      <td>[16655285, 30933497]</td>\n",
       "      <td>Sydney–Melbourne_rail_corridor</td>\n",
       "      <td>Heavy_Rocks</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>237</td>\n",
       "      <td>[58467944, 44144112]</td>\n",
       "      <td>CS_Rapid_București_(men\\'s_basketball)</td>\n",
       "      <td>Korean_Oriental_Pharmacist</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>253</td>\n",
       "      <td>[25154381, 56806373]</td>\n",
       "      <td>Villalba_v_Merrill_Lynch_&amp;_Co_Inc</td>\n",
       "      <td>Lists_of_governors</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>261</td>\n",
       "      <td>[25292957, 48611457]</td>\n",
       "      <td>Edzard_I,_Count_of_East_Frisia</td>\n",
       "      <td>2015_Bharuch_riots</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>267</td>\n",
       "      <td>[30958480, 14436302]</td>\n",
       "      <td>Voorschoten_\\'97</td>\n",
       "      <td>Mimulus_nudatus</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>274</td>\n",
       "      <td>[12923840, 42047110]</td>\n",
       "      <td>Uvariodendron_occidentale</td>\n",
       "      <td>CA1P</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>281</td>\n",
       "      <td>[4378601, 24510484]</td>\n",
       "      <td>Cutthroat_eel</td>\n",
       "      <td>Freshwater_smelt</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000536</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>289</td>\n",
       "      <td>[55685427, 51517532]</td>\n",
       "      <td>Ana_Maria_Savu</td>\n",
       "      <td>Muñoz_West,_Roxas,_Isabela</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>306</td>\n",
       "      <td>[53119993, 61809749]</td>\n",
       "      <td>Nicolle_Galyon</td>\n",
       "      <td>Mzamane</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>359</td>\n",
       "      <td>[35791427, 55071247]</td>\n",
       "      <td>Aba_Airport</td>\n",
       "      <td>Christopher_Mends</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>374</td>\n",
       "      <td>[55280446, 56850631]</td>\n",
       "      <td>Cylindrocopturus</td>\n",
       "      <td>Driving_in_Mexico</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>381</td>\n",
       "      <td>[7685415, 23799215]</td>\n",
       "      <td>Australian_Aboriginal_culture</td>\n",
       "      <td>Mary_Vincent</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000809</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>388</td>\n",
       "      <td>[13642850, 51146352]</td>\n",
       "      <td>Basti</td>\n",
       "      <td>S.P._Bansal</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>404</td>\n",
       "      <td>[37686490, 37961211]</td>\n",
       "      <td>Tea:_A_Mirror_of_Soul</td>\n",
       "      <td>V._echinata</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>422</td>\n",
       "      <td>[34975852, 21557785]</td>\n",
       "      <td>Quest_Pistols_Show</td>\n",
       "      <td>Madeleine_Taylor</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>428</td>\n",
       "      <td>[15922685, 44975523]</td>\n",
       "      <td>Avrainville,_Vosges</td>\n",
       "      <td>Juan_Manuel_Ferreira</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>467</td>\n",
       "      <td>[47305372, 4066404]</td>\n",
       "      <td>Chionodes_cusor</td>\n",
       "      <td>Chicken_Ranch</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>476</td>\n",
       "      <td>[60260220, 12249813]</td>\n",
       "      <td>2000/01_NTFL_season</td>\n",
       "      <td>Handelsman</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000605</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>486</td>\n",
       "      <td>[2206457, 35570338]</td>\n",
       "      <td>1912_North_Mount_Lyell_disaster</td>\n",
       "      <td>Jankov</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>499</td>\n",
       "      <td>[59548795, 2922225]</td>\n",
       "      <td>Abraham_L._Artz</td>\n",
       "      <td>Khibiny</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>545</td>\n",
       "      <td>[30473086, 51548170]</td>\n",
       "      <td>Dawn_(1985_film)</td>\n",
       "      <td>Business_Trading_Company</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000939</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>563</td>\n",
       "      <td>[14446998, 61743502]</td>\n",
       "      <td>Gui_d\\'Ussel</td>\n",
       "      <td>Makudi_railway_station</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>575</td>\n",
       "      <td>[22777772, 40983809]</td>\n",
       "      <td>Coolie_itch</td>\n",
       "      <td>Khushal</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>579</td>\n",
       "      <td>[8589718, 57724727]</td>\n",
       "      <td>The_Wizard_of_Oz_on_television</td>\n",
       "      <td>Bouabdellah</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>583</td>\n",
       "      <td>[45423007, 53108129]</td>\n",
       "      <td>Alastair_Willis</td>\n",
       "      <td>Külhanlı</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>600</td>\n",
       "      <td>[30710463, 29176103]</td>\n",
       "      <td>Andrew_D._Morgan</td>\n",
       "      <td>Outsourced</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>603</td>\n",
       "      <td>[5917746, 50353646]</td>\n",
       "      <td>Soft-body_dynamics</td>\n",
       "      <td>A._agrestis</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>627</td>\n",
       "      <td>[36130371, 42353313]</td>\n",
       "      <td>Razi,_Golestan</td>\n",
       "      <td>Scharfenberg_Castle</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>667</td>\n",
       "      <td>[5629957, 41254519]</td>\n",
       "      <td>Franck_Atsou</td>\n",
       "      <td>Tazehabad-e_Amin</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>675</td>\n",
       "      <td>[36643389, 51061922]</td>\n",
       "      <td>Julianne_Schultz</td>\n",
       "      <td>Three_Principles</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>680</td>\n",
       "      <td>[37736113, 29893650]</td>\n",
       "      <td>Porcellio_auritus</td>\n",
       "      <td>Edes</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>687</td>\n",
       "      <td>[53967096, 10835657]</td>\n",
       "      <td>2010_Southern_Nevada_Coyotes_baseball_team</td>\n",
       "      <td>What_I_Want</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000798</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>752</td>\n",
       "      <td>[37270499, 478692]</td>\n",
       "      <td>William_Crawford_(Canadian_politician)</td>\n",
       "      <td>UCAR</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>785</td>\n",
       "      <td>[57712729, 42003063]</td>\n",
       "      <td>White_Ring_(band)</td>\n",
       "      <td>Inconceivable</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>787</td>\n",
       "      <td>[39141749, 55033763]</td>\n",
       "      <td>Puzeh-ye_Lakhar</td>\n",
       "      <td>Lee_Shing_Chak</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>806</td>\n",
       "      <td>[36614216, 36379534]</td>\n",
       "      <td>Caldron_Linn_(Idaho)</td>\n",
       "      <td>Naimabad</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>807</td>\n",
       "      <td>[36379534, 1252529]</td>\n",
       "      <td>Naimabad</td>\n",
       "      <td>HHP</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000775</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>848</td>\n",
       "      <td>[24578055, 37429295]</td>\n",
       "      <td>Tormé_(album)</td>\n",
       "      <td>Kunihiro</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>891</td>\n",
       "      <td>[34087159, 30208451]</td>\n",
       "      <td>Tommie_Ginn</td>\n",
       "      <td>Institute_for_Practical_Research_and_Training</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>900</td>\n",
       "      <td>[35841612, 20398311]</td>\n",
       "      <td>Galina_Inzhuvatova</td>\n",
       "      <td>Caseworker</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>912</td>\n",
       "      <td>[50887542, 26526258]</td>\n",
       "      <td>Jambhavali</td>\n",
       "      <td>Claudio_Cavalieri</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>923</td>\n",
       "      <td>[46629574, 61395520]</td>\n",
       "      <td>All_Saints\\'_Church,_Pavement,_York</td>\n",
       "      <td>Hell_(novel)</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>924</td>\n",
       "      <td>[61395520, 5280173]</td>\n",
       "      <td>Hell_(novel)</td>\n",
       "      <td>Egvad</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.000552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>951</td>\n",
       "      <td>[43523718, 29665332]</td>\n",
       "      <td>The_Feather_and_Father_Gang</td>\n",
       "      <td>Girma</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>991</td>\n",
       "      <td>[14248609, 47584767]</td>\n",
       "      <td>A._E._Backus_Gallery_&amp;_Museum</td>\n",
       "      <td>Martin_Creek_(Larabee_Creek_tributary)</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0</td>\n",
       "      <td>[]</td>\n",
       "      <td>0.001488</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Combination                                        Start Title  \\\n",
       "13     [517095, 34234410]                           Reduced-gravity_aircraft   \n",
       "50   [15178198, 60307883]                                          Istishhad   \n",
       "65    [7185151, 35943315]                             Powered_roller_coaster   \n",
       "82   [19986355, 37576611]                              Zuan_Francesco_Venier   \n",
       "126  [21494511, 62032496]                          Olympic-Wallowa_Lineament   \n",
       "137  [43317723, 20358901]                                    Sebastián_Salem   \n",
       "145  [11055223, 41285185]                                         Soleto_Map   \n",
       "149  [19589870, 24021338]                        Bilbarin,_Western_Australia   \n",
       "153    [60888293, 742593]                                Waiheke_Local_Board   \n",
       "170   [4961443, 13972839]  List_of_rasa\\'il_in_the_Encyclopedia_of_the_Br...   \n",
       "202  [16655285, 30933497]                     Sydney–Melbourne_rail_corridor   \n",
       "237  [58467944, 44144112]             CS_Rapid_București_(men\\'s_basketball)   \n",
       "253  [25154381, 56806373]                  Villalba_v_Merrill_Lynch_&_Co_Inc   \n",
       "261  [25292957, 48611457]                     Edzard_I,_Count_of_East_Frisia   \n",
       "267  [30958480, 14436302]                                   Voorschoten_\\'97   \n",
       "274  [12923840, 42047110]                          Uvariodendron_occidentale   \n",
       "281   [4378601, 24510484]                                      Cutthroat_eel   \n",
       "289  [55685427, 51517532]                                     Ana_Maria_Savu   \n",
       "306  [53119993, 61809749]                                     Nicolle_Galyon   \n",
       "359  [35791427, 55071247]                                        Aba_Airport   \n",
       "374  [55280446, 56850631]                                   Cylindrocopturus   \n",
       "381   [7685415, 23799215]                      Australian_Aboriginal_culture   \n",
       "388  [13642850, 51146352]                                              Basti   \n",
       "404  [37686490, 37961211]                              Tea:_A_Mirror_of_Soul   \n",
       "422  [34975852, 21557785]                                 Quest_Pistols_Show   \n",
       "428  [15922685, 44975523]                                Avrainville,_Vosges   \n",
       "467   [47305372, 4066404]                                    Chionodes_cusor   \n",
       "476  [60260220, 12249813]                                2000/01_NTFL_season   \n",
       "486   [2206457, 35570338]                    1912_North_Mount_Lyell_disaster   \n",
       "499   [59548795, 2922225]                                    Abraham_L._Artz   \n",
       "545  [30473086, 51548170]                                   Dawn_(1985_film)   \n",
       "563  [14446998, 61743502]                                       Gui_d\\'Ussel   \n",
       "575  [22777772, 40983809]                                        Coolie_itch   \n",
       "579   [8589718, 57724727]                     The_Wizard_of_Oz_on_television   \n",
       "583  [45423007, 53108129]                                    Alastair_Willis   \n",
       "600  [30710463, 29176103]                                   Andrew_D._Morgan   \n",
       "603   [5917746, 50353646]                                 Soft-body_dynamics   \n",
       "627  [36130371, 42353313]                                     Razi,_Golestan   \n",
       "667   [5629957, 41254519]                                       Franck_Atsou   \n",
       "675  [36643389, 51061922]                                   Julianne_Schultz   \n",
       "680  [37736113, 29893650]                                  Porcellio_auritus   \n",
       "687  [53967096, 10835657]         2010_Southern_Nevada_Coyotes_baseball_team   \n",
       "752    [37270499, 478692]             William_Crawford_(Canadian_politician)   \n",
       "785  [57712729, 42003063]                                  White_Ring_(band)   \n",
       "787  [39141749, 55033763]                                    Puzeh-ye_Lakhar   \n",
       "806  [36614216, 36379534]                               Caldron_Linn_(Idaho)   \n",
       "807   [36379534, 1252529]                                           Naimabad   \n",
       "848  [24578055, 37429295]                                      Tormé_(album)   \n",
       "891  [34087159, 30208451]                                        Tommie_Ginn   \n",
       "900  [35841612, 20398311]                                 Galina_Inzhuvatova   \n",
       "912  [50887542, 26526258]                                         Jambhavali   \n",
       "923  [46629574, 61395520]                All_Saints\\'_Church,_Pavement,_York   \n",
       "924   [61395520, 5280173]                                       Hell_(novel)   \n",
       "951  [43523718, 29665332]                        The_Feather_and_Father_Gang   \n",
       "991  [14248609, 47584767]                      A._E._Backus_Gallery_&_Museum   \n",
       "\n",
       "                                        Goal Title  Paths Found All Paths  \\\n",
       "13                                  Siha_Mashariki            0        []   \n",
       "50               Christ_Is_Risen!_Christ_Is_Risen!            0        []   \n",
       "65                                         McCatty            0        []   \n",
       "82                                     Irish_heath            0        []   \n",
       "126          List_of_Za_sklom_(TV_series)_episodes            0        []   \n",
       "137                                     Tigerville            0        []   \n",
       "145                               Darreh_Panbehdan            0        []   \n",
       "149                       Shumbi,_Papua_New_Guinea            0        []   \n",
       "153                                          Guyuk            0        []   \n",
       "170                                 Macroglossinae            0        []   \n",
       "202                                    Heavy_Rocks            0        []   \n",
       "237                     Korean_Oriental_Pharmacist            0        []   \n",
       "253                             Lists_of_governors            0        []   \n",
       "261                             2015_Bharuch_riots            0        []   \n",
       "267                                Mimulus_nudatus            0        []   \n",
       "274                                           CA1P            0        []   \n",
       "281                               Freshwater_smelt            0        []   \n",
       "289                     Muñoz_West,_Roxas,_Isabela            0        []   \n",
       "306                                        Mzamane            0        []   \n",
       "359                              Christopher_Mends            0        []   \n",
       "374                              Driving_in_Mexico            0        []   \n",
       "381                                   Mary_Vincent            0        []   \n",
       "388                                    S.P._Bansal            0        []   \n",
       "404                                    V._echinata            0        []   \n",
       "422                               Madeleine_Taylor            0        []   \n",
       "428                           Juan_Manuel_Ferreira            0        []   \n",
       "467                                  Chicken_Ranch            0        []   \n",
       "476                                     Handelsman            0        []   \n",
       "486                                         Jankov            0        []   \n",
       "499                                        Khibiny            0        []   \n",
       "545                       Business_Trading_Company            0        []   \n",
       "563                         Makudi_railway_station            0        []   \n",
       "575                                        Khushal            0        []   \n",
       "579                                    Bouabdellah            0        []   \n",
       "583                                       Külhanlı            0        []   \n",
       "600                                     Outsourced            0        []   \n",
       "603                                    A._agrestis            0        []   \n",
       "627                            Scharfenberg_Castle            0        []   \n",
       "667                               Tazehabad-e_Amin            0        []   \n",
       "675                               Three_Principles            0        []   \n",
       "680                                           Edes            0        []   \n",
       "687                                    What_I_Want            0        []   \n",
       "752                                           UCAR            0        []   \n",
       "785                                  Inconceivable            0        []   \n",
       "787                                 Lee_Shing_Chak            0        []   \n",
       "806                                       Naimabad            0        []   \n",
       "807                                            HHP            0        []   \n",
       "848                                       Kunihiro            0        []   \n",
       "891  Institute_for_Practical_Research_and_Training            0        []   \n",
       "900                                     Caseworker            0        []   \n",
       "912                              Claudio_Cavalieri            0        []   \n",
       "923                                   Hell_(novel)            0        []   \n",
       "924                                          Egvad            0        []   \n",
       "951                                          Girma            0        []   \n",
       "991         Martin_Creek_(Larabee_Creek_tributary)            0        []   \n",
       "\n",
       "     Shortest Path Length Shortest Path  Time Taken  \n",
       "13                      0            []    0.000863  \n",
       "50                      0            []    0.000867  \n",
       "65                      0            []    0.000827  \n",
       "82                      0            []    0.001000  \n",
       "126                     0            []    0.001468  \n",
       "137                     0            []    0.000939  \n",
       "145                     0            []    0.001066  \n",
       "149                     0            []    0.000874  \n",
       "153                     0            []    0.000870  \n",
       "170                     0            []    0.000759  \n",
       "202                     0            []    0.000587  \n",
       "237                     0            []    0.000809  \n",
       "253                     0            []    0.000809  \n",
       "261                     0            []    0.001552  \n",
       "267                     0            []    0.000788  \n",
       "274                     0            []    0.001048  \n",
       "281                     0            []    0.000536  \n",
       "289                     0            []    0.000652  \n",
       "306                     0            []    0.001137  \n",
       "359                     0            []    0.001590  \n",
       "374                     0            []    0.001935  \n",
       "381                     0            []    0.000809  \n",
       "388                     0            []    0.000731  \n",
       "404                     0            []    0.000607  \n",
       "422                     0            []    0.000571  \n",
       "428                     0            []    0.000979  \n",
       "467                     0            []    0.000825  \n",
       "476                     0            []    0.000605  \n",
       "486                     0            []    0.000827  \n",
       "499                     0            []    0.000914  \n",
       "545                     0            []    0.000939  \n",
       "563                     0            []    0.000588  \n",
       "575                     0            []    0.000860  \n",
       "579                     0            []    0.000625  \n",
       "583                     0            []    0.001354  \n",
       "600                     0            []    0.000878  \n",
       "603                     0            []    0.000808  \n",
       "627                     0            []    0.001580  \n",
       "667                     0            []    0.000955  \n",
       "675                     0            []    0.000856  \n",
       "680                     0            []    0.001469  \n",
       "687                     0            []    0.000798  \n",
       "752                     0            []    0.000836  \n",
       "785                     0            []    0.001353  \n",
       "787                     0            []    0.000604  \n",
       "806                     0            []    0.001006  \n",
       "807                     0            []    0.000775  \n",
       "848                     0            []    0.000861  \n",
       "891                     0            []    0.001355  \n",
       "900                     0            []    0.001140  \n",
       "912                     0            []    0.000844  \n",
       "923                     0            []    0.000561  \n",
       "924                     0            []    0.000552  \n",
       "951                     0            []    0.001265  \n",
       "991                     0            []    0.001488  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mini = analysis['Paths Found'].min()\n",
    "analysis.loc[analysis['Paths Found']==mini]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = analysis['Paths Found'].plot.hist(bins=20, alpha=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}