Centrality analysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import GMLs\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "SNet = nx.read_gml(\"data/graphs/snet.gml\")\n",
    "SNetF = nx.read_gml(\"data/graphs/snetf.gml\")\n",
    "SNetT = nx.read_gml(\"data/graphs/snett.gml\")\n",
    "UserNet = nx.read_gml(\"data/graphs/usernet.gml\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: \n",
      "Type: Graph\n",
      "Number of nodes: 4191\n",
      "Number of edges: 135974\n",
      "Average degree:  64.8886\n",
      "Name: \n",
      "Type: Graph\n",
      "Number of nodes: 4191\n",
      "Number of edges: 6113\n",
      "Average degree:   2.9172\n",
      "Name: \n",
      "Type: Graph\n",
      "Number of nodes: 39\n",
      "Number of edges: 741\n",
      "Average degree:  38.0000\n",
      "Name: \n",
      "Type: DiGraph\n",
      "Number of nodes: 18975\n",
      "Number of edges: 102043\n",
      "Average in degree:   5.3778\n",
      "Average out degree:   5.3778\n"
     ]
    }
   ],
   "source": [
    "print(nx.info(SNet))\n",
    "print(nx.info(SNetF))\n",
    "print(nx.info(SNetT))\n",
    "print(nx.info(UserNet))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Centrality analysis\n",
    "\n",
    "## 16 Degree, closeness and betweenness centralities. Summary of most notable elements "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "def centralities(graph):\n",
    "    centralities = pd.DataFrame(graph.nodes(), columns=['subreddit'])\n",
    "    if nx.is_directed(graph):\n",
    "        dir_degree = directed_degree_centrality(graph)\n",
    "        centralities[\"in_dc\"] = nx.in_degree_centrality(graph).values()\n",
    "        centralities[\"out_dc\"] = nx.out_degree_centrality(graph).values()\n",
    "        \n",
    "    centralities[\"dc\"] = nx.degree_centrality(graph).values()\n",
    "    centralities[\"cc\"] = nx.closeness_centrality(graph).values()\n",
    "    centralities[\"bc\"] = nx.betweenness_centrality(graph).values()\n",
    "\n",
    "    return centralities\n",
    "\n",
    "def print_export_all(cs, graph_name, columns=None, first_n=None):\n",
    "    \n",
    "    def export_centrality(centrality_name):\n",
    "        df_ = cs[[cs.columns[0], centrality_name]].round({centrality_name: 5}).sort_values(centrality_name, ascending=False).iloc[:10]\n",
    "        df_.to_csv(f\"data/pandas/centrality-analysis/{graph_name}/{centrality_name}_centrality.csv\")\n",
    "    \n",
    "    \n",
    "    columns_to_write = cs.columns if columns == None else columns\n",
    "    n = first_n if first_n != None else len(cs)\n",
    "\n",
    "    for i in range(1, len(cs.columns)):\n",
    "        if cs.columns[i] in columns_to_write:\n",
    "            print(cs.columns[i])\n",
    "            export_centrality(cs.columns[i])\n",
    "            display(cs[[cs.columns[0], cs.columns[i]]].sort_values(cs.columns[i], ascending=False).iloc[:n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "def write(graph_name, centrality):\n",
    "    pickle.dump(centrality, open(f\"data/centralities/{graph_name.lower()}_centralities\", \"wb\"))\n",
    "    \n",
    "def get_centrality(graph_name, graph, overwrite_centrality=False):\n",
    "    def create_and_write(graph_name, graph):\n",
    "            centrality = centralities(graph)\n",
    "            write(graph_name, centrality)\n",
    "            return centrality\n",
    "        \n",
    "    try:\n",
    "        if overwrite_centrality:\n",
    "            return create_and_write(graph_name, graph)\n",
    "        else:\n",
    "            return pickle.load(open(f\"data/centralities/{graph_name.lower()}_centralities\", \"rb\"))\n",
    "    except (OSError, IOError, FileNotFoundError) as e:\n",
    "        return create_and_write(graph_name, graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "snet_centralities = get_centrality(\"SNet\", SNet) #, overwrite_centrality=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dc\n"
     ]
    },
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       "      <td>reddit.com</td>\n",
       "      <td>0.714320</td>\n",
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       "    </tr>\n",
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       "      <th>90</th>\n",
       "      <td>technology</td>\n",
       "      <td>0.489499</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>pics</td>\n",
       "      <td>0.480907</td>\n",
       "    </tr>\n",
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       "      <td>0.456325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.454654</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "         subreddit        dc\n",
       "0       reddit.com  0.714320\n",
       "2         politics  0.489976\n",
       "90      technology  0.489499\n",
       "38            pics  0.480907\n",
       "135          funny  0.468496\n",
       "1          science  0.464678\n",
       "5    entertainment  0.456325\n",
       "42       worldnews  0.454654\n",
       "7      programming  0.450119\n",
       "103            WTF  0.449403"
      ]
     },
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     "output_type": "display_data"
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     "text": [
      "cc\n"
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       "      <th>subreddit</th>\n",
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       "      <td>reddit.com</td>\n",
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       "      <th>90</th>\n",
       "      <td>technology</td>\n",
       "      <td>0.576672</td>\n",
       "    </tr>\n",
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       "      <th>2</th>\n",
       "      <td>politics</td>\n",
       "      <td>0.576304</td>\n",
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       "      <td>pics</td>\n",
       "      <td>0.571567</td>\n",
       "    </tr>\n",
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       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>0.565136</td>\n",
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       "      <td>0.559424</td>\n",
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       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.558732</td>\n",
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       "      <th>7</th>\n",
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      "text/plain": [
       "         subreddit        cc\n",
       "0       reddit.com  0.722837\n",
       "90      technology  0.576672\n",
       "2         politics  0.576304\n",
       "38            pics  0.571567\n",
       "135          funny  0.565136\n",
       "1          science  0.563258\n",
       "5    entertainment  0.559424\n",
       "42       worldnews  0.558732\n",
       "7      programming  0.555755\n",
       "103            WTF  0.555755"
      ]
     },
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     "output_type": "display_data"
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      "bc\n"
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       "      <th>subreddit</th>\n",
       "      <th>bc</th>\n",
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       "      <th>90</th>\n",
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       "      <td>0.031858</td>\n",
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       "      <td>0.029536</td>\n",
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       "      <td>politics</td>\n",
       "      <td>0.028278</td>\n",
       "    </tr>\n",
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       "      <th>8</th>\n",
       "      <td>business</td>\n",
       "      <td>0.026771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>pics</td>\n",
       "      <td>0.025234</td>\n",
       "    </tr>\n",
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       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.024741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.021677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>0.021132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>science</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit        bc\n",
       "0       reddit.com  0.248260\n",
       "90      technology  0.031858\n",
       "7      programming  0.029536\n",
       "2         politics  0.028278\n",
       "8         business  0.026771\n",
       "38            pics  0.025234\n",
       "5    entertainment  0.024741\n",
       "42       worldnews  0.021677\n",
       "135          funny  0.021132\n",
       "1          science  0.020552"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snet_centralities, \"SNet\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "snetf_centralities = get_centrality(\"SnetF\", SNetF) #, overwrite_centrality=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
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     "text": [
      "dc\n"
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       "      <td>0.047971</td>\n",
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       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>WTF</td>\n",
       "      <td>0.046539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.046062</td>\n",
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      "text/plain": [
       "         subreddit        dc\n",
       "0       reddit.com  0.057041\n",
       "38            pics  0.050597\n",
       "2         politics  0.050119\n",
       "1          science  0.049403\n",
       "90      technology  0.049403\n",
       "135          funny  0.048687\n",
       "42       worldnews  0.047971\n",
       "103            WTF  0.046539\n",
       "5    entertainment  0.046062\n",
       "7      programming  0.044391"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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     "name": "stdout",
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     "text": [
      "cc\n"
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       "      <td>funny</td>\n",
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       "      <td>0.049104</td>\n",
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       "      <td>WTF</td>\n",
       "      <td>0.048098</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.047772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>programming</td>\n",
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      "text/plain": [
       "         subreddit        cc\n",
       "0       reddit.com  0.057056\n",
       "38            pics  0.051061\n",
       "2         politics  0.050694\n",
       "1          science  0.050152\n",
       "90      technology  0.050152\n",
       "135          funny  0.049623\n",
       "42       worldnews  0.049104\n",
       "103            WTF  0.048098\n",
       "5    entertainment  0.047772\n",
       "7      programming  0.046665"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bc\n"
     ]
    },
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       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>0.000138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.000134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>WTF</td>\n",
       "      <td>0.000107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.000103</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit        bc\n",
       "0       reddit.com  0.000857\n",
       "2         politics  0.000180\n",
       "38            pics  0.000178\n",
       "90      technology  0.000150\n",
       "1          science  0.000148\n",
       "7      programming  0.000140\n",
       "135          funny  0.000138\n",
       "42       worldnews  0.000134\n",
       "103            WTF  0.000107\n",
       "5    entertainment  0.000103"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snetf_centralities, \"SNetF\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "snett_centralities = get_centrality(\"SNetT\", SNetT)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dc\n"
     ]
    },
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       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>geek</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>photography</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
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       "      <th>30</th>\n",
       "      <td>history</td>\n",
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      ],
      "text/plain": [
       "      subreddit   dc\n",
       "0    reddit.com  1.0\n",
       "29        funny  1.0\n",
       "22      atheism  1.0\n",
       "23       bestof  1.0\n",
       "24   technology  1.0\n",
       "25          WTF  1.0\n",
       "26       canada  1.0\n",
       "27         geek  1.0\n",
       "28  photography  1.0\n",
       "30      history  1.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cc\n"
     ]
    },
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>geek</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>photography</td>\n",
       "      <td>1.0</td>\n",
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       "      <th>30</th>\n",
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       "      subreddit   cc\n",
       "0    reddit.com  1.0\n",
       "29        funny  1.0\n",
       "22      atheism  1.0\n",
       "23       bestof  1.0\n",
       "24   technology  1.0\n",
       "25          WTF  1.0\n",
       "26       canada  1.0\n",
       "27         geek  1.0\n",
       "28  photography  1.0\n",
       "30      history  1.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bc\n"
     ]
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       "      <th>27</th>\n",
       "      <td>geek</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>photography</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>history</td>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      subreddit   bc\n",
       "0    reddit.com  0.0\n",
       "29        funny  0.0\n",
       "22      atheism  0.0\n",
       "23       bestof  0.0\n",
       "24   technology  0.0\n",
       "25          WTF  0.0\n",
       "26       canada  0.0\n",
       "27         geek  0.0\n",
       "28  photography  0.0\n",
       "30      history  0.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snett_centralities, \"SNetT\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "usernet_centralities = get_centrality(\"UserNet\", UserNet) #, overwrite_centrality=True) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "in_dc\n"
     ]
    },
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>mutatron</td>\n",
       "      <td>0.021292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>Poromenos</td>\n",
       "      <td>0.017392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>fingers</td>\n",
       "      <td>0.016338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>457</th>\n",
       "      <td>matts2</td>\n",
       "      <td>0.015969</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>760</th>\n",
       "      <td>amstrdamordeath</td>\n",
       "      <td>0.015811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>MrKlaatu</td>\n",
       "      <td>0.015811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1113</th>\n",
       "      <td>nixonrichard</td>\n",
       "      <td>0.015495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>455</th>\n",
       "      <td>malcontent</td>\n",
       "      <td>0.015284</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            subreddit     in_dc\n",
       "353   NoMoreNicksLeft  0.024507\n",
       "47               7oby  0.022873\n",
       "27           mutatron  0.021292\n",
       "177         Poromenos  0.017392\n",
       "368           fingers  0.016338\n",
       "457            matts2  0.015969\n",
       "760   amstrdamordeath  0.015811\n",
       "60           MrKlaatu  0.015811\n",
       "1113     nixonrichard  0.015495\n",
       "455        malcontent  0.015284"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "out_dc\n"
     ]
    },
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       "      <th>86</th>\n",
       "      <td>qgyh2</td>\n",
       "      <td>0.039791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>355</th>\n",
       "      <td>deuteros</td>\n",
       "      <td>0.029092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>tsteele93</td>\n",
       "      <td>0.027511</td>\n",
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       "    <tr>\n",
       "      <th>798</th>\n",
       "      <td>bobcat</td>\n",
       "      <td>0.023032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>209</th>\n",
       "      <td>grauenwolf</td>\n",
       "      <td>0.017919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1689</th>\n",
       "      <td>Aerik</td>\n",
       "      <td>0.017340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>AMerrickanGirl</td>\n",
       "      <td>0.017129</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           subreddit    out_dc\n",
       "1508          alllie  0.055866\n",
       "47              7oby  0.049120\n",
       "1179          rmuser  0.045272\n",
       "86             qgyh2  0.039791\n",
       "355         deuteros  0.029092\n",
       "92         tsteele93  0.027511\n",
       "798           bobcat  0.023032\n",
       "209       grauenwolf  0.017919\n",
       "1689           Aerik  0.017340\n",
       "33    AMerrickanGirl  0.017129"
      ]
     },
     "metadata": {},
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    },
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     "text": [
      "dc\n"
     ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subreddit</th>\n",
       "      <th>dc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>7oby</td>\n",
       "      <td>0.071993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1508</th>\n",
       "      <td>alllie</td>\n",
       "      <td>0.066249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1179</th>\n",
       "      <td>rmuser</td>\n",
       "      <td>0.050701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>qgyh2</td>\n",
       "      <td>0.047855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>355</th>\n",
       "      <td>deuteros</td>\n",
       "      <td>0.038421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>tsteele93</td>\n",
       "      <td>0.035997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>353</th>\n",
       "      <td>NoMoreNicksLeft</td>\n",
       "      <td>0.034784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>798</th>\n",
       "      <td>bobcat</td>\n",
       "      <td>0.031042</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>mutatron</td>\n",
       "      <td>0.028249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>jordanlund</td>\n",
       "      <td>0.025772</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            subreddit        dc\n",
       "47               7oby  0.071993\n",
       "1508           alllie  0.066249\n",
       "1179           rmuser  0.050701\n",
       "86              qgyh2  0.047855\n",
       "355          deuteros  0.038421\n",
       "92          tsteele93  0.035997\n",
       "353   NoMoreNicksLeft  0.034784\n",
       "798            bobcat  0.031042\n",
       "27           mutatron  0.028249\n",
       "82         jordanlund  0.025772"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cc\n"
     ]
    },
    {
     "data": {
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       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>7oby</td>\n",
       "      <td>0.191426</td>\n",
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       "    <tr>\n",
       "      <th>353</th>\n",
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       "      <td>0.189188</td>\n",
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       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>mutatron</td>\n",
       "      <td>0.183276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>fingers</td>\n",
       "      <td>0.182613</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>Poromenos</td>\n",
       "      <td>0.182364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>760</th>\n",
       "      <td>amstrdamordeath</td>\n",
       "      <td>0.181606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>MrKlaatu</td>\n",
       "      <td>0.181215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>sakebomb69</td>\n",
       "      <td>0.180446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>485</th>\n",
       "      <td>uteunawaytay</td>\n",
       "      <td>0.178815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1113</th>\n",
       "      <td>nixonrichard</td>\n",
       "      <td>0.177569</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            subreddit        cc\n",
       "47               7oby  0.191426\n",
       "353   NoMoreNicksLeft  0.189188\n",
       "27           mutatron  0.183276\n",
       "368           fingers  0.182613\n",
       "177         Poromenos  0.182364\n",
       "760   amstrdamordeath  0.181606\n",
       "60           MrKlaatu  0.181215\n",
       "466        sakebomb69  0.180446\n",
       "485      uteunawaytay  0.178815\n",
       "1113     nixonrichard  0.177569"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bc\n"
     ]
    },
    {
     "data": {
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       "      <th>47</th>\n",
       "      <td>7oby</td>\n",
       "      <td>0.038758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1508</th>\n",
       "      <td>alllie</td>\n",
       "      <td>0.021461</td>\n",
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       "      <th>86</th>\n",
       "      <td>qgyh2</td>\n",
       "      <td>0.015406</td>\n",
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       "    <tr>\n",
       "      <th>1179</th>\n",
       "      <td>rmuser</td>\n",
       "      <td>0.014558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>353</th>\n",
       "      <td>NoMoreNicksLeft</td>\n",
       "      <td>0.012480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>mutatron</td>\n",
       "      <td>0.010970</td>\n",
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       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>tsteele93</td>\n",
       "      <td>0.010731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>355</th>\n",
       "      <td>deuteros</td>\n",
       "      <td>0.009837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>798</th>\n",
       "      <td>bobcat</td>\n",
       "      <td>0.008828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>445</th>\n",
       "      <td>glengyron</td>\n",
       "      <td>0.008512</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            subreddit        bc\n",
       "47               7oby  0.038758\n",
       "1508           alllie  0.021461\n",
       "86              qgyh2  0.015406\n",
       "1179           rmuser  0.014558\n",
       "353   NoMoreNicksLeft  0.012480\n",
       "27           mutatron  0.010970\n",
       "92          tsteele93  0.010731\n",
       "355          deuteros  0.009837\n",
       "798            bobcat  0.008828\n",
       "445         glengyron  0.008512"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(usernet_centralities, \"UserNet\", first_n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 17 Most important actors by *Eigenvector* centrality? What can we deduce? \n",
    "\n",
    "Variant of the degree centrality which takes into consideration the node's neighborhood. We can learn about it's power and influence.\n",
    "* A more powerful node is that node which stands out as the one with the most edges, controling the troughput\n",
    "* A more influencal node is that node which blends into a well connected neighborhood, having many edges as well"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eigenvector_centrality2(graph):\n",
    "    dict_ec = nx.eigenvector_centrality(graph, weight=\"weight\")\n",
    "    ec = pd.DataFrame.from_dict(dict_ec, orient=\"index\", columns=[\"eigenvector_centrality\"])\n",
    "    ec.index.name = \"subreddit\"\n",
    "    ec.sort_values(by=\"eigenvector_centrality\", ascending=False, inplace=True)\n",
    "    return ec\n",
    "\n",
    "def eigenvector_centrality(graph, centralities):\n",
    "    centralities[\"evc\"] = nx.eigenvector_centrality(graph, weight=\"weight\").values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvector_centrality(SNet, snet_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evc\n"
     ]
    },
    {
     "data": {
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       "      <th>subreddit</th>\n",
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       "      <td>politics</td>\n",
       "      <td>0.315704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>pics</td>\n",
       "      <td>0.292063</td>\n",
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       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>0.280539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>science</td>\n",
       "      <td>0.273836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>technology</td>\n",
       "      <td>0.265365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.258570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>WTF</td>\n",
       "      <td>0.253545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.253039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>programming</td>\n",
       "      <td>0.220225</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit       evc\n",
       "0       reddit.com  0.384282\n",
       "2         politics  0.315704\n",
       "38            pics  0.292063\n",
       "135          funny  0.280539\n",
       "1          science  0.273836\n",
       "90      technology  0.265365\n",
       "42       worldnews  0.258570\n",
       "103            WTF  0.253545\n",
       "5    entertainment  0.253039\n",
       "7      programming  0.220225"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snet_centralities, \"SNet\", columns=\"evc\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvector_centrality(SNetF, snetf_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evc\n"
     ]
    },
    {
     "data": {
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       "      <th>103</th>\n",
       "      <td>WTF</td>\n",
       "      <td>0.253581</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.253076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>programming</td>\n",
       "      <td>0.220253</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit       evc\n",
       "0       reddit.com  0.384340\n",
       "2         politics  0.315757\n",
       "38            pics  0.292108\n",
       "135          funny  0.280581\n",
       "1          science  0.273877\n",
       "90      technology  0.265404\n",
       "42       worldnews  0.258607\n",
       "103            WTF  0.253581\n",
       "5    entertainment  0.253076\n",
       "7      programming  0.220253"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snetf_centralities, \"SNetF\", columns=\"evc\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvector_centrality(SNetT, snett_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evc\n"
     ]
    },
    {
     "data": {
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       "      <th>24</th>\n",
       "      <td>technology</td>\n",
       "      <td>0.268279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>0.261412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>WTF</td>\n",
       "      <td>0.256010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>0.255542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>programming</td>\n",
       "      <td>0.222823</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        subreddit       evc\n",
       "0      reddit.com  0.388978\n",
       "2        politics  0.319382\n",
       "15           pics  0.295185\n",
       "29          funny  0.283491\n",
       "1         science  0.276774\n",
       "24     technology  0.268279\n",
       "16      worldnews  0.261412\n",
       "25            WTF  0.256010\n",
       "3   entertainment  0.255542\n",
       "4     programming  0.222823"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(snett_centralities, \"SNetT\", columns=\"evc\", first_n=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvector_centrality(UserNet, usernet_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "evc\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subreddit</th>\n",
       "      <th>evc</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>455</th>\n",
       "      <td>malcontent</td>\n",
       "      <td>0.610884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>445</th>\n",
       "      <td>glengyron</td>\n",
       "      <td>0.489433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>457</th>\n",
       "      <td>matts2</td>\n",
       "      <td>0.193855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1764</th>\n",
       "      <td>eaturbrainz</td>\n",
       "      <td>0.154584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>353</th>\n",
       "      <td>NoMoreNicksLeft</td>\n",
       "      <td>0.152510</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>7oby</td>\n",
       "      <td>0.135996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>43P04T34</td>\n",
       "      <td>0.105374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>mexicodoug</td>\n",
       "      <td>0.098352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1129</th>\n",
       "      <td>otakucode</td>\n",
       "      <td>0.095792</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>sakebomb69</td>\n",
       "      <td>0.095213</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            subreddit       evc\n",
       "455        malcontent  0.610884\n",
       "445         glengyron  0.489433\n",
       "457            matts2  0.193855\n",
       "1764      eaturbrainz  0.154584\n",
       "353   NoMoreNicksLeft  0.152510\n",
       "47               7oby  0.135996\n",
       "129          43P04T34  0.105374\n",
       "333        mexicodoug  0.098352\n",
       "1129        otakucode  0.095792\n",
       "466        sakebomb69  0.095213"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print_export_all(usernet_centralities, \"UserNet\", columns=\"evc\", first_n=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 18 Rank nodes using the *Katz* centrality with parameter variation. Play with the beta parameter for the subreddit \"reddit.com\". Show most important actors, with and without specific betas\n",
    "\n",
    "* Katz centrality computes the centrality for a node based on the centrality of its neighbors. It is a generalization of the eigenvector centrality.\n",
    "* The parameter  controls the initial centrality \n",
    "\n",
    " \n",
    "* Katz centrality computes the relative influence of a node within a network by measuring the number of the immediate neighbors (first degree nodes) and also all other nodes in the network that connect to the node under consideration through these immediate neighbors.\n",
    "\n",
    "* This algorithm it uses the power method to find the eigenvector corresponding to the largest eigenvalue of the adjacency matrix of G. The parameter alpha should be strictly less than the inverse of largest eigenvalue of the adjacency matrix for the algorithm to converge. You can use max(nx.adjacency_spectrum(G)) to get  the largest eigenvalue of the adjacency matrix. The iteration will stop after max_iter iterations or an error tolerance of number_of_nodes(G) * tol has been reached.\n",
    "\n",
    "* When $$ \\alpha=\\frac{1}{\\lambda} $$ and $$\\beta=0$$ , Katz centrality is the same as eigenvector centrality."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_alpha(graph):\n",
    "    lambda_max = max(nx.adjacency_spectrum(graph))\n",
    "    print(f\"Max Lambda: {lambda_max}\")\n",
    "    print(f\"alpha need to be < {1.0/lambda_max}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max Lambda: (158672.32654746872+0j)\n",
      "alpha need to be < (6.30229619593331e-06+0j)\n",
      "Max Lambda: (158645.5693695278+0j)\n",
      "alpha need to be < (6.30335914185371e-06+0j)\n",
      "Max Lambda: (155722.39506192337+0j)\n",
      "alpha need to be < (6.421683917732884e-06+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(None, None, None)"
      ]
     },
     "execution_count": 329,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_alpha(SNet), get_alpha(SNetF), get_alpha(SNetT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since there is no need to run UserNet against a subreddit, I will skip Katz' centrality for it.\n",
    "\n",
    "Also, alpha need to be smaller than all three values, so I will take 6.0e-06 as a smaller value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 6e-8 # must be smaller then 0.000006[302... 6.30229619593331e-06]\n",
    "special_node = \"reddit.com\"\n",
    "special_bets = [1.0, 2.0, 4.0, 64.0, 4096.0] # experiment\n",
    "\n",
    "def katz_centrality(graph, beta=1.0):\n",
    "    dict_kc = nx.katz_centrality(graph, alpha=alpha, beta=beta, weight=\"weight\")\n",
    "    kc = pd.DataFrame.from_dict(dict_kc, orient=\"index\", columns=[\"katz_centrality\"])\n",
    "    kc.index.name = \"subreddit\"\n",
    "    kc.sort_values(by=\"katz_centrality\", ascending=False, inplace=True)\n",
    "    return kc\n",
    "\n",
    "def special_katz_centrality(graph, special_beta):\n",
    "    beta_dict = dict([(node, 1.0) for node in graph.nodes()])\n",
    "    beta_dict[special_node] = special_beta\n",
    "    return katz_centrality(graph, beta_dict)\n",
    "\n",
    "def run_katz_regular_and_experiments(graph_name, graph):\n",
    "    def export_katz(graph_name, kc, beta):\n",
    "        df_ = kc.round({\"katz_centrality\": 5}).iloc[:10]\n",
    "        df_.to_csv(f\"data/pandas/centrality-analysis/{graph_name}/katz_centrality_{beta}.csv\")\n",
    "        \n",
    "    print(f\"{graph_name}'s Katz centrality\")\n",
    "\n",
    "    for i in range(len(special_bets)):\n",
    "        print(f\"Beta value: {special_bets[i]}\")\n",
    "        kc = special_katz_centrality(graph, special_bets[i])\n",
    "        if i in [0, 1, 4]:\n",
    "            export_katz(graph_name, kc, special_bets[i])\n",
    "        display(kc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SNet's Katz centrality\n",
      "Beta value: 1.0\n"
     ]
    },
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       "      <th>subreddit</th>\n",
       "      <th></th>\n",
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       "      <th>reddit.com</th>\n",
       "      <td>0.015769</td>\n",
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       "      <th>politics</th>\n",
       "      <td>0.015705</td>\n",
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       "      <td>0.015689</td>\n",
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       "      <td>0.015676</td>\n",
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       "      <th>...</th>\n",
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       "      <th>cts</th>\n",
       "      <td>0.015446</td>\n",
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       "    <tr>\n",
       "      <th>TUPOEorg</th>\n",
       "      <td>0.015446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Joseph4u</th>\n",
       "      <td>0.015446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>globalpoon</th>\n",
       "      <td>0.015446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AllAccess</th>\n",
       "      <td>0.015446</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>4191 rows × 1 columns</p>\n",
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      ],
      "text/plain": [
       "            katz_centrality\n",
       "subreddit                  \n",
       "reddit.com         0.015769\n",
       "politics           0.015705\n",
       "pics               0.015689\n",
       "funny              0.015679\n",
       "science            0.015676\n",
       "...                     ...\n",
       "cts                0.015446\n",
       "TUPOEorg           0.015446\n",
       "Joseph4u           0.015446\n",
       "globalpoon         0.015446\n",
       "AllAccess          0.015446\n",
       "\n",
       "[4191 rows x 1 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta value: 2.0\n"
     ]
    },
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       "      <th>reddit.com</th>\n",
       "      <td>0.031203</td>\n",
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       "      <th>politics</th>\n",
       "      <td>0.015724</td>\n",
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       "      <th>science</th>\n",
       "      <td>0.015688</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>OhWord</th>\n",
       "      <td>0.015440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>oseun</th>\n",
       "      <td>0.015440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oliviaryan</th>\n",
       "      <td>0.015440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>webmaster123</th>\n",
       "      <td>0.015440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dilipm</th>\n",
       "      <td>0.015440</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>4191 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              katz_centrality\n",
       "subreddit                    \n",
       "reddit.com           0.031203\n",
       "politics             0.015724\n",
       "pics                 0.015704\n",
       "funny                0.015692\n",
       "science              0.015688\n",
       "...                       ...\n",
       "OhWord               0.015440\n",
       "oseun                0.015440\n",
       "Oliviaryan           0.015440\n",
       "webmaster123         0.015440\n",
       "dilipm               0.015440\n",
       "\n",
       "[4191 rows x 1 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta value: 4.0\n"
     ]
    },
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       "      <td>0.015418</td>\n",
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       "      <td>0.015418</td>\n",
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       "      <th>adnerds</th>\n",
       "      <td>0.015418</td>\n",
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       "      <td>0.015418</td>\n",
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       "                     katz_centrality\n",
       "subreddit                           \n",
       "reddit.com                  0.061994\n",
       "politics                    0.015751\n",
       "pics                        0.015721\n",
       "funny                       0.015708\n",
       "science                     0.015702\n",
       "...                              ...\n",
       "downloadfromyoutube         0.015418\n",
       "Subzero                     0.015418\n",
       "OddSizeBeds                 0.015418\n",
       "adnerds                     0.015418\n",
       "cts                         0.015418\n",
       "\n",
       "[4191 rows x 1 columns]"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
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     "text": [
      "Beta value: 64.0\n"
     ]
    },
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       "      <td>0.010982</td>\n",
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       "      <th>newsfusion</th>\n",
       "      <td>0.010982</td>\n",
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       "    <tr>\n",
       "      <th>akilito</th>\n",
       "      <td>0.010982</td>\n",
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       "    <tr>\n",
       "      <th>Cliche</th>\n",
       "      <td>0.010982</td>\n",
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      "text/plain": [
       "                katz_centrality\n",
       "subreddit                      \n",
       "reddit.com             0.703061\n",
       "politics               0.012287\n",
       "pics                   0.012053\n",
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       "technology             0.011984\n",
       "...                         ...\n",
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       "newsfusion             0.010982\n",
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       "\n",
       "[4191 rows x 1 columns]"
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      "Beta value: 4096.0\n"
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       "                 katz_centrality\n",
       "subreddit                       \n",
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       "pics                    0.001545\n",
       "funny                   0.001473\n",
       "technology              0.001468\n",
       "...                          ...\n",
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       "\n",
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   "source": [
    "run_katz_regular_and_experiments(\"SNet\", SNet)"
   ]
  },
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      "SNetF's Katz centrality\n",
      "Beta value: 1.0\n"
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       "               katz_centrality\n",
       "subreddit                     \n",
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       "politics              0.015698\n",
       "pics                  0.015683\n",
       "funny                 0.015673\n",
       "science               0.015669\n",
       "...                        ...\n",
       "ManchesterUTD         0.015446\n",
       "apod                  0.015446\n",
       "implead               0.015446\n",
       "FREE                  0.015446\n",
       "timelapses            0.015446\n",
       "\n",
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       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.031195\n",
       "politics              0.015717\n",
       "pics                  0.015697\n",
       "funny                 0.015686\n",
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       "...                        ...\n",
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       "implead               0.015440\n",
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       "\n",
       "[4191 rows x 1 columns]"
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      "Beta value: 4.0\n"
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       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.061986\n",
       "politics              0.015745\n",
       "pics                  0.015715\n",
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       "...                        ...\n",
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       "implead               0.015418\n",
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       "\n",
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      "Beta value: 64.0\n"
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       "               katz_centrality\n",
       "subreddit                     \n",
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       "politics              0.012282\n",
       "pics                  0.012048\n",
       "funny                 0.011991\n",
       "technology            0.011979\n",
       "...                        ...\n",
       "ManchesterUTD         0.010982\n",
       "apod                  0.010982\n",
       "implead               0.010982\n",
       "FREE                  0.010982\n",
       "timelapses            0.010982\n",
       "\n",
       "[4191 rows x 1 columns]"
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      "text/plain": [
       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.999862\n",
       "politics              0.001868\n",
       "pics                  0.001545\n",
       "funny                 0.001473\n",
       "technology            0.001468\n",
       "...                        ...\n",
       "ManchesterUTD         0.000244\n",
       "apod                  0.000244\n",
       "implead               0.000244\n",
       "FREE                  0.000244\n",
       "timelapses            0.000244\n",
       "\n",
       "[4191 rows x 1 columns]"
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   "source": [
    "run_katz_regular_and_experiments(\"SNetF\", SNetF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SNetT's Katz centrality\n",
      "Beta value: 1.0\n"
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       "               katz_centrality\n",
       "subreddit                     \n",
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       "               katz_centrality\n",
       "subreddit                     \n",
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       "      <td>0.135440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>software</th>\n",
       "      <td>0.135389</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>guns</th>\n",
       "      <td>0.135385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>joel</th>\n",
       "      <td>0.135346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ideas</th>\n",
       "      <td>0.135339</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.543589\n",
       "politics              0.137812\n",
       "pics                  0.137558\n",
       "funny                 0.137455\n",
       "science               0.137407\n",
       "technology            0.137364\n",
       "worldnews             0.137272\n",
       "entertainment         0.137264\n",
       "WTF                   0.137229\n",
       "business              0.137000\n",
       "programming           0.136989\n",
       "offbeat               0.136441\n",
       "gaming                0.136421\n",
       "atheism               0.136098\n",
       "comics                0.136072\n",
       "Economics             0.136037\n",
       "AskReddit             0.136035\n",
       "nsfw                  0.135988\n",
       "videos                0.135977\n",
       "environment           0.135973\n",
       "gadgets               0.135965\n",
       "geek                  0.135900\n",
       "obama                 0.135812\n",
       "bestof                0.135656\n",
       "news                  0.135649\n",
       "linux                 0.135648\n",
       "Health                0.135579\n",
       "scifi                 0.135572\n",
       "cogsci                0.135545\n",
       "math                  0.135513\n",
       "philosophy            0.135507\n",
       "netsec                0.135503\n",
       "history               0.135449\n",
       "canada                0.135443\n",
       "photography           0.135440\n",
       "software              0.135389\n",
       "guns                  0.135385\n",
       "joel                  0.135346\n",
       "ideas                 0.135339"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta value: 64.0\n"
     ]
    },
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       "      <th>obama</th>\n",
       "      <td>0.015806</td>\n",
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       "    <tr>\n",
       "      <th>linux</th>\n",
       "      <td>0.015712</td>\n",
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       "    <tr>\n",
       "      <th>news</th>\n",
       "      <td>0.015699</td>\n",
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       "      <th>bestof</th>\n",
       "      <td>0.015698</td>\n",
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       "      <td>0.015670</td>\n",
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       "      <th>netsec</th>\n",
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       "      <th>philosophy</th>\n",
       "      <td>0.015631</td>\n",
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       "      <td>0.015601</td>\n",
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       "      <td>0.015601</td>\n",
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       "      <td>0.015576</td>\n",
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       "      <th>guns</th>\n",
       "      <td>0.015574</td>\n",
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       "      <th>joel</th>\n",
       "      <td>0.015564</td>\n",
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       "    <tr>\n",
       "      <th>ideas</th>\n",
       "      <td>0.015552</td>\n",
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      "text/plain": [
       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.995084\n",
       "politics              0.017342\n",
       "pics                  0.017011\n",
       "funny                 0.016932\n",
       "technology            0.016917\n",
       "science               0.016883\n",
       "entertainment         0.016868\n",
       "worldnews             0.016801\n",
       "WTF                   0.016738\n",
       "business              0.016725\n",
       "programming           0.016640\n",
       "gaming                0.016178\n",
       "offbeat               0.016153\n",
       "atheism               0.015967\n",
       "Economics             0.015936\n",
       "comics                0.015932\n",
       "AskReddit             0.015912\n",
       "nsfw                  0.015902\n",
       "environment           0.015889\n",
       "gadgets               0.015883\n",
       "videos                0.015882\n",
       "geek                  0.015829\n",
       "obama                 0.015806\n",
       "linux                 0.015712\n",
       "news                  0.015699\n",
       "bestof                0.015698\n",
       "Health                0.015670\n",
       "scifi                 0.015662\n",
       "cogsci                0.015647\n",
       "math                  0.015639\n",
       "netsec                0.015634\n",
       "philosophy            0.015631\n",
       "canada                0.015606\n",
       "history               0.015601\n",
       "photography           0.015601\n",
       "software              0.015576\n",
       "guns                  0.015574\n",
       "joel                  0.015564\n",
       "ideas                 0.015552"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Beta value: 4096.0\n"
     ]
    },
    {
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       "      <th>obama</th>\n",
       "      <td>0.000465</td>\n",
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       "    <tr>\n",
       "      <th>linux</th>\n",
       "      <td>0.000385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>news</th>\n",
       "      <td>0.000370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bestof</th>\n",
       "      <td>0.000369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Health</th>\n",
       "      <td>0.000348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scifi</th>\n",
       "      <td>0.000340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cogsci</th>\n",
       "      <td>0.000328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>math</th>\n",
       "      <td>0.000323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>netsec</th>\n",
       "      <td>0.000319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>philosophy</th>\n",
       "      <td>0.000315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>canada</th>\n",
       "      <td>0.000296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>photography</th>\n",
       "      <td>0.000291</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>history</th>\n",
       "      <td>0.000290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>software</th>\n",
       "      <td>0.000270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>guns</th>\n",
       "      <td>0.000269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>joel</th>\n",
       "      <td>0.000262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ideas</th>\n",
       "      <td>0.000251</td>\n",
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      "text/plain": [
       "               katz_centrality\n",
       "subreddit                     \n",
       "reddit.com            0.999987\n",
       "politics              0.001868\n",
       "pics                  0.001545\n",
       "funny                 0.001472\n",
       "technology            0.001467\n",
       "entertainment         0.001427\n",
       "science               0.001426\n",
       "worldnews             0.001354\n",
       "business              0.001305\n",
       "WTF                   0.001291\n",
       "programming           0.001215\n",
       "gaming                0.000790\n",
       "offbeat               0.000760\n",
       "atheism               0.000603\n",
       "Economics             0.000577\n",
       "comics                0.000569\n",
       "AskReddit             0.000552\n",
       "nsfw                  0.000547\n",
       "environment           0.000534\n",
       "gadgets               0.000530\n",
       "videos                0.000527\n",
       "geek                  0.000479\n",
       "obama                 0.000465\n",
       "linux                 0.000385\n",
       "news                  0.000370\n",
       "bestof                0.000369\n",
       "Health                0.000348\n",
       "scifi                 0.000340\n",
       "cogsci                0.000328\n",
       "math                  0.000323\n",
       "netsec                0.000319\n",
       "philosophy            0.000315\n",
       "canada                0.000296\n",
       "photography           0.000291\n",
       "history               0.000290\n",
       "software              0.000270\n",
       "guns                  0.000269\n",
       "joel                  0.000262\n",
       "ideas                 0.000251"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "run_katz_regular_and_experiments(\"SNetT\", SNetT)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  19 Taking into account the previous results, create a composite centrality (heuristic) used for finding the most influencial actors. Take into consideration the direction of network's edges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [],
   "source": [
    "columns = ['dc', 'cc', 'bc', 'evc']\n",
    "cross_correlation_matrix = pd.DataFrame(columns = columns, index = columns)\n",
    "p_val_matrix = pd.DataFrame(columns = columns, index = columns)\n",
    "\n",
    "def display_network_centralities_corelation(centralities):\n",
    "    for ind in columns:\n",
    "        for col in columns:\n",
    "            cross_correlation_matrix[ind][col], p_val_matrix[ind][col] =  stats.kendalltau(centralities[ind], centralities[col])\n",
    "    display(cross_correlation_matrix)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "metadata": {},
   "outputs": [],
   "source": [
    "def display_network_centralities_corelation_directed(centralities):\n",
    "    columns = ['in_dc', 'out_dc', 'dc', 'cc', 'bc', 'evc']\n",
    "    cross_correlation_matrix = pd.DataFrame(columns = columns, index = columns)\n",
    "    p_val_matrix = pd.DataFrame(columns = columns, index = columns)\n",
    "\n",
    "    def display_network_centralities_corelation(centralities):\n",
    "        for ind in columns:\n",
    "            for col in columns:\n",
    "                cross_correlation_matrix[ind][col], p_val_matrix[ind][col] =  stats.kendalltau(centralities[ind], centralities[col])\n",
    "        display(cross_correlation_matrix)\n",
    "        \n",
    "    display_network_centralities_corelation(centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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       "      <th>dc</th>\n",
       "      <td>1</td>\n",
       "      <td>0.911422</td>\n",
       "      <td>0.609986</td>\n",
       "      <td>0.886224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cc</th>\n",
       "      <td>0.911422</td>\n",
       "      <td>1</td>\n",
       "      <td>0.589153</td>\n",
       "      <td>0.93076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc</th>\n",
       "      <td>0.609986</td>\n",
       "      <td>0.589153</td>\n",
       "      <td>1</td>\n",
       "      <td>0.611159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>evc</th>\n",
       "      <td>0.886224</td>\n",
       "      <td>0.93076</td>\n",
       "      <td>0.611159</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           dc        cc        bc       evc\n",
       "dc          1  0.911422  0.609986  0.886224\n",
       "cc   0.911422         1  0.589153   0.93076\n",
       "bc   0.609986  0.589153         1  0.611159\n",
       "evc  0.886224   0.93076  0.611159         1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_network_centralities_corelation(snet_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {
    "scrolled": true
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   "outputs": [
    {
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       "      <th>evc</th>\n",
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       "      <th>dc</th>\n",
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       "      <td>0.999833</td>\n",
       "      <td>0.601048</td>\n",
       "      <td>0.998407</td>\n",
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       "    <tr>\n",
       "      <th>cc</th>\n",
       "      <td>0.999833</td>\n",
       "      <td>1</td>\n",
       "      <td>0.60102</td>\n",
       "      <td>0.99835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc</th>\n",
       "      <td>0.601048</td>\n",
       "      <td>0.60102</td>\n",
       "      <td>1</td>\n",
       "      <td>0.600725</td>\n",
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       "    <tr>\n",
       "      <th>evc</th>\n",
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      "text/plain": [
       "           dc        cc        bc       evc\n",
       "dc          1  0.999833  0.601048  0.998407\n",
       "cc   0.999833         1   0.60102   0.99835\n",
       "bc   0.601048   0.60102         1  0.600725\n",
       "evc  0.998407   0.99835  0.600725         1"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "display_network_centralities_corelation(snetf_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "      <th>evc</th>\n",
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       "      <th>cc</th>\n",
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       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>evc</th>\n",
       "      <td>NaN</td>\n",
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      ],
      "text/plain": [
       "      dc   cc   bc  evc\n",
       "dc   NaN  NaN  NaN  NaN\n",
       "cc   NaN  NaN  NaN  NaN\n",
       "bc   NaN  NaN  NaN  NaN\n",
       "evc  NaN  NaN  NaN    1"
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "display_network_centralities_corelation(snett_centralities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no correlation between the centralities as SNetT is a complete graph, but this is not the case for SNet and SnetF.\n",
    "\n",
    "As we can see, the DC, CC, BC and ECV were positivly coupled, we can merely get the product of the four.\n",
    "\n",
    "**Composite Centrality = DC x CC x BC x EC**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>in_dc</th>\n",
       "      <th>out_dc</th>\n",
       "      <th>dc</th>\n",
       "      <th>cc</th>\n",
       "      <th>bc</th>\n",
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       "      <th>in_dc</th>\n",
       "      <td>1</td>\n",
       "      <td>0.0101579</td>\n",
       "      <td>0.572156</td>\n",
       "      <td>0.791484</td>\n",
       "      <td>0.506611</td>\n",
       "      <td>0.776835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>out_dc</th>\n",
       "      <td>0.0101579</td>\n",
       "      <td>1</td>\n",
       "      <td>0.569698</td>\n",
       "      <td>-0.0156851</td>\n",
       "      <td>0.626385</td>\n",
       "      <td>-0.0191839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dc</th>\n",
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       "      <td>0.441165</td>\n",
       "      <td>0.625256</td>\n",
       "      <td>0.430959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cc</th>\n",
       "      <td>0.791484</td>\n",
       "      <td>-0.0156851</td>\n",
       "      <td>0.441165</td>\n",
       "      <td>1</td>\n",
       "      <td>0.434603</td>\n",
       "      <td>0.926985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>bc</th>\n",
       "      <td>0.506611</td>\n",
       "      <td>0.626385</td>\n",
       "      <td>0.625256</td>\n",
       "      <td>0.434603</td>\n",
       "      <td>1</td>\n",
       "      <td>0.427817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>evc</th>\n",
       "      <td>0.776835</td>\n",
       "      <td>-0.0191839</td>\n",
       "      <td>0.430959</td>\n",
       "      <td>0.926985</td>\n",
       "      <td>0.427817</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            in_dc     out_dc        dc         cc        bc        evc\n",
       "in_dc           1  0.0101579  0.572156   0.791484  0.506611   0.776835\n",
       "out_dc  0.0101579          1  0.569698 -0.0156851  0.626385 -0.0191839\n",
       "dc       0.572156   0.569698         1   0.441165  0.625256   0.430959\n",
       "cc       0.791484 -0.0156851  0.441165          1  0.434603   0.926985\n",
       "bc       0.506611   0.626385  0.625256   0.434603         1   0.427817\n",
       "evc      0.776835 -0.0191839  0.430959   0.926985  0.427817          1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_network_centralities_corelation_directed(usernet_centralities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we get an interesting example: The Out-degree is negativly coupled! \n",
    "So for the UserNet's composite, I would drop the DC and rearrange the In_DC and Out_DC\n",
    "\n",
    "**Composite Centrality UserNet = (In_DC / Out_DC) x CC x BC x EC**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "todo rewrite\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "def composite_centrality_SNet(graph_name, centralities):\n",
    "    copy = centralities\n",
    "    columns = [\"dc\", \"cc\", \"bc\", \"evc\"]\n",
    "\n",
    "    for metric in columns:\n",
    "        copy[f\"{metric}_rank\"] = copy[metric].rank(ascending=False) \n",
    "\n",
    "    copy['composite_rank'] = copy['dc_rank'] * copy['cc_rank'] * copy['bc_rank'] * copy['evc_rank']\n",
    "    cc = copy[[\"subreddit\", \"composite_rank\"]].sort_values(['composite_rank'], ascending=True).head(10)\n",
    "    \n",
    "    cc.to_csv(f\"data/pandas/centrality-analysis/{graph_name}/composite_centrality.csv\")\n",
    "    display(cc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>subreddit</th>\n",
       "      <th>composite_rank</th>\n",
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       "      <th>0</th>\n",
       "      <td>reddit.com</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>politics</td>\n",
       "      <td>48.0</td>\n",
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       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>technology</td>\n",
       "      <td>72.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>pics</td>\n",
       "      <td>288.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>900.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>science</td>\n",
       "      <td>1800.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>programming</td>\n",
       "      <td>2565.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>3087.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>3584.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>business</td>\n",
       "      <td>6655.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit  composite_rank\n",
       "0       reddit.com             1.0\n",
       "2         politics            48.0\n",
       "90      technology            72.0\n",
       "38            pics           288.0\n",
       "135          funny           900.0\n",
       "1          science          1800.0\n",
       "7      programming          2565.0\n",
       "5    entertainment          3087.0\n",
       "42       worldnews          3584.0\n",
       "8         business          6655.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "composite_centrality_SNet(\"SNet\", snet_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>subreddit</th>\n",
       "      <th>composite_rank</th>\n",
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       "      <th>0</th>\n",
       "      <td>reddit.com</td>\n",
       "      <td>1.00</td>\n",
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       "      <th>2</th>\n",
       "      <td>politics</td>\n",
       "      <td>36.00</td>\n",
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       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>pics</td>\n",
       "      <td>36.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>technology</td>\n",
       "      <td>486.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>science</td>\n",
       "      <td>506.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>funny</td>\n",
       "      <td>1008.00</td>\n",
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       "      <th>42</th>\n",
       "      <td>worldnews</td>\n",
       "      <td>2744.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103</th>\n",
       "      <td>WTF</td>\n",
       "      <td>4608.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>programming</td>\n",
       "      <td>6000.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>7290.00</td>\n",
       "    </tr>\n",
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       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         subreddit  composite_rank\n",
       "0       reddit.com            1.00\n",
       "2         politics           36.00\n",
       "38            pics           36.00\n",
       "90      technology          486.00\n",
       "1          science          506.25\n",
       "135          funny         1008.00\n",
       "42       worldnews         2744.00\n",
       "103            WTF         4608.00\n",
       "7      programming         6000.00\n",
       "5    entertainment         7290.00"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "composite_centrality_SNet(\"SNetF\", snetf_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "      <td>8000.0</td>\n",
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       "      <td>politics</td>\n",
       "      <td>16000.0</td>\n",
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       "      <th>15</th>\n",
       "      <td>pics</td>\n",
       "      <td>24000.0</td>\n",
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       "      <th>29</th>\n",
       "      <td>funny</td>\n",
       "      <td>32000.0</td>\n",
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       "      <td>56000.0</td>\n",
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       "      <th>25</th>\n",
       "      <td>WTF</td>\n",
       "      <td>64000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>entertainment</td>\n",
       "      <td>72000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>programming</td>\n",
       "      <td>80000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        subreddit  composite_rank\n",
       "0      reddit.com          8000.0\n",
       "2        politics         16000.0\n",
       "15           pics         24000.0\n",
       "29          funny         32000.0\n",
       "1         science         40000.0\n",
       "24     technology         48000.0\n",
       "16      worldnews         56000.0\n",
       "25            WTF         64000.0\n",
       "3   entertainment         72000.0\n",
       "4     programming         80000.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "composite_centrality_SNet(\"SNetT\", snett_centralities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def composite_centrality_UserNet(graph_name, centralities):\n",
    "    copy = centralities\n",
    "    columns = [\"in_dc\", \"out_dc\", \"cc\", \"bc\", \"evc\"]\n",
    "\n",
    "    for metric in columns:\n",
    "        copy[f\"{metric}_rank\"] = copy[metric].rank(ascending=False)\n",
    "\n",
    "    copy['composite_rank'] = copy['cc_rank'] * copy['bc_rank'] * copy['evc_rank'] * copy['in_dc_rank'] / copy['out_dc_rank']\n",
    "    cc = copy.sort_values(['composite_rank'], ascending=True).head(10)\n",
    "    \n",
    "    cc[[\"subreddit\", \"composite_rank\"]].round({\"composite_rank\":5}).to_csv(f\"data/pandas/centrality-analysis/{graph_name}/composite_centrality.csv\")\n",
    "    display(cc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subreddit</th>\n",
       "      <th>in_dc</th>\n",
       "      <th>out_dc</th>\n",
       "      <th>dc</th>\n",
       "      <th>cc</th>\n",
       "      <th>bc</th>\n",
       "      <th>evc</th>\n",
       "      <th>in_dc_rank</th>\n",
       "      <th>out_dc_rank</th>\n",
       "      <th>cc_rank</th>\n",
       "      <th>bc_rank</th>\n",
       "      <th>evc_rank</th>\n",
       "      <th>composite_rank</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>353</th>\n",
       "      <td>NoMoreNicksLeft</td>\n",
       "      <td>0.024507</td>\n",
       "      <td>0.010277</td>\n",
       "      <td>0.034784</td>\n",
       "      <td>0.189188</td>\n",
       "      <td>0.012480</td>\n",
       "      <td>0.152510</td>\n",
       "      <td>1.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>7oby</td>\n",
       "      <td>0.022873</td>\n",
       "      <td>0.049120</td>\n",
       "      <td>0.071993</td>\n",
       "      <td>0.191426</td>\n",
       "      <td>0.038758</td>\n",
       "      <td>0.135996</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>mutatron</td>\n",
       "      <td>0.021292</td>\n",
       "      <td>0.006957</td>\n",
       "      <td>0.028249</td>\n",
       "      <td>0.183276</td>\n",
       "      <td>0.010970</td>\n",
       "      <td>0.079680</td>\n",
       "      <td>3.0</td>\n",
       "      <td>83.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>9.108434</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>455</th>\n",
       "      <td>malcontent</td>\n",
       "      <td>0.015284</td>\n",
       "      <td>0.005639</td>\n",
       "      <td>0.020923</td>\n",
       "      <td>0.177307</td>\n",
       "      <td>0.005668</td>\n",
       "      <td>0.610884</td>\n",
       "      <td>10.0</td>\n",
       "      <td>120.5</td>\n",
       "      <td>11.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>17.344398</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>fingers</td>\n",
       "      <td>0.016338</td>\n",
       "      <td>0.002899</td>\n",
       "      <td>0.019237</td>\n",
       "      <td>0.182613</td>\n",
       "      <td>0.004657</td>\n",
       "      <td>0.056537</td>\n",
       "      <td>5.0</td>\n",
       "      <td>341.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>29.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>40.821114</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>760</th>\n",
       "      <td>amstrdamordeath</td>\n",
       "      <td>0.015811</td>\n",
       "      <td>0.003689</td>\n",
       "      <td>0.019500</td>\n",
       "      <td>0.181606</td>\n",
       "      <td>0.005810</td>\n",
       "      <td>0.080378</td>\n",
       "      <td>7.5</td>\n",
       "      <td>255.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>18.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>41.294118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>457</th>\n",
       "      <td>matts2</td>\n",
       "      <td>0.015969</td>\n",
       "      <td>0.003373</td>\n",
       "      <td>0.019342</td>\n",
       "      <td>0.177058</td>\n",
       "      <td>0.003335</td>\n",
       "      <td>0.193855</td>\n",
       "      <td>6.0</td>\n",
       "      <td>288.5</td>\n",
       "      <td>14.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>43.674177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>sakebomb69</td>\n",
       "      <td>0.014494</td>\n",
       "      <td>0.001687</td>\n",
       "      <td>0.016180</td>\n",
       "      <td>0.180446</td>\n",
       "      <td>0.003050</td>\n",
       "      <td>0.095213</td>\n",
       "      <td>11.0</td>\n",
       "      <td>629.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>72.750397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>177</th>\n",
       "      <td>Poromenos</td>\n",
       "      <td>0.017392</td>\n",
       "      <td>0.002582</td>\n",
       "      <td>0.019975</td>\n",
       "      <td>0.182364</td>\n",
       "      <td>0.002872</td>\n",
       "      <td>0.055088</td>\n",
       "      <td>4.0</td>\n",
       "      <td>388.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>28.0</td>\n",
       "      <td>80.824742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>MrKlaatu</td>\n",
       "      <td>0.015811</td>\n",
       "      <td>0.001845</td>\n",
       "      <td>0.017656</td>\n",
       "      <td>0.181215</td>\n",
       "      <td>0.004245</td>\n",
       "      <td>0.030794</td>\n",
       "      <td>7.5</td>\n",
       "      <td>572.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>184.484266</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           subreddit     in_dc    out_dc        dc        cc        bc  \\\n",
       "353  NoMoreNicksLeft  0.024507  0.010277  0.034784  0.189188  0.012480   \n",
       "47              7oby  0.022873  0.049120  0.071993  0.191426  0.038758   \n",
       "27          mutatron  0.021292  0.006957  0.028249  0.183276  0.010970   \n",
       "455       malcontent  0.015284  0.005639  0.020923  0.177307  0.005668   \n",
       "368          fingers  0.016338  0.002899  0.019237  0.182613  0.004657   \n",
       "760  amstrdamordeath  0.015811  0.003689  0.019500  0.181606  0.005810   \n",
       "457           matts2  0.015969  0.003373  0.019342  0.177058  0.003335   \n",
       "466       sakebomb69  0.014494  0.001687  0.016180  0.180446  0.003050   \n",
       "177        Poromenos  0.017392  0.002582  0.019975  0.182364  0.002872   \n",
       "60          MrKlaatu  0.015811  0.001845  0.017656  0.181215  0.004245   \n",
       "\n",
       "          evc  in_dc_rank  out_dc_rank  cc_rank  bc_rank  evc_rank  \\\n",
       "353  0.152510         1.0         40.0      2.0      5.0       5.0   \n",
       "47   0.135996         2.0          2.0      1.0      1.0       6.0   \n",
       "27   0.079680         3.0         83.0      3.0      6.0      14.0   \n",
       "455  0.610884        10.0        120.5     11.0     19.0       1.0   \n",
       "368  0.056537         5.0        341.0      4.0     29.0      24.0   \n",
       "760  0.080378         7.5        255.0      6.0     18.0      13.0   \n",
       "457  0.193855         6.0        288.5     14.0     50.0       3.0   \n",
       "466  0.095213        11.0        629.0      8.0     52.0      10.0   \n",
       "177  0.055088         4.0        388.0      5.0     56.0      28.0   \n",
       "60   0.030794         7.5        572.0      7.0     30.0      67.0   \n",
       "\n",
       "     composite_rank  \n",
       "353        1.250000  \n",
       "47         6.000000  \n",
       "27         9.108434  \n",
       "455       17.344398  \n",
       "368       40.821114  \n",
       "760       41.294118  \n",
       "457       43.674177  \n",
       "466       72.750397  \n",
       "177       80.824742  \n",
       "60       184.484266  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "composite_centrality_UserNet(\"UserNet\", usernet_centralities)"
   ]
  }
 ],
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