conference_notebooks/ASONAM_2019/Weighted_Link_Prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Weighted Link Prediction w/ Uncertainty using cuGraph and the Epinions Trust Network Dataset\n",
    "\n",
    "This notebook builds a binary nearest neighbor classifier using a weighted average of the weighted jaccard similarity measure, where the labels of the closer neighbors are weighted more heavily. A hyper-parameter is provided to trade-off the influence of labels from very distant vertices. The weighted average is passed through a sigmoid function and used as a classifier to predict the likelihood of trust, or distrust, between vertices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cugraph\n",
    "import cuml\n",
    "import cudf\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as p\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset_path = \"../data/epinions.txt\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 392 ms, sys: 768 ms, total: 1.16 s\n",
      "Wall time: 1.15 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gdf = cudf.read_csv(dataset_path, sep=\"\\t\", header=0, names=[\"src\", \"dst\", \"trust\"], dtype=[\"int32\", \"int32\", \"float32\"]).fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data represents a social network graph from source users to destination users with weights `-1` for untrusted and `1` for trusted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 100 ms, sys: 28 ms, total: 128 ms\n",
      "Wall time: 133 ms\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>128552</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>155</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   src     dst  trust\n",
       "0    0       1   -1.0\n",
       "1    1  128552   -1.0\n",
       "2    2       3    1.0\n",
       "3    4       5   -1.0\n",
       "4    4     155   -1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "gdf.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we want to get a feel for the distribution of the trust labels. The labels are not represented evenly across our dataset. There are almost twice as many positive labels are negative labels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
      "Wall time: 23.2 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fd6475d7e10>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "gdf[\"trust\"].to_pandas().hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now look at the distribution of the labels among the vertices. We can see we have some vertices with "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 152 ms, sys: 40 ms, total: 192 ms\n",
      "Wall time: 232 ms\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>src</th>\n",
       "      <th>trust</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>189</th>\n",
       "      <td>167</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>371</th>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>408</th>\n",
       "      <td>353</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2086</th>\n",
       "      <td>1652</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1178</th>\n",
       "      <td>966</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>774</th>\n",
       "      <td>655</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1366</th>\n",
       "      <td>1118</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2120</th>\n",
       "      <td>1682</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1120</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1033</th>\n",
       "      <td>852</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>20</td>\n",
       "      <td>1.0</td>\n",
       "      <td>967</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>890</th>\n",
       "      <td>735</td>\n",
       "      <td>1.0</td>\n",
       "      <td>881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>692</th>\n",
       "      <td>578</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>708</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2031</th>\n",
       "      <td>1608</td>\n",
       "      <td>1.0</td>\n",
       "      <td>690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>211</td>\n",
       "      <td>1.0</td>\n",
       "      <td>664</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1861</th>\n",
       "      <td>1480</td>\n",
       "      <td>1.0</td>\n",
       "      <td>585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2383</th>\n",
       "      <td>1894</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1569</th>\n",
       "      <td>1287</td>\n",
       "      <td>1.0</td>\n",
       "      <td>517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>1.0</td>\n",
       "      <td>498</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>481</th>\n",
       "      <td>410</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1673</th>\n",
       "      <td>1352</td>\n",
       "      <td>1.0</td>\n",
       "      <td>476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1032</th>\n",
       "      <td>851</td>\n",
       "      <td>1.0</td>\n",
       "      <td>451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1916</th>\n",
       "      <td>1512</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>535</th>\n",
       "      <td>450</td>\n",
       "      <td>1.0</td>\n",
       "      <td>426</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>427</th>\n",
       "      <td>366</td>\n",
       "      <td>1.0</td>\n",
       "      <td>419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2026</th>\n",
       "      <td>1605</td>\n",
       "      <td>1.0</td>\n",
       "      <td>419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>176</th>\n",
       "      <td>155</td>\n",
       "      <td>1.0</td>\n",
       "      <td>410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1765</th>\n",
       "      <td>1420</td>\n",
       "      <td>1.0</td>\n",
       "      <td>393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1263</th>\n",
       "      <td>1037</td>\n",
       "      <td>1.0</td>\n",
       "      <td>381</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1786</th>\n",
       "      <td>1438</td>\n",
       "      <td>1.0</td>\n",
       "      <td>371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2446</th>\n",
       "      <td>1938</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2449</th>\n",
       "      <td>1940</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2450</th>\n",
       "      <td>1941</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2451</th>\n",
       "      <td>1941</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2452</th>\n",
       "      <td>1942</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2462</th>\n",
       "      <td>1949</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2489</th>\n",
       "      <td>1963</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2490</th>\n",
       "      <td>1964</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2491</th>\n",
       "      <td>1965</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2494</th>\n",
       "      <td>1967</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2500</th>\n",
       "      <td>1971</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2506</th>\n",
       "      <td>1974</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2507</th>\n",
       "      <td>1975</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2508</th>\n",
       "      <td>1976</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2510</th>\n",
       "      <td>1978</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2511</th>\n",
       "      <td>1980</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2513</th>\n",
       "      <td>1982</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2517</th>\n",
       "      <td>1985</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2519</th>\n",
       "      <td>1987</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2521</th>\n",
       "      <td>1991</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2522</th>\n",
       "      <td>1992</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2523</th>\n",
       "      <td>1994</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2524</th>\n",
       "      <td>1995</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2526</th>\n",
       "      <td>1997</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2527</th>\n",
       "      <td>1998</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2531</th>\n",
       "      <td>2003</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2532</th>\n",
       "      <td>2003</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2533</th>\n",
       "      <td>2004</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2539</th>\n",
       "      <td>2009</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2541</th>\n",
       "      <td>2010</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2543 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       src  trust  count\n",
       "189    167    1.0   1893\n",
       "371    321    1.0   1776\n",
       "408    353    1.0   1740\n",
       "2086  1652   -1.0   1562\n",
       "1178   966   -1.0   1217\n",
       "774    655   -1.0   1193\n",
       "1366  1118   -1.0   1137\n",
       "2120  1682   -1.0   1120\n",
       "1033   852    1.0   1017\n",
       "23      20    1.0    967\n",
       "890    735    1.0    881\n",
       "692    578   -1.0    708\n",
       "2031  1608    1.0    690\n",
       "245    211    1.0    664\n",
       "1861  1480    1.0    585\n",
       "2383  1894   -1.0    528\n",
       "1569  1287    1.0    517\n",
       "6        5    1.0    498\n",
       "5        5   -1.0    491\n",
       "481    410   -1.0    482\n",
       "1673  1352    1.0    476\n",
       "1032   851    1.0    451\n",
       "1916  1512   -1.0    429\n",
       "535    450    1.0    426\n",
       "427    366    1.0    419\n",
       "2026  1605    1.0    419\n",
       "176    155    1.0    410\n",
       "1765  1420    1.0    393\n",
       "1263  1037    1.0    381\n",
       "1786  1438    1.0    371\n",
       "...    ...    ...    ...\n",
       "2446  1938    1.0      1\n",
       "2449  1940    1.0      1\n",
       "2450  1941   -1.0      1\n",
       "2451  1941    1.0      1\n",
       "2452  1942   -1.0      1\n",
       "2462  1949   -1.0      1\n",
       "2489  1963    1.0      1\n",
       "2490  1964    1.0      1\n",
       "2491  1965    1.0      1\n",
       "2494  1967    1.0      1\n",
       "2500  1971   -1.0      1\n",
       "2506  1974    1.0      1\n",
       "2507  1975    1.0      1\n",
       "2508  1976    1.0      1\n",
       "2510  1978    1.0      1\n",
       "2511  1980    1.0      1\n",
       "2513  1982   -1.0      1\n",
       "2517  1985    1.0      1\n",
       "2519  1987   -1.0      1\n",
       "2521  1991    1.0      1\n",
       "2522  1992    1.0      1\n",
       "2523  1994   -1.0      1\n",
       "2524  1995    1.0      1\n",
       "2526  1997   -1.0      1\n",
       "2527  1998    1.0      1\n",
       "2531  2003   -1.0      1\n",
       "2532  2003    1.0      1\n",
       "2533  2004   -1.0      1\n",
       "2539  2009   -1.0      1\n",
       "2541  2010    0.0      1\n",
       "\n",
       "[2543 rows x 3 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "gdf.groupby([\"src\", \"trust\"]).count().reset_index().rename({\"dst\":\"count\"}).sort_values(\"count\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build a cuGraph using the edge lists and weights from our cuDF"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4 ms, sys: 4 ms, total: 8 ms\n",
      "Wall time: 5.9 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "G = cugraph.Graph()\n",
    "G.add_edge_list(gdf.src, gdf.dst, gdf.trust)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since our graph is bipartite, we will want to use the two-hop neighborhoods for computing our Jaccard similarity weights. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 ms, sys: 24 ms, total: 44 ms\n",
      "Wall time: 44.5 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "two_hop = G.get_two_hop_neighbors()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct a search list to compute the Jaccard similarity for a given source vertex to all other destination vertices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 300 ms, sys: 0 ns, total: 300 ms\n",
      "Wall time: 465 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "new_gdf = cudf.DataFrame()\n",
    "new_gdf[\"second\"] = gdf.dst.unique().astype(\"int32\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 120 ms, sys: 12 ms, total: 132 ms\n",
      "Wall time: 209 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "new_gdf[\"first\"] = 61\n",
    "new_gdf.first = new_gdf.first.astype(\"int32\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute Jaccard similarities and weight by the pagerank scores. This will put a higher weight on nodes that are more influential in the network. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 64 ms, sys: 28 ms, total: 92 ms\n",
      "Wall time: 99.3 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "jacc = cugraph.jaccard_w(G, cugraph.pagerank(G)[\"pagerank\"], new_gdf.first, new_gdf.second)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Join our jaccard weights with our original cuDF so that we can explore the relationships"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 60 ms, sys: 20 ms, total: 80 ms\n",
      "Wall time: 76.8 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gdf2 = cudf.merge(jacc, gdf, left_on=\"destination\", right_on=\"src\", how=\"left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Drop unused columns that resulted from the join"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 3.74 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gdf2 = gdf2.drop([\"source\", \"destination\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sort our new cuDF in descending order by the Jaccard similarities to get a feel for the vertices that are similar to our query vertex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 112 ms, sys: 52 ms, total: 164 ms\n",
      "Wall time: 208 ms\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>1068</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>61</td>\n",
       "      <td>321</td>\n",
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       "      <td>1.000000</td>\n",
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       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>100927</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1846</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33059</th>\n",
       "      <td>0.884775</td>\n",
       "      <td>1405</td>\n",
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       "      <th>33090</th>\n",
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       "    <tr>\n",
       "      <th>16124</th>\n",
       "      <td>0.821978</td>\n",
       "      <td>583</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>16154</th>\n",
       "      <td>0.821978</td>\n",
       "      <td>583</td>\n",
       "      <td>584</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>436</th>\n",
       "      <td>0.818677</td>\n",
       "      <td>320</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>468</th>\n",
       "      <td>0.818677</td>\n",
       "      <td>320</td>\n",
       "      <td>6800</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43240</th>\n",
       "      <td>0.812159</td>\n",
       "      <td>1126</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43268</th>\n",
       "      <td>0.812159</td>\n",
       "      <td>1126</td>\n",
       "      <td>1127</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75280</th>\n",
       "      <td>0.754608</td>\n",
       "      <td>595</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75312</th>\n",
       "      <td>0.754608</td>\n",
       "      <td>595</td>\n",
       "      <td>594</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75328</th>\n",
       "      <td>0.754608</td>\n",
       "      <td>595</td>\n",
       "      <td>596</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54752</th>\n",
       "      <td>0.710325</td>\n",
       "      <td>1200</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54784</th>\n",
       "      <td>0.710325</td>\n",
       "      <td>1200</td>\n",
       "      <td>1199</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54804</th>\n",
       "      <td>0.710325</td>\n",
       "      <td>1200</td>\n",
       "      <td>94521</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54823</th>\n",
       "      <td>0.710325</td>\n",
       "      <td>1200</td>\n",
       "      <td>108957</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22971</th>\n",
       "      <td>0.654320</td>\n",
       "      <td>915</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23003</th>\n",
       "      <td>0.654320</td>\n",
       "      <td>915</td>\n",
       "      <td>441</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23030</th>\n",
       "      <td>0.654320</td>\n",
       "      <td>915</td>\n",
       "      <td>916</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8034</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8065</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>741</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8088</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>742</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8110</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>743</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9217</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>744</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>0.616696</td>\n",
       "      <td>1062</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>354</th>\n",
       "      <td>0.616696</td>\n",
       "      <td>1062</td>\n",
       "      <td>961</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>380</th>\n",
       "      <td>0.616696</td>\n",
       "      <td>1062</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>402</th>\n",
       "      <td>0.616696</td>\n",
       "      <td>1062</td>\n",
       "      <td>3775</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127481</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78074</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127482</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78075</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>127483</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78076</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127484</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78077</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127485</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78078</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127486</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78079</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127487</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78080</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127488</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78081</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127489</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78082</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127490</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78083</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127491</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78084</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127492</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78085</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127493</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78086</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127494</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78087</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127495</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78088</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127496</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78089</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127497</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78090</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127498</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78091</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127499</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78092</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127500</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78093</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127501</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78094</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127502</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78095</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127503</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78096</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127504</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78097</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127505</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78098</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127506</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78099</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127507</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78100</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127508</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78101</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127509</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78102</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127510</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>852</td>\n",
       "      <td>78103</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>127511 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        jaccard_coeff   src     dst trust\n",
       "1068         1.000000    61     321   1.0\n",
       "71729        1.000000  1257     321   1.0\n",
       "100927       1.000000  1846     321   1.0\n",
       "33059        0.884775  1405     321   1.0\n",
       "33090        0.884775  1405    1406   1.0\n",
       "16124        0.821978   583     321   1.0\n",
       "16154        0.821978   583     584   1.0\n",
       "436          0.818677   320     321   1.0\n",
       "468          0.818677   320    6800   1.0\n",
       "43240        0.812159  1126     321   1.0\n",
       "43268        0.812159  1126    1127   1.0\n",
       "75280        0.754608   595     321   1.0\n",
       "75312        0.754608   595     594   1.0\n",
       "75328        0.754608   595     596   1.0\n",
       "54752        0.710325  1200     321   1.0\n",
       "54784        0.710325  1200    1199   1.0\n",
       "54804        0.710325  1200   94521   1.0\n",
       "54823        0.710325  1200  108957   1.0\n",
       "22971        0.654320   915     321   1.0\n",
       "23003        0.654320   915     441   1.0\n",
       "23030        0.654320   915     916   1.0\n",
       "8034         0.641840   740     321   1.0\n",
       "8065         0.641840   740     741   1.0\n",
       "8088         0.641840   740     742   1.0\n",
       "8110         0.641840   740     743   1.0\n",
       "9217         0.641840   740     744   1.0\n",
       "323          0.616696  1062     321   1.0\n",
       "354          0.616696  1062     961   1.0\n",
       "380          0.616696  1062    2643   1.0\n",
       "402          0.616696  1062    3775   1.0\n",
       "...               ...   ...     ...   ...\n",
       "127481       0.000000   852   78074   1.0\n",
       "127482       0.000000   852   78075   1.0\n",
       "127483       0.000000   852   78076   1.0\n",
       "127484       0.000000   852   78077   1.0\n",
       "127485       0.000000   852   78078   1.0\n",
       "127486       0.000000   852   78079   1.0\n",
       "127487       0.000000   852   78080   1.0\n",
       "127488       0.000000   852   78081   1.0\n",
       "127489       0.000000   852   78082   1.0\n",
       "127490       0.000000   852   78083   1.0\n",
       "127491       0.000000   852   78084   1.0\n",
       "127492       0.000000   852   78085   1.0\n",
       "127493       0.000000   852   78086   1.0\n",
       "127494       0.000000   852   78087   1.0\n",
       "127495       0.000000   852   78088   1.0\n",
       "127496       0.000000   852   78089   1.0\n",
       "127497       0.000000   852   78090   1.0\n",
       "127498       0.000000   852   78091   1.0\n",
       "127499       0.000000   852   78092   1.0\n",
       "127500       0.000000   852   78093   1.0\n",
       "127501       0.000000   852   78094   1.0\n",
       "127502       0.000000   852   78095   1.0\n",
       "127503       0.000000   852   78096   1.0\n",
       "127504       0.000000   852   78097   1.0\n",
       "127505       0.000000   852   78098   1.0\n",
       "127506       0.000000   852   78099   1.0\n",
       "127507       0.000000   852   78100   1.0\n",
       "127508       0.000000   852   78101   1.0\n",
       "127509       0.000000   852   78102   1.0\n",
       "127510       0.000000   852   78103   1.0\n",
       "\n",
       "[127511 rows x 4 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "gdf2.sort_values(\"jaccard_coeff\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the cuDF above shows mostly trusted nodes, query some untrusted nodes as a sanity check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 304 ms, sys: 40 ms, total: 344 ms\n",
      "Wall time: 370 ms\n"
     ]
    },
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
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       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1455</td>\n",
       "      <td>7</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1458</td>\n",
       "      <td>20374</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1462</td>\n",
       "      <td>865</td>\n",
       "      <td>-1.0</td>\n",
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       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1481</td>\n",
       "      <td>25</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    jaccard_coeff   src    dst  trust\n",
       "0             0.0  1451  98037   -1.0\n",
       "4             0.0  1455      7   -1.0\n",
       "7             0.0  1458  20374   -1.0\n",
       "11            0.0  1462    865   -1.0\n",
       "29            0.0  1481     25   -1.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "gdf2[gdf2.trust == -1.0].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a random destination vertex and look at the distribution of trust compared to the Jaccard weights. Based on similar vertices, it appears that we would want to weight distrusting this node higher than trusting it. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 24 ms, sys: 24 ms, total: 48 ms\n",
      "Wall time: 47.9 ms\n"
     ]
    },
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>84227</th>\n",
       "      <td>0.006323</td>\n",
       "      <td>1682</td>\n",
       "      <td>852</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118760</th>\n",
       "      <td>0.004857</td>\n",
       "      <td>1652</td>\n",
       "      <td>852</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69815</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1325</td>\n",
       "      <td>852</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        jaccard_coeff   src  dst  trust\n",
       "84227        0.006323  1682  852   -1.0\n",
       "118760       0.004857  1652  852   -1.0\n",
       "69815        0.000000  1325  852    1.0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "gdf2[gdf2.dst==852].sort_values(\"jaccard_coeff\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute a weighted average so that we can quantify our uncertainty. Just computing a simple weighted average would give no influence from the global view, since Jaccard weights of the most distant vertices are `0.0`. To give them some low level of influence, let's choose some parameter gamma, which we can add to all the weights, to allow a trade-off between local and global influence. Let's set it to the lowest Jaccard weight - `1e-3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 48 ms, sys: 24 ms, total: 72 ms\n",
      "Wall time: 73.1 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "gamma = gdf2[gdf2.jaccard_coeff > 0.0].jaccard_coeff.min() - 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0030643285028636455"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a simple function to loop through our local and global neighborhoods around a destination vertex and compute the weighted average, adjusted by gamma. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_weighted_avg(jacc_series, trust_series):\n",
    "    cur_sum = 0\n",
    "    for i in range(len(jacc_series)):\n",
    "        jacc = jacc_series[i]\n",
    "        trust = trust_series[i]\n",
    "        cur_sum += 10*((jacc+gamma)*trust)\n",
    "        \n",
    "        \n",
    "    return cur_sum / len(jacc_series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better quantify uncertainty, we can map our resulting value to a sigmoid. Values closer to 0.5 will be less certain than values closer to 0.0 or 1.0. Notice we scale each weighted value in the sum above by 10 so that it better maps to the sigmoid. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sigmoid(x):\n",
    "    return np.exp(x)/(1+np.exp(x))\n",
    "\n",
    "x = np.arange(-10, 10, .005)\n",
    "\n",
    "S = sigmoid(x)\n",
    "\n",
    "p.plot(x, S, color='red', lw=5)\n",
    "p.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a simple function to classify the sigmoid of the weighted average as untrusted if it falls below the threshold of 0.5 and trusted otherwise. This initially assumes an unbiased distribution of classes, but `thres` can be adjusted accordingly based on actual bias of your dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def classify(x, thres=0.5):\n",
    "    return -1.0 if sigmoid(x) < thres else 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's classify our destination vertex from above. We can see this classification has a low level of certainty (value is close to 0.5) since we have low Jaccard weights and conflicting trust labels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 40 ms, sys: 16 ms, total: 56 ms\n",
      "Wall time: 55.1 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "query_df = gdf2[gdf2.dst==852]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
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       "    <tr>\n",
       "      <th>84227</th>\n",
       "      <td>0.006323</td>\n",
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       "      <th>118760</th>\n",
       "      <td>0.004857</td>\n",
       "      <td>1652</td>\n",
       "      <td>852</td>\n",
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      ],
      "text/plain": [
       "        jaccard_coeff   src  dst  trust\n",
       "69815        0.000000  1325  852    1.0\n",
       "84227        0.006323  1682  852   -1.0\n",
       "118760       0.004857  1652  852   -1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "query_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 4 ms, total: 4 ms\n",
      "Wall time: 3.11 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "val = compute_weighted_avg(query_df.jaccard_coeff, query_df.trust)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.047480855683485666"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48813201562533"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classify(val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And choose another destination vertex to classify. We can see this vertex has a much higher certainty since the Jaccard weight is higher and there are no conflicting trust labels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 36 ms, sys: 20 ms, total: 56 ms\n",
      "Wall time: 53.5 ms\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
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       "      <th>8088</th>\n",
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       "      <td>740</td>\n",
       "      <td>742</td>\n",
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      "text/plain": [
       "      jaccard_coeff  src  dst  trust\n",
       "8088        0.64184  740  742    1.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "query_df = gdf2[gdf2.dst==742]\n",
    "query_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4 ms, sys: 0 ns, total: 4 ms\n",
      "Wall time: 1.82 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "val = compute_weighted_avg(query_df.jaccard_coeff, query_df.trust)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.449040711633861"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9984204598215562"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classify(val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at a destination vertex that contains both a high Jaccard weight and some conflicting labels in the global dissimilar vertices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 ms, sys: 28 ms, total: 48 ms\n",
      "Wall time: 48.9 ms\n"
     ]
    },
    {
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       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
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       "      <td>1782</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "      <th>126474</th>\n",
       "      <td>0.000000</td>\n",
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      ],
      "text/plain": [
       "        jaccard_coeff   src   dst  trust\n",
       "380          0.616696  1062  2643    1.0\n",
       "1936         0.000000   423  2643    1.0\n",
       "2020         0.000000   421  2643    1.0\n",
       "2927         0.000000   700  2643    1.0\n",
       "3273         0.000000  1459  2643    1.0\n",
       "3595         0.066799   205  2643    1.0\n",
       "6830         0.000000   689  2643    1.0\n",
       "10904        0.000000   666  2643    1.0\n",
       "11212        0.025272  1622  2643    1.0\n",
       "14027        0.000000   717  2643    1.0\n",
       "15031        0.000000   314  2643    1.0\n",
       "24774        0.000000  1083  2643   -1.0\n",
       "25868        0.000000  1923  2643    1.0\n",
       "26882        0.000000  1957  2643    1.0\n",
       "29084        0.000000   922  2643    1.0\n",
       "38919        0.000000  1782  2643    1.0\n",
       "44818        0.000000   657  2643    1.0\n",
       "45402        0.000000  1127  2643    1.0\n",
       "45580        0.000000   549  2643    1.0\n",
       "46800        0.000000  1308  2643    1.0\n",
       "47389        0.000000   944  2643    1.0\n",
       "48708        0.000000  1120  2643    1.0\n",
       "51363        0.000000  1121  2643    1.0\n",
       "56335        0.000000  1039  2643    1.0\n",
       "60355        0.000000  1825  2643    1.0\n",
       "74323        0.000000    79  2643    1.0\n",
       "75885        0.007077  1118  2643   -1.0\n",
       "81451        0.000000  1027  2643    1.0\n",
       "91571        0.000000  1498  2643    1.0\n",
       "94388        0.000000  1491  2643   -1.0\n",
       "98215        0.000000  1493  2643    1.0\n",
       "126474       0.000000  1972  2643    1.0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "query_df = gdf2[gdf2.dst==2643]\n",
    "query_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 20 ms, sys: 0 ns, total: 20 ms\n",
      "Wall time: 20.9 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "val = compute_weighted_avg(query_df.jaccard_coeff, query_df.trust)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2441755973489491"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5607424015898242"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classify(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 32 ms, sys: 20 ms, total: 52 ms\n",
      "Wall time: 48.9 ms\n"
     ]
    },
    {
     "data": {
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       "      <th>380</th>\n",
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       "      <td>2643</td>\n",
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       "    <tr>\n",
       "      <th>3595</th>\n",
       "      <td>0.066799</td>\n",
       "      <td>205</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>11212</th>\n",
       "      <td>0.025272</td>\n",
       "      <td>1622</td>\n",
       "      <td>2643</td>\n",
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       "    <tr>\n",
       "      <th>75885</th>\n",
       "      <td>0.007077</td>\n",
       "      <td>1118</td>\n",
       "      <td>2643</td>\n",
       "      <td>-1.0</td>\n",
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       "    <tr>\n",
       "      <th>1936</th>\n",
       "      <td>0.000000</td>\n",
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       "      <td>1.0</td>\n",
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       "      <th>2020</th>\n",
       "      <td>0.000000</td>\n",
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       "      <th>2927</th>\n",
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       "      <th>3273</th>\n",
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       "      <th>6830</th>\n",
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       "      <th>14027</th>\n",
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       "      <td>717</td>\n",
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       "      <th>15031</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>314</td>\n",
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       "      <td>1.0</td>\n",
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       "      <th>24774</th>\n",
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       "      <th>25868</th>\n",
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       "      <td>1.0</td>\n",
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       "      <th>29084</th>\n",
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       "      <td>922</td>\n",
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       "      <th>38919</th>\n",
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       "      <th>44818</th>\n",
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       "      <td>657</td>\n",
       "      <td>2643</td>\n",
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       "      <th>45402</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1127</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "      <th>45580</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>549</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>46800</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1308</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>47389</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>944</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48708</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1120</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>51363</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1121</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>56335</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1039</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60355</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1825</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74323</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>79</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81451</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1027</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91571</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1498</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94388</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1491</td>\n",
       "      <td>2643</td>\n",
       "      <td>-1.0</td>\n",
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       "    <tr>\n",
       "      <th>98215</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1493</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>126474</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1972</td>\n",
       "      <td>2643</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        jaccard_coeff   src   dst  trust\n",
       "380          0.616696  1062  2643    1.0\n",
       "3595         0.066799   205  2643    1.0\n",
       "11212        0.025272  1622  2643    1.0\n",
       "75885        0.007077  1118  2643   -1.0\n",
       "1936         0.000000   423  2643    1.0\n",
       "2020         0.000000   421  2643    1.0\n",
       "2927         0.000000   700  2643    1.0\n",
       "3273         0.000000  1459  2643    1.0\n",
       "6830         0.000000   689  2643    1.0\n",
       "10904        0.000000   666  2643    1.0\n",
       "14027        0.000000   717  2643    1.0\n",
       "15031        0.000000   314  2643    1.0\n",
       "24774        0.000000  1083  2643   -1.0\n",
       "25868        0.000000  1923  2643    1.0\n",
       "26882        0.000000  1957  2643    1.0\n",
       "29084        0.000000   922  2643    1.0\n",
       "38919        0.000000  1782  2643    1.0\n",
       "44818        0.000000   657  2643    1.0\n",
       "45402        0.000000  1127  2643    1.0\n",
       "45580        0.000000   549  2643    1.0\n",
       "46800        0.000000  1308  2643    1.0\n",
       "47389        0.000000   944  2643    1.0\n",
       "48708        0.000000  1120  2643    1.0\n",
       "51363        0.000000  1121  2643    1.0\n",
       "56335        0.000000  1039  2643    1.0\n",
       "60355        0.000000  1825  2643    1.0\n",
       "74323        0.000000    79  2643    1.0\n",
       "81451        0.000000  1027  2643    1.0\n",
       "91571        0.000000  1498  2643    1.0\n",
       "94388        0.000000  1491  2643   -1.0\n",
       "98215        0.000000  1493  2643    1.0\n",
       "126474       0.000000  1972  2643    1.0"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "query_df.sort_values(\"jaccard_coeff\", ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We could lower gamma to reduce the global weight and put more weight on the local neighborhood of similar vertices. We can see here where that can have an impact on the classification result, when there is high uncertainty. If we set `gamma` to `0.0001` then we end up with a final classifiation of `-1`, since we have a Jaccard weight that is much higher than the others with a label of `-1`. If we increase the influence of more distance neighborhoods, by adjusting `gamma` to be `0.001`, the final classified label will be `1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "gamma = 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 72 ms, sys: 28 ms, total: 100 ms\n",
      "Wall time: 99.9 ms\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
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       "      <th>trust</th>\n",
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       "      <td>1481</td>\n",
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       "      <td>0.000000</td>\n",
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       "      <td>1481</td>\n",
       "      <td>-1.0</td>\n",
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       "      <td>1335</td>\n",
       "      <td>1481</td>\n",
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       "      <td>1481</td>\n",
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       "      <th>35964</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1956</td>\n",
       "      <td>1481</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>47187</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>20</td>\n",
       "      <td>1481</td>\n",
       "      <td>1.0</td>\n",
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       "    <tr>\n",
       "      <th>49655</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>365</td>\n",
       "      <td>1481</td>\n",
       "      <td>-1.0</td>\n",
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       "      <td>1481</td>\n",
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       "      <th>92909</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1484</td>\n",
       "      <td>1481</td>\n",
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       "    </tr>\n",
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       "</table>\n",
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      ],
      "text/plain": [
       "        jaccard_coeff   src   dst  trust\n",
       "96670        0.013826  1512  1481   -1.0\n",
       "123836       0.004546   353  1481    1.0\n",
       "125649       0.004064   167  1481    1.0\n",
       "400          0.000000  1055  1481    1.0\n",
       "2246         0.000000  1474  1481    1.0\n",
       "3591         0.000000   251  1481    1.0\n",
       "7664         0.000000   487  1481    1.0\n",
       "16143        0.000000   553  1481   -1.0\n",
       "21508        0.000000  1335  1481    1.0\n",
       "22622        0.000000  1458  1481    1.0\n",
       "35436        0.000000  1380  1481    1.0\n",
       "35469        0.000000  1399  1481    1.0\n",
       "35964        0.000000  1956  1481    1.0\n",
       "47187        0.000000    20  1481    1.0\n",
       "49655        0.000000   365  1481   -1.0\n",
       "54800        0.000000  1244  1481    1.0\n",
       "55701        0.000000  1235  1481    1.0\n",
       "68169        0.000000    23  1481   -1.0\n",
       "92909        0.000000  1484  1481    1.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "query_df = gdf2[gdf2.dst==1481]\n",
    "query_df.sort_values(\"jaccard_coeff\", ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 12 ms, sys: 4 ms, total: 16 ms\n",
      "Wall time: 14.2 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "val = compute_weighted_avg(query_df.jaccard_coeff, query_df.trust)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0030443163314147993"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5007610784950562"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classify(val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's an example where we have Jaccard weights for all the source vertices in our voting committee, but since we have some neighbors with exact similarity, we are going to prioritize those labels much higher than the more distant neighbors.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 40 ms, sys: 20 ms, total: 60 ms\n",
      "Wall time: 55.5 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "query_df = gdf2[gdf2.dst==321]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 44 ms, sys: 4 ms, total: 48 ms\n",
      "Wall time: 47.1 ms\n"
     ]
    },
    {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>jaccard_coeff</th>\n",
       "      <th>src</th>\n",
       "      <th>dst</th>\n",
       "      <th>trust</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1068</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>61</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71729</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1257</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100927</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1846</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33059</th>\n",
       "      <td>0.884775</td>\n",
       "      <td>1405</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16124</th>\n",
       "      <td>0.821978</td>\n",
       "      <td>583</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>436</th>\n",
       "      <td>0.818677</td>\n",
       "      <td>320</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43240</th>\n",
       "      <td>0.812159</td>\n",
       "      <td>1126</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75280</th>\n",
       "      <td>0.754608</td>\n",
       "      <td>595</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54752</th>\n",
       "      <td>0.710325</td>\n",
       "      <td>1200</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22971</th>\n",
       "      <td>0.654320</td>\n",
       "      <td>915</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8034</th>\n",
       "      <td>0.641840</td>\n",
       "      <td>740</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>0.616696</td>\n",
       "      <td>1062</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>543</th>\n",
       "      <td>0.614259</td>\n",
       "      <td>704</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>952</th>\n",
       "      <td>0.570165</td>\n",
       "      <td>1576</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54775</th>\n",
       "      <td>0.551062</td>\n",
       "      <td>1249</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23011</th>\n",
       "      <td>0.530775</td>\n",
       "      <td>929</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>374</th>\n",
       "      <td>0.527757</td>\n",
       "      <td>1102</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100926</th>\n",
       "      <td>0.499780</td>\n",
       "      <td>1845</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71739</th>\n",
       "      <td>0.376021</td>\n",
       "      <td>1270</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87617</th>\n",
       "      <td>0.364766</td>\n",
       "      <td>2000</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75289</th>\n",
       "      <td>0.344141</td>\n",
       "      <td>609</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1067</th>\n",
       "      <td>0.332665</td>\n",
       "      <td>59</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6023</th>\n",
       "      <td>0.317860</td>\n",
       "      <td>536</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76102</th>\n",
       "      <td>0.303592</td>\n",
       "      <td>603</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22987</th>\n",
       "      <td>0.271945</td>\n",
       "      <td>942</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16183</th>\n",
       "      <td>0.254803</td>\n",
       "      <td>547</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54836</th>\n",
       "      <td>0.250733</td>\n",
       "      <td>1243</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23004</th>\n",
       "      <td>0.222561</td>\n",
       "      <td>916</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9226</th>\n",
       "      <td>0.177180</td>\n",
       "      <td>766</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4542</th>\n",
       "      <td>0.144692</td>\n",
       "      <td>187</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33600</th>\n",
       "      <td>0.051504</td>\n",
       "      <td>1950</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56021</th>\n",
       "      <td>0.051329</td>\n",
       "      <td>1323</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37820</th>\n",
       "      <td>0.045223</td>\n",
       "      <td>1757</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30642</th>\n",
       "      <td>0.042932</td>\n",
       "      <td>141</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36192</th>\n",
       "      <td>0.039953</td>\n",
       "      <td>352</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47468</th>\n",
       "      <td>0.038433</td>\n",
       "      <td>1149</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6259</th>\n",
       "      <td>0.037412</td>\n",
       "      <td>1463</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46540</th>\n",
       "      <td>0.037209</td>\n",
       "      <td>809</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5930</th>\n",
       "      <td>0.036186</td>\n",
       "      <td>1905</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15178</th>\n",
       "      <td>0.034740</td>\n",
       "      <td>1358</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6516</th>\n",
       "      <td>0.030989</td>\n",
       "      <td>1650</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10352</th>\n",
       "      <td>0.030257</td>\n",
       "      <td>1443</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21276</th>\n",
       "      <td>0.029091</td>\n",
       "      <td>462</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34450</th>\n",
       "      <td>0.027841</td>\n",
       "      <td>1370</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39236</th>\n",
       "      <td>0.025272</td>\n",
       "      <td>1622</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61718</th>\n",
       "      <td>0.024840</td>\n",
       "      <td>1784</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37196</th>\n",
       "      <td>0.024121</td>\n",
       "      <td>1962</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60390</th>\n",
       "      <td>0.021739</td>\n",
       "      <td>1213</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19106</th>\n",
       "      <td>0.018655</td>\n",
       "      <td>661</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54055</th>\n",
       "      <td>0.014910</td>\n",
       "      <td>410</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98131</th>\n",
       "      <td>0.014515</td>\n",
       "      <td>1288</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83607</th>\n",
       "      <td>0.013927</td>\n",
       "      <td>1306</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88295</th>\n",
       "      <td>0.013826</td>\n",
       "      <td>1512</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98136</th>\n",
       "      <td>0.012999</td>\n",
       "      <td>1287</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69476</th>\n",
       "      <td>0.009161</td>\n",
       "      <td>211</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>106383</th>\n",
       "      <td>0.007077</td>\n",
       "      <td>1118</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78627</th>\n",
       "      <td>0.006323</td>\n",
       "      <td>1682</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118714</th>\n",
       "      <td>0.004857</td>\n",
       "      <td>1652</td>\n",
       "      <td>321</td>\n",
       "      <td>-1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121497</th>\n",
       "      <td>0.004546</td>\n",
       "      <td>353</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126734</th>\n",
       "      <td>0.004064</td>\n",
       "      <td>167</td>\n",
       "      <td>321</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>74 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        jaccard_coeff   src  dst  trust\n",
       "1068         1.000000    61  321    1.0\n",
       "71729        1.000000  1257  321    1.0\n",
       "100927       1.000000  1846  321    1.0\n",
       "33059        0.884775  1405  321    1.0\n",
       "16124        0.821978   583  321    1.0\n",
       "436          0.818677   320  321    1.0\n",
       "43240        0.812159  1126  321    1.0\n",
       "75280        0.754608   595  321    1.0\n",
       "54752        0.710325  1200  321    1.0\n",
       "22971        0.654320   915  321    1.0\n",
       "8034         0.641840   740  321    1.0\n",
       "323          0.616696  1062  321    1.0\n",
       "543          0.614259   704  321    1.0\n",
       "952          0.570165  1576  321    1.0\n",
       "54775        0.551062  1249  321    1.0\n",
       "23011        0.530775   929  321    1.0\n",
       "374          0.527757  1102  321    1.0\n",
       "100926       0.499780  1845  321    1.0\n",
       "71739        0.376021  1270  321    1.0\n",
       "87617        0.364766  2000  321    1.0\n",
       "75289        0.344141   609  321    1.0\n",
       "1067         0.332665    59  321    1.0\n",
       "6023         0.317860   536  321    1.0\n",
       "76102        0.303592   603  321    1.0\n",
       "22987        0.271945   942  321   -1.0\n",
       "16183        0.254803   547  321    1.0\n",
       "54836        0.250733  1243  321    1.0\n",
       "23004        0.222561   916  321    1.0\n",
       "9226         0.177180   766  321    1.0\n",
       "4542         0.144692   187  321    1.0\n",
       "...               ...   ...  ...    ...\n",
       "33600        0.051504  1950  321   -1.0\n",
       "56021        0.051329  1323  321    1.0\n",
       "37820        0.045223  1757  321    1.0\n",
       "30642        0.042932   141  321   -1.0\n",
       "36192        0.039953   352  321    1.0\n",
       "47468        0.038433  1149  321   -1.0\n",
       "6259         0.037412  1463  321    1.0\n",
       "46540        0.037209   809  321    1.0\n",
       "5930         0.036186  1905  321   -1.0\n",
       "15178        0.034740  1358  321    1.0\n",
       "6516         0.030989  1650  321   -1.0\n",
       "10352        0.030257  1443  321    1.0\n",
       "21276        0.029091   462  321   -1.0\n",
       "34450        0.027841  1370  321    1.0\n",
       "39236        0.025272  1622  321    1.0\n",
       "61718        0.024840  1784  321   -1.0\n",
       "37196        0.024121  1962  321   -1.0\n",
       "60390        0.021739  1213  321    1.0\n",
       "19106        0.018655   661  321   -1.0\n",
       "54055        0.014910   410  321   -1.0\n",
       "98131        0.014515  1288  321   -1.0\n",
       "83607        0.013927  1306  321   -1.0\n",
       "88295        0.013826  1512  321   -1.0\n",
       "98136        0.012999  1287  321    1.0\n",
       "69476        0.009161   211  321    1.0\n",
       "106383       0.007077  1118  321   -1.0\n",
       "78627        0.006323  1682  321   -1.0\n",
       "118714       0.004857  1652  321   -1.0\n",
       "121497       0.004546   353  321    1.0\n",
       "126734       0.004064   167  321    1.0\n",
       "\n",
       "[74 rows x 4 columns]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "query_df.sort_values(\"jaccard_coeff\", ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 44 ms, sys: 0 ns, total: 44 ms\n",
      "Wall time: 44.3 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "val = compute_weighted_avg(query_df.jaccard_coeff, query_df.trust)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3063480230818527"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "val"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9094014166928449"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classify(val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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