peertrust.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c9ef025f-0eff-43c2-8331-9f3ee7e0ace4",
   "metadata": {},
   "source": [
    "# Peertrust Algorithm for Reputation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7eb0d72-dd07-41fd-81b3-4179d71301bb",
   "metadata": {},
   "source": [
    "Peertrust model has two main features. First, three basic trust parameters and two adaptavtive factors in computing trustworthiness of peers, namely, feedback a perr receives from other peers, the total number of transactions a peer performs, the credibility of the feedback sources, transaction context factor and the community context factor. Second, a general metric to combine all these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dd1b8587-5398-4745-bb12-126fbaa0f45e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(linewidth=200)\n",
    "from tabulate import tabulate, SEPARATING_LINE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4df3691-e77e-4ad5-bfcf-9a6182008d67",
   "metadata": {},
   "source": [
    "G = nx.Graph()\n",
    "G.add_edges_from([(0, 1), (1,6), (1,7), (0,4),(1,8),(0, 2), (0, 3), (0,18),(2, 5), (5,9), (5,10), (5,11), (5,12), (0,13), (0,14), (0,15), (1,16), (2,17), (17,18), (18,14),(18,21),(2,21), (17,19), (17,20), (14,21),(14,2),\n",
    "                 (6,12),(6,22),(6,23),(6,24),(7,23),(12,25),(12,26),(12,27), (25,28),(25,29),(29,9), (15,3), (3,4), (7,8)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "881674a2-54ce-4970-b7d2-eba3b68a4b33",
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()\n",
    "G.add_edges_from([(0, 1), (1,6), (1,7), (0,4),(1,8),(0, 2), (0, 3), (0,18),(2, 5), (5,9), (5,10), (5,11), (11,12), (0,13), (0,14), (0,15), (1,16), (2,17), (17,18), (18,14), (17,19), (14,2),\n",
    "                 (6,12), (15,3), (3,4), (7,8), (10,11), (6,16)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c1ae1b17-5f17-414e-90c0-bb6a2bcc630f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nodelist = [x for x in range(len(G.nodes))]\n",
    "print(nodelist)\n",
    "len(nodelist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0373d34a-0447-46d4-b0fd-f3488a15ab4c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(20, 20)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],\n",
       "       [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0],\n",
       "       [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
       "       [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
       "       [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1],\n",
       "       [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions()\n",
    "np.set_printoptions(precision=0)\n",
    "adjs = nx.adjacency_matrix(G, nodelist=nodelist).todense()\n",
    "print(adjs.shape)\n",
    "adjs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dd29e726-f2ec-4b98-89f0-5f134e65c756",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16937acf-c21f-4533-b569-77453849b07a",
   "metadata": {},
   "source": [
    "Given a recent time window, let $I(u,v)$ denote the total number of transactions performed by peer $u$ with $v$, $I(u)$ denote the total number of transactions performed by peer $u$ with all other peers, $p(u,i)$ denote the other participating peer in peer $u$'s $i$th transaction, $S(u,i)$ denote the normalized amount of satisfaction peer $u$ receives from $p(u,i)$ in its $i$th transaction, $Cr(v)$ denote the credibility of the feedback submitted by $v$, $TF(u,i)$ denote the adaptative transaction context factor for perr $u's$ $i$th transaction, $CF(u, t_{k}, t)$ denote the adaptative community context factor for peer $u$ during the period of $t_k$ and $t$.\n",
    "\n",
    "The trust value of peer $u$ during the period of time $t_k$ and $t$, denoted by $T(u, t_k, t)$ is defined as:\n",
    "\n",
    "$T(u) = \\alpha * \\sum_{i=1}^{I(u)} S(u,i) * Cr(p(u,i)) * TF(u,i) + \\beta * CF(u)$\n",
    "\n",
    "where $\\alpha$ and $\\beta$ denote the normalized weigth factors for the collective evaluation and the community context factor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "37cc6e21-0a91-43ba-a106-981d844db348",
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_peer_review():\n",
    "    np.random.seed(42214)\n",
    "    rng = np.random.default_rng()\n",
    "    n, p = 1, 0.68\n",
    "    s = rng.binomial(n, p, random.randint(1, 20))\n",
    "    #s[s==0]= -1 \n",
    "    # this is because it generates numbers either 0 or 1, so zeros are replaced by -1\n",
    "    return sum(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a2682a7-2c07-4097-ac58-31db1b9dd8f1",
   "metadata": {},
   "source": [
    "### Local Trust Values\n",
    "\n",
    "In a distributed environment, peers may still rate each other after each transaction, as in the eBay system.\n",
    "\n",
    "For example, each time peer $i$ makes a transaction with peer $j$, it may rate the transaction as:\n",
    "- positive $tr(i, j) = +1$ \n",
    "\n",
    "or \n",
    "\n",
    "- negative $tr(i, j) = −1$.\n",
    "\n",
    "Like in the eBay model, we may define a *local trust value* $s_{ij}$ as the sum of the ratings of the individual transactions that peer $i$ has\n",
    "done with peer $j$: \n",
    "\n",
    "$s_{ij} = \\sum tr_{ij}$.\n",
    "\n",
    "The simplest notion of trust is just a log of your own interactions with others that you yourself can keep. So whenever Alice wants to download a file from Bob, and the file turns out to be the Nickelback song you were looking for, Alice keeps a log of “Bob +1” (starting with 0 for Bob if she’s never interacted with him). If the file is white noise, Alice logs “Bob -1”. Alice does the same with her interactions with Charlie and David. The problem is, of course, that this is just Alice’s own opinion, and in a huge peer-to-peer network it would take a long time for Alice to build strong opinions on enough others."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2e46da2c-ed70-433c-97ba-3e0f84265072",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate random transactions and rates and calculate local trust values\n",
    "loc_tru = np.zeros(adjs.shape)\n",
    "\n",
    "def gene_local_trust(adjs):\n",
    "    for i in range(adjs.shape[0]):\n",
    "        for j in range(adjs.shape[1]):\n",
    "            if (adjs[i][j]== 1):\n",
    "                loc_tru[i][j]=generate_peer_review()\n",
    "    return loc_tru\n",
    "\n",
    "s = gene_local_trust(adjs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "703b20bf-4e40-41d8-a2c3-ca9ce5db8667",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[PosixPath('example.npy'),\n",
       " PosixPath('example_with_nan.npy'),\n",
       " PosixPath('soctrust.npy')]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pathlib import Path\n",
    "list(Path('.').glob('*.npy'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9af627a9-50bf-4c84-9d41-8ae2ae2b7055",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = gene_local_trust(adjs)\n",
    "with open('soctrust.npy', 'wb') as f:\n",
    "    np.save(f, s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8f3c9889-9c4f-4cab-95c3-44713ad350c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  5.,  8.,  2.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  8.,  1.,  2.,  0.,  0.,  5.,  0.],\n",
       "       [ 7.,  0.,  0.,  0.,  0.,  0.,  5.,  4., 11.,  0.,  0.,  0.,  0.,  0.,  0.,  0., 14.,  0.,  0.,  0.],\n",
       "       [ 6.,  0.,  0.,  0.,  0., 13.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., 10.,  0.,  0.,  8.,  0.,  0.],\n",
       "       [ 3.,  0.,  0.,  0., 14.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  2.,  0.,  0.,  0.,  0.],\n",
       "       [ 6.,  0.,  0.,  8.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  9.,  0.,  0.,  0.,  0.,  0.,  0.,  7.,  3.,  4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0., 12.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  7.,  0.,  0.,  0.,  8.,  0.,  0.,  0.],\n",
       "       [ 0.,  7.,  0.,  0.,  0.,  0.,  0.,  0.,  5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  6.,  0.,  0.,  0.,  0.,  0.,  7.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  9.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  8.,  0.,  0.,  0.,  0.,  0.,  9.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  9.,  0.,  0.,  0.,  0.,  4.,  0.,  8.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  2.,  0.,  0.,  0.,  0., 11.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 7.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 6.,  0.,  9.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  9.,  0.],\n",
       "       [ 7.,  0.,  0., 10.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0., 11.,  0.,  0.,  0.,  0., 11.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  2.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., 13.,  5.],\n",
       "       [ 4.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  9.,  0.,  0.,  4.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0., 10.,  0.,  0.]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with open('soctrust.npy', 'rb') as f:\n",
    "    s = np.load(f)\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b3cae668-a9c6-455a-8916-fd981fc61d07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(41.0, 7.0)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_sum = np.sum(s, axis=1, keepdims=True)\n",
    "node_size = s_sum.flatten().tolist()\n",
    "max(node_size), min(node_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "31db9f34-71d6-4478-af41-44274f19d350",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                  0    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19\n",
      "--------------------  ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----\n",
      "node_degree             8    5    4    3    2    4    3    2    2    1     2     3     2     1     3     2     2     3     3     1\n",
      "node_agg_local_trust   46   37   25   26   16   39   18   11   16    7     7    24    15     8    20     4    22    22    27     5\n",
      "trust_per_degree        6    7    6    9    8   10    6    6    8    7     4     8     8     8     7     2    11     7     9     5\n",
      "--------------------  ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----\n"
     ]
    }
   ],
   "source": [
    "def print_metrics():\n",
    "    node_degree = np.sum(adjs,axis=1, keepdims=True).T\n",
    "    node_agg_local_trust = np.sum(s, axis=0, keepdims=True)\n",
    "    avg_trust = node_agg_local_trust / node_degree\n",
    "\n",
    "    node_degree = node_degree.flatten().tolist()\n",
    "    node_agg_local_trust = node_agg_local_trust.flatten().tolist()\n",
    "    avg_trust = avg_trust.flatten().tolist()\n",
    "\n",
    "    node_degree.insert(0,'node_degree')\n",
    "    node_agg_local_trust.insert(0,'node_agg_local_trust')\n",
    "    avg_trust.insert(0,'trust_per_degree')\n",
    "\n",
    "    table=[node_degree, node_agg_local_trust,avg_trust, SEPARATING_LINE]\n",
    "    print(tabulate(table,headers=['metric'] + nodelist, floatfmt=\".0f\"))\n",
    "print_metrics()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32a9a4c1-e53e-420b-890b-45d7d40eb4b7",
   "metadata": {},
   "source": [
    "`node_agg_local_trust` is the sum of each collum, which is the trust given to a peer by whoever is connected to it."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70f4ffdb-87a8-4abf-9f25-0b74dbdf51a4",
   "metadata": {},
   "source": [
    "### Normalizing *Local Trust Values*\n",
    "\n",
    "In order to aggregate local trust values, it is necessary to normalize them in some manner. Otherwise, malicious peers can assign arbitrarily high local trust values to other malicious peers, and arbitrarily low local trust values to good peers, easily subverting the system. \n",
    "\n",
    "We define a *normalized local trust value*, $c_{ij}$ , as follows:\n",
    "\n",
    "$c_{ij} = \\dfrac{max(s_{ij},0)}{\\sum_{j} max(s_{ij},0)}$\n",
    "\n",
    "**This ensures that all values will be between 0 and 1.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "73a483f2-7109-4161-a816-ea401acca4ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_c():\n",
    "    c = np.zeros(s.shape)\n",
    "    s_max = np.maximum(s,c)\n",
    "    s_sum_max = np.sum(s_max, axis=1, keepdims=True)\n",
    "    float_formatter = \"{:.2f}\".format\n",
    "    np.set_printoptions(formatter={'float_kind':float_formatter})\n",
    "    #c = np.where(s_max == 0, 0, s_max / s_sum_max)\n",
    "    with np.errstate(divide='ignore',invalid='ignore'):\n",
    "        c =  s_max / s_sum_max\n",
    "    return c\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8139f164-9bdf-48b1-8eb4-19148c741437",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.00, 0.03, 0.16, 0.25, 0.06, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.25, 0.03, 0.06, 0.00, 0.00, 0.16, 0.00],\n",
       "       [0.17, 0.00, 0.00, 0.00, 0.00, 0.00, 0.12, 0.10, 0.27, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.34, 0.00, 0.00, 0.00],\n",
       "       [0.16, 0.00, 0.00, 0.00, 0.00, 0.35, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.27, 0.00, 0.00, 0.22, 0.00, 0.00],\n",
       "       [0.16, 0.00, 0.00, 0.00, 0.74, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.11, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.43, 0.00, 0.00, 0.57, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.39, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.30, 0.13, 0.17, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.44, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.26, 0.00, 0.00, 0.00, 0.30, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.58, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.42, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.46, 0.00, 0.00, 0.00, 0.00, 0.00, 0.54, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.00, 0.00, 0.00, 0.47, 0.00, 0.00, 0.00, 0.00, 0.00, 0.53, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.00, 0.00, 0.00, 0.43, 0.00, 0.00, 0.00, 0.00, 0.19, 0.00, 0.38, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.15, 0.00, 0.00, 0.00, 0.00, 0.85, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.25, 0.00, 0.38, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.38, 0.00],\n",
       "       [0.41, 0.00, 0.00, 0.59, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.50, 0.00, 0.00, 0.00, 0.00, 0.50, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.10, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.65, 0.25],\n",
       "       [0.24, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.53, 0.00, 0.00, 0.24, 0.00, 0.00],\n",
       "       [0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = make_c()\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "569b5256-1892-4bea-85d7-a250c86b87c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]\n",
      " [1.00]]\n"
     ]
    }
   ],
   "source": [
    "# Notice that every i (line) it is normalized over j\n",
    "print(np.sum(c, axis=1, keepdims=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f04a756-123f-45e8-8a5a-b3399f0826a1",
   "metadata": {},
   "source": [
    "### Interpretation of $c_{ij}$\n",
    "\n",
    "It is values are relative (no absolute interpretation) and it somehow conveys the reputation of $j$ in the eyes of peer $i$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91bd3e0f-bfe1-466c-8dde-132eb80f6ac1",
   "metadata": {},
   "source": [
    "There are some drawbacks to normalizing in this manner:\n",
    "- For one, the normalized trust values do not distinguish between a peer with whom peer $i$ did not interact and a peer with whom peer $i$ has had poor experience. \n",
    "- Also, these $c_{ij}$ values are relative, and there is no absolute interpretation. That is, if $c_{ij} = c_{ik}$, we know that peer $j$ has the same reputation as peer $k$ in the eyes of peer $i$, but we don’t know if both of them are very reputable, or if both of them are mediocre.\n",
    "\n",
    "Notice that when $\\sum_{j} max(s_{ij}) = 0$, then $c_{ij}$ is undefined, `nan`. This issue is addressed in Section `Practical Issues`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0928a801",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold', node_size=ns)\n",
    "nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f1bcdebf-44aa-4488-993c-a1f8d5224dbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def tabula_trust_values(line):\n",
    "    adja = adjs[line].tolist()\n",
    "    adja.insert(0,'adjacency')\n",
    "    adja.append(sum(adjs[line]))\n",
    "    \n",
    "    newli = s[line].tolist()\n",
    "    newli.insert(0,'local trust value')\n",
    "    newli.append(sum(s[line]))\n",
    "    \n",
    "    newci = c[line].tolist()\n",
    "    newci.insert(0,'normalized local trust value')\n",
    "    newci.append(sum(c[line]))\n",
    "    \n",
    "    table=[adja, newli,newci,SEPARATING_LINE]\n",
    "    print(tabulate(table, headers=['metric'] + nodelist + ['sum'], floatfmt=\".2f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c419a23f-5b95-4cc7-a0f5-f037f4752d8c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                           0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    sum\n",
      "----------------------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n",
      "adjacency                     0.00  1.00  1.00  1.00  1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00  1.00  1.00  0.00  0.00  1.00  0.00   8.00\n",
      "local trust value             0.00  1.00  5.00  8.00  2.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  8.00  1.00  2.00  0.00  0.00  5.00  0.00  32.00\n",
      "normalized local trust value  0.00  0.03  0.16  0.25  0.06  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.25  0.03  0.06  0.00  0.00  0.16  0.00   1.00\n",
      "----------------------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n"
     ]
    }
   ],
   "source": [
    "tabula_trust_values(line=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2f34ecf-7575-4ded-aa84-c72dbff327f8",
   "metadata": {},
   "source": [
    "Again, notice that the normalized trust values do not distinguish between a peer with whom peer $i$ did not interact and a peer with whom peer $i$ has had poor experience. As you can see above, negative local trust values are normalized to zero, due to the rule $max(s_{ij},0)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "07583819-2e52-4fc4-9471-0395f454cf28",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                           0     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    sum\n",
      "----------------------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n",
      "adjacency                     1.00  0.00  1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  1.00  0.00   3.00\n",
      "local trust value             6.00  0.00  9.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  9.00  0.00  24.00\n",
      "normalized local trust value  0.25  0.00  0.38  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.38  0.00   1.00\n",
      "----------------------------  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n"
     ]
    }
   ],
   "source": [
    "tabula_trust_values(line=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b131edca-df85-41db-ad63-1c7e774b76a0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                           0     1     2     3     4      5     6     7     8     9    10    11    12    13     14    15    16    17    18    19    sum\n",
      "----------------------------  ----  ----  ----  ----  ----  -----  ----  ----  ----  ----  ----  ----  ----  ----  -----  ----  ----  ----  ----  ----  -----\n",
      "adjacency                     1.00  0.00  0.00  0.00  0.00   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00   1.00  0.00  0.00  1.00  0.00  0.00   4.00\n",
      "local trust value             6.00  0.00  0.00  0.00  0.00  13.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  10.00  0.00  0.00  8.00  0.00  0.00  37.00\n",
      "normalized local trust value  0.16  0.00  0.00  0.00  0.00   0.35  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00   0.27  0.00  0.00  0.22  0.00  0.00   1.00\n",
      "----------------------------  ----  ----  ----  ----  ----  -----  ----  ----  ----  ----  ----  ----  ----  ----  -----  ----  ----  ----  ----  ----  -----\n"
     ]
    }
   ],
   "source": [
    "tabula_trust_values(line=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a49799c6-abef-4e44-b72c-46e9e4cfabd4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                           0     1     2      3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    sum\n",
      "----------------------------  ----  ----  ----  -----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n",
      "adjacency                     1.00  0.00  0.00   1.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00   2.00\n",
      "local trust value             7.00  0.00  0.00  10.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  17.00\n",
      "normalized local trust value  0.41  0.00  0.00   0.59  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00   1.00\n",
      "----------------------------  ----  ----  ----  -----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----  -----\n"
     ]
    }
   ],
   "source": [
    "tabula_trust_values(line=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b242c37f-dfa7-4550-8312-d926ad941cde",
   "metadata": {},
   "source": [
    "### Weight Average by $Cr(p(u,i))$\n",
    "\n",
    "The problem is, that, credibility of feedback, is a **qualitative** measure and needs to be computed based on past behavior of peers who file feedback.\n",
    "\n",
    "1- solicit separate feedback for feedback themselves.\n",
    "2- Infer or compute the credibility value of a peer implicitly.\n",
    "\n",
    "- use a function of the trust value of a peer as its credibility factor so feedback from trustworthy peers are considered more credible and thus weighted ,ore than those from untrustworthy peers.\n",
    "\n",
    "\n",
    "- $I(u,v)$ denote the total number of transactions performed by peer $u$ with $v$, \n",
    "- $I(u)$ denote the total number of transactions performed by peer $u$ with all other peers, \n",
    "- $p(u,i)$ denote the other participating peer in peer $u$'s $i$th transaction, \n",
    "- $S(u,i)$ denote the normalized amount of satisfaction peer $u$ receives from $p(u,i)$ in its $i$th transaction.\n",
    "\n",
    "$\\Large T_{TVM}(u) = \\displaystyle\\sum_{i=1}^{I(u)} S(u,i) * \\dfrac{T(p(u,i))}{\\sum_{i=1}^{I(u)}T(p(u,i))}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9e7add50-3494-45ce-8678-7d309fb81869",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e4d699b9-9ddc-4d34-b6b5-6d48410399ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.ones((20,))/20\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "004a1b3e-b16e-4cc4-b918-87ada7655b1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 0.00, 0.00, 0.00, 0.00, 0.05, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thelp = t*adjs[9]\n",
    "thelp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "53299913-1aa7-429a-95df-8d1df84dfe5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00, 0.00, 0.00, 0.00, 0.00, 1.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tnorm = thelp/np.sum(thelp)\n",
    "tnorm = tnorm.reshape((20,))\n",
    "tnorm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e80ab87d-b435-4de4-9863-5e98622ba5a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "t[9] = sum(c[9]*tnorm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0d71c349-319b-4fdb-92b1-513ff7c89f68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 1.00, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05, 0.05])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "fe0e47eb-18b6-471a-81af-218651b98691",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0,20):\n",
    "    thelp = t*adjs[i]\n",
    "    tnorm = thelp/np.sum(thelp)\n",
    "    tnorm = tnorm.reshape((20,))\n",
    "    t[i] = sum(c[i]*tnorm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c5e9abe0-9deb-4a05-959f-7b25432ceb07",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.12, 0.19, 0.23, 0.27, 0.53, 0.31, 0.39, 0.55, 0.52, 1.00, 0.48, 0.29, 0.45, 1.00, 0.34, 0.53, 0.50, 0.21, 0.38, 1.00])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "00b45f4e-d3d7-4de3-b48f-07124d8a2a47",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "metric                  0    1    2    3    4    5    6    7    8    9    10    11    12    13    14    15    16    17    18    19\n",
      "--------------------  ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----\n",
      "node_degree             8    5    4    3    2    4    3    2    2    1     2     3     2     1     3     2     2     3     3     1\n",
      "node_agg_local_trust   46   37   25   26   16   39   18   11   16    7     7    24    15     8    20     4    22    22    27     5\n",
      "trust_per_degree        6    7    6    9    8   10    6    6    8    7     4     8     8     8     7     2    11     7     9     5\n",
      "--------------------  ---  ---  ---  ---  ---  ---  ---  ---  ---  ---  ----  ----  ----  ----  ----  ----  ----  ----  ----  ----\n"
     ]
    }
   ],
   "source": [
    "print_metrics()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d5c8250-ec68-40db-9d3a-d2539b8839fd",
   "metadata": {},
   "source": [
    "## The Basic Metric\n",
    "\n",
    "- $I(u)$ denote the total number of transactions performed by peer $u$ with all other peers, \n",
    "- $I(u,v)$ denote the total number of transactions performed by peer $u$ with $v$, \n",
    "- $S(u,i)$ denote the normalized amount of satisfaction peer $u$ receives from $p(u,i)$ in its $i$th transaction.\n",
    "\n",
    "$T_{(u)} = \\displaystyle\\sum_{i=1}^{I(u)} S(u,i)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "c7f068ce-98a7-4b4e-8d40-18aaab488d28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 6, 7, 4, 8, 2, 3, 18, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "bd325e49-e9ba-4d70-b96d-5d87af90938b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1), (0, 4), (0, 2), (0, 3), (0, 18), (0, 13), (0, 14), (0, 15), (1, 6), (1, 7), (1, 8), (1, 16), (6, 12), (6, 16), (7, 8), (4, 3), (2, 5), (2, 17), (2, 14), (3, 15), (18, 17), (18, 14), (5, 9), (5, 10), (5, 11), (10, 11), (11, 12), (17, 19)]\n"
     ]
    }
   ],
   "source": [
    "print(G.edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "8b86f237-a8ea-41ae-8445-8f96152a8966",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_new_transaction(u_sorted, v_sorted):\n",
    "    rate = []\n",
    "    if (u_sorted in feedback.keys()):\n",
    "        transaction = feedback[u_sorted]\n",
    "        if (transaction):\n",
    "            if v_sorted in transaction.keys():\n",
    "                transaction[v_sorted].append(random.random())\n",
    "            else:\n",
    "                rate.append(random.random())\n",
    "                transaction[v_sorted] = rate\n",
    "        else:\n",
    "            transaction={}\n",
    "            rate.append(random.random())\n",
    "            transaction[v_sorted] = rate\n",
    "        feedback[u_sorted] = transaction\n",
    "    else:\n",
    "        transaction={}\n",
    "        rate.append(random.random())\n",
    "        transaction[v_sorted] = rate\n",
    "        feedback[u_sorted] = transaction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "74946373-9fbe-4c58-9bb0-22e7719dccf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def flatten(lista):\n",
    "    regular_list = [it for it in lista.values()]\n",
    "    flat_list = [item for sublist in regular_list for item in sublist]\n",
    "    return flat_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "b3f694d8-3063-4bc6-818c-75a01ba31520",
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(a=12345, version=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "a50a262e-ed96-4b1c-a209-a99a939df1c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "feedback={}\n",
    "I={}\n",
    "S={}\n",
    "\n",
    "# produce random transactions and record them into feedback dict\n",
    "for i in range(150):\n",
    "    u_sorted = random.choice(list(G.nodes))\n",
    "    u_peers = [x[1] for x in list(G.edges(u_sorted))]\n",
    "    v_sorted = random.choice(u_peers)\n",
    "    add_new_transaction(u_sorted, v_sorted)\n",
    "    add_new_transaction(v_sorted, u_sorted)\n",
    "    \n",
    "# prduce I[u] the total number of transactions performed by peer 𝑢\n",
    "for u in G.nodes:\n",
    "    I[u] = sum([len(feedback[u][x]) for x in feedback[u].keys()])\n",
    "\n",
    "# produce S(u,i) normalized amount of satisfaction between 0 and 1\n",
    "for u in G.nodes:\n",
    "    helper = dict()\n",
    "    for x in feedback[u].items():\n",
    "        k, lista = x\n",
    "        new_lista = [x/sum(flatten(feedback[u])) for x in lista]        \n",
    "        helper[k] = new_lista\n",
    "    S[u]=helper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "e60b5f76-01e5-4fa8-8ce9-0cd7ec4c5304",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 34, 1: 24, 6: 14, 7: 22, 4: 10, 8: 22, 2: 17, 3: 13, 18: 9, 5: 20, 9: 6, 10: 13, 11: 12, 12: 11, 13: 6, 14: 12, 15: 15, 16: 11, 17: 21, 19: 8}\n"
     ]
    }
   ],
   "source": [
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "ff9ad1ff-d911-432f-9355-2e325c11a657",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{5: [0.04855504190445612, 0.15706339266343916, 0.11306457301894487, 0.04939683211069661, 0.013562201190294668, 0.007267900811516789, 0.014302322455604583, 0.16765603085901618, 0.0911347733546735], 11: [0.055204564684390646, 0.10245876288085874, 0.08095984563148495, 0.09937375843462345]}\n"
     ]
    }
   ],
   "source": [
    "print(S[10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "18a1b203-b61c-42c4-8880-a461e9c84652",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.2688444744336037, 0.32016746554782305, 0.7831536269382824, 0.34648483980952016, 0.9656392153447096, 0.7966854818899191, 0.6907560367577495, 0.531592431314921, 0.6923780901879453, 0.3387230118708402, 0.10222842885663086, 0.8582605975393666, 0.4595436214646851, 0.9582520011879929, 0.7319784813523641, 0.5743774116338538, 0.4270765425506674, 0.6861287710443013, 0.24237756295233337, 0.3531938303956982]\n"
     ]
    }
   ],
   "source": [
    "T=[random.random() for x in G.nodes]\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "c0576e61-4de0-4e78-bf94-9974d8a36684",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.009186725473217196"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T[10]/sum(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "bb46390c-ba0b-4edb-8d9a-afcb81ef9387",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_items([(5, [0.04855504190445612, 0.15706339266343916, 0.11306457301894487, 0.04939683211069661, 0.013562201190294668, 0.007267900811516789, 0.014302322455604583, 0.16765603085901618, 0.0911347733546735]), (11, [0.055204564684390646, 0.10245876288085874, 0.08095984563148495, 0.09937375843462345])])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S[10].items()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "b74cd5cf-d16d-4d3a-a433-b1009a10b3b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Tant = T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "id": "050690b2-62ac-40d0-9de4-f6200cccac7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# soma ponderada dos S(u,i) * Cr(p(u,i))\n",
    "# feedback normalizado de cada interação vezes a reputação do peer envolvido com u na transação i\n",
    "for u in G.nodes:\n",
    "    i = 0\n",
    "    while i < 6:\n",
    "        T0 = T[u]\n",
    "        Cr={}\n",
    "        helper = 0\n",
    "        for it in S[u].items():\n",
    "            k, v = it\n",
    "            Cr[k] = T[k]/sum(T)\n",
    "            helper =+ sum(np.array(v)*Cr[k])\n",
    "        T[u]=helper\n",
    "        T[u]\n",
    "        if (abs(T[u]-T0) < 0.01):\n",
    "            break\n",
    "        i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "430dc14a-198e-4cd8-ad1d-6ce3cd9455e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.002613336124723618, 0.008286227266454185, 0.033874532247179574, 5.760544044843236e-05, 0.001489459540650029, 0.0012422634211100565, 0.016599558214399335, 0.05636581923682228, 0.005289833376445048, 0.000246893025302669, 0.05816882196323808, 2.3525537108107606e-05, 0.002138705407977712, 0.0009627819085705877, 0.003306745530111472, 1.2403419225234639e-05, 0.0037159080188836095, 0.025741833223380844, 0.04438195183996303, 0.07504010182151309]\n"
     ]
    }
   ],
   "source": [
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "3212355e-b80e-4aaa-b910-fff2e18f29fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView((0, 1, 6, 7, 4, 8, 2, 3, 18, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19))"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12de0985-8d70-46f0-88f6-39ea90c8f4a7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7beef3af-8378-4f41-b752-162f786062c5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0276b5ed-cb18-4788-9680-7112fb4908a0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ed8f1631-fab4-4d2a-9ab8-209c3e03aad6",
   "metadata": {},
   "source": [
    "### Aggregating *Local Trust Values*\n",
    "\n",
    "A natural way to do this in a distributed environment is for peer $i$ to ask its acquaintances about their opinions about other peers. \n",
    "\n",
    "It would make sense to weight their opinions by the trust peer $i$ places in them:\n",
    "\n",
    "$t_{ik} = \\sum_{j} c_{ij}c_{jk}$\n",
    "\n",
    "where $t_{ik}$ represents the trust that peer $i$ places in peer $k$ based on asking his friends.\n",
    "\n",
    "Back to Alice's example. So instead, **why doesn’t she also ask those peers that she already trusts, for their opinion on their friends?** So if Alice now wants to download from David, who she’s never interacted with before, she checks with Bob (who she’s logged as +5) and with Charlie (who she’s logged as +15) for their opinions of David, and Alice weights Charlie’s opinion of David higher than Bob’s, because she trusts him more than Bob based on her own interactions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7a3e190-cf6d-4889-a54c-27744339f981",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.zeros(c.shape)\n",
    "for i in range(c.shape[0]):\n",
    "    for k in range(c.shape[0]):\n",
    "        for j in range(c.shape[0]):\n",
    "            t[i][k] += c[i][j] * c[j][k]\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "406d45b2-fd72-4aaa-903d-8330bb1d5c7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.sum(t, axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a83613f8-c0cf-49e4-b8cb-2c2b9b0cf0df",
   "metadata": {},
   "outputs": [],
   "source": [
    "def tabula_aggregate_trust_values(line):\n",
    "    adja = adjs[line].tolist()\n",
    "    adja.insert(0,'adjacency')\n",
    "    adja.append(sum(adjs[line]))\n",
    "    \n",
    "    newli = s[line].tolist()\n",
    "    newli.insert(0,'local trust value')\n",
    "    newli.append(sum(s[line]))\n",
    "    \n",
    "    newci = c[line].tolist()\n",
    "    newci.insert(0,'normalized local trust value')\n",
    "    newci.append(sum(c[line]))\n",
    "    \n",
    "    agg = t[line].tolist()\n",
    "    agg.insert(0,'aggregated local trust value')\n",
    "    agg.append(sum(t[line]))\n",
    "    \n",
    "    table=[adja, newli,newci,agg, SEPARATING_LINE]\n",
    "    print(tabulate(table, headers=['metric'] + nodelist + ['agg'], floatfmt=\".2f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "944d8a4e-b612-4422-9e5c-9db397339b8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "203c7355-dd32-42c4-a6de-7ee71fc45ab0",
   "metadata": {},
   "outputs": [],
   "source": [
    "tabula_aggregate_trust_values(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "161566b2-d19b-47f1-90d5-17681722c41e",
   "metadata": {},
   "source": [
    "Interpretation: $t_{ik}$ represents the trust that peer $i$ places in peer $k$. However, this trust is an aggregation of the trust of the direct peers of $i$ places on $k$. \n",
    "\n",
    "In other words, this is based on opinions of $i$'s friends about their friends, factored on $i$'s opinion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8840a373-5043-4a0b-8a8f-796e44cc9c78",
   "metadata": {},
   "outputs": [],
   "source": [
    "tabula_aggregate_trust_values(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "20b856fc-a538-4bf0-acbd-4a00ebcdf9cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "tabula_aggregate_trust_values(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a304c0dd-4f19-4dc1-becf-6fdcf9f142d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "tabula_aggregate_trust_values(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a9ebfd0-f812-4888-888d-afde6b1699ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "#np.sum(t, axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea7ebc2-672d-4936-80a0-285b2b1bc523",
   "metadata": {},
   "source": [
    "We can write $t_{ik} = \\sum_{j} c_{ij}c_{jk}$ in matrix notation.\n",
    "\n",
    "If we define $C$ to be the matrix $[c_{ij}]$ and $\\overrightarrow{t_{i}}$ to be the vector containing the values $t_{ik}$, then $\\overrightarrow{t_{i}} = C^T \\overrightarrow{c_{i}}$. (Note that $\\sum_{j} t_{ij} = 1$ as desired)\n",
    "\n",
    "This is a useful way to have each peer gain a view of the network that is wider than his own experience.\n",
    "\n",
    "#### Remark:\n",
    "\n",
    "#### $t_{ik}$ is the value that $i$'s acquaintances places on $k$ weight by how much trust $i$ places on each acquaintance.\n",
    "\n",
    "#### $\\overrightarrow{t_{i}}$ is the **vector** containing the reputation of $k$ that arrives on $i$ by the transmission from its acquaintances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5fe12587-a164-4667-b2e2-7e1c1d991983",
   "metadata": {},
   "outputs": [],
   "source": [
    "t[0], sum(t[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d8dcfb60-ec78-41e0-834f-7007d3b41d2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(c.T,c[0]) == t[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2cc5c46-ad10-4b66-b34b-b88d3ae01155",
   "metadata": {},
   "source": [
    "$\\overrightarrow{t_{i}} = C^T \\overrightarrow{c_{i}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44640e0c-d5bd-4ce1-8ff3-530adbfcaf62",
   "metadata": {},
   "outputs": [],
   "source": [
    "# vetor t[0]\n",
    "np.dot(c.T,c[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "129a7491-8396-410c-8822-257bc126bfee",
   "metadata": {},
   "source": [
    "However, the trust values stored by peer $i$ still reflect only the experience of peer $i$ and his acquantainces. \n",
    "\n",
    "In order to get a wider view, peer $i$ may wish to ask his friends’ friends $\\overrightarrow{t_{i}} = (C^T)^2 \\overrightarrow{c_{i}}$\n",
    "\n",
    "If he continues in this manner, $\\overrightarrow{t_{i}} = (C^T)^n \\overrightarrow{c_{i}}$, he will have a complete view of the network after $n = $large iterations (under the assumptions that C is irreducible and aperiodic.\n",
    "\n",
    "Fortunately, if $n$ is large, the trust vector $\\overrightarrow{t_{i}}$ will converge to the same vector for every peer $i$. Namely, it will converge to the left principal eigenvector of $C$. In other words,$\\overrightarrow{t}$ is a global trust vector in this model. Its elements, $t_j$ , quantify how much trust the system as a whole places peer $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6345f4-231e-491b-b619-b6de242d32bb",
   "metadata": {},
   "source": [
    "#### Probabilistic Interpretation\n",
    "It is useful to note that there exists a straightforward probabilistic interpretation of this method, similar to the *Random Surfer model* of [L. Page, S. Brin, R. Motwani, and T. Winograd. The\n",
    "PageRank Citation Ranking: Bringing Order to the Web. Technical report, Stanford Digital Library Technologies Project, 1998.]. If an agent were searching for reputable peers, it can crawl\n",
    "the network using the following rule: at each peer $i$, it will crawl to peer $j$ with probability $c_{ij}$ . After crawling for a while in this manner, the agent is more likely to be at reputable peers than unreputable peers. The stationary distribution of the Markov chain defined by the normalized local trust matrix C is our global trust vector $\\overrightarrow{t}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09413a7e-e2a2-48e1-906b-825f168c84cf",
   "metadata": {},
   "source": [
    "### Basic EigenTrust\n",
    "\n",
    "$\\overrightarrow{e}$ to be the $m$-vector representing a uniform probability distribution over all $m$ peers, $e_i = 1/m$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b48e7c7-73f0-4864-aca4-c09a8ba50fb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#e = adjs/np.sum(adjs, axis=1, keepdims=True)\n",
    "#e = adjs/np.sum(adjs)\n",
    "#np.sum(e, axis=1, keepdims=True).T\n",
    "#e[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7d8a009-853b-4ced-a05f-c9d453d8bddf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this is the distribution, 1 / len(nodes)\n",
    "e = np.ones((len(nodelist)))/len(nodelist)\n",
    "e.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8149b68b-d022-4adb-9c90-9b55b0b4f5ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08f749a0-8b19-400c-b92e-52f35a0aa79a",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09db51c7-ea48-4894-abff-799acdf3d603",
   "metadata": {},
   "outputs": [],
   "source": [
    "def basic_eigen(initial_vec):\n",
    "    counter = 0\n",
    "    rep = initial_vec\n",
    "    epsilon = 0.0005\n",
    "    while True:\n",
    "        t_vec = np.dot(c.T,rep)\n",
    "        theta = np.abs(t_vec - rep)\n",
    "        rep = t_vec\n",
    "        if ((theta < epsilon).all()):\n",
    "            break\n",
    "        if counter >= 2000: \n",
    "            break\n",
    "        counter += 1\n",
    "    return dict(t_vec=t_vec, counter=counter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94910584-b29b-449d-92c3-938fa1e9a1a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(nodelist)):\n",
    "    print(basic_eigen(c[i]),'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4c365cb-52c8-4944-8f29-9d1a6931c839",
   "metadata": {},
   "source": [
    "Above the proof that, if $n$ is large, the trust vector $\\overrightarrow{t_{i}}$ will converge to the same vector for every peer $i$. Namely, it will converge to the left principal eigenvector of $C$. \n",
    "\n",
    "In other words,$\\overrightarrow{t}$ is a global trust vector in this model. Its elements, $t_j$ , quantify how much trust the system as a whole places peer $j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "38466755-049f-4ee9-8955-d52fe778c219",
   "metadata": {},
   "outputs": [],
   "source": [
    "te = basic_eigen(e)\n",
    "te"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b0931b4-5532-4f5d-a32e-0b79e5d657d3",
   "metadata": {},
   "source": [
    "(In Section 4.2, we said we wish to compute $\\overrightarrow{t_{i}} = (C^T)^n \\overrightarrow{c_{i}}$, where $\\overrightarrow{c_{i}}$ is the normalized local trust vector of some peer $i$. \n",
    "\n",
    "However, since they both converge to the principal left eigenvector of $C$, we may use $\\overrightarrow{e}$ instead.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c5f97e2a-d099-4c56-93ac-c3fa541426f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def tabula_eigentrust_values(eigenvector):\n",
    "    node_degree = np.sum(adjs,axis=1, keepdims=True).T\n",
    "    node_agg_local_trust = np.sum(s, axis=0, keepdims=True)\n",
    "    avg_trust = node_agg_local_trust / node_degree\n",
    "\n",
    "    node_degree = node_degree.flatten().tolist()\n",
    "    node_agg_local_trust = node_agg_local_trust.flatten().tolist()\n",
    "    avg_trust = avg_trust.flatten().tolist()\n",
    "    eig = eigenvector.tolist()\n",
    "\n",
    "    node_degree.insert(0,'node_degree')\n",
    "    node_agg_local_trust.insert(0,'node_agg_local_trust')\n",
    "    avg_trust.insert(0,'trust_per_degree')\n",
    "    eig.insert(0,'eigenvector trust value')\n",
    "\n",
    "    table=[node_degree, node_agg_local_trust,avg_trust, eig, SEPARATING_LINE]\n",
    "    print(tabulate(table,headers=['metric'] + nodelist, floatfmt=\".2f\"))\n",
    "        \n",
    "    #eig = eigenvector.tolist()\n",
    "    #eig.insert(0,'eigenvector trust value')\n",
    "    #eig.append(np.sum(eigenvector))\n",
    "    \n",
    "    #table=[eig]\n",
    "    #print(tabulate(table, headers=['metric'] + nodelist + ['agg'], floatfmt=\".2f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ea342897-e111-4242-a4ed-178d05ad4c82",
   "metadata": {},
   "outputs": [],
   "source": [
    "tabula_eigentrust_values(te['t_vec'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa6cca61-01bc-47a2-821e-5db66ad6eced",
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ae22973-253f-4933-8a27-1e159e44ea91",
   "metadata": {},
   "source": [
    "Fortunately, if $n$ is large, the trust vector $\\overrightarrow{t_{i}}$ will converge to the same vector for every peer $i$. Namely, it will converge to the left principal eigenvector of $C$. In other words,$\\overrightarrow{t}$ is a global trust vector in this model. Its elements, $t_j$ , quantify how much trust **\"The System\"** as a whole places peer $j$.\n",
    "\n",
    "In Eigentrust, the global reputation of each peer $i$ is given by the local trust values assigned to peer $i$ by other peers, weighted by the global reputations of the assigning peers."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07f1fe40-4be7-4bb4-81eb-4338e43e718d",
   "metadata": {},
   "source": [
    "### Practical Issues\n",
    "\n",
    "There are three practical issues that are not addressed by this simple algorithm: \n",
    "- a priori notions of trust, \n",
    "- inactive peers, \n",
    "- and malicious collectives.\n",
    "\n",
    "\n",
    "**A priori notions of trust**. Often, there are some peers in the network that are known to be trustworthy. For example, the first few peers to join a network are often known to be trustworthy, since the designers and early users of a P2P network are likely to have less motivation to destroy the network they built. It would be useful to incorporate such notions of trust in a natural and seamless manner. We do this by defining some distribution $\\overrightarrow{p}$ over pre-trusted peers.\n",
    "\n",
    "For example, if some set of peers $P$ are known to be trusted, we may define $p_i = \\dfrac{1}{|P|}$ if $i ∈ P$, and $p_i = 0$ otherwise. We use this distribution $\\overrightarrow{p}$ in three ways. First of all, in the presence of malicious peers, $\\overrightarrow{t} = (C^T)^n \\overrightarrow{p}$ will generally converge faster than $\\overrightarrow{t} = (C^T)^n \\overrightarrow{e}$, so we use $\\overrightarrow{p}$ as our start vector.\n",
    "\n",
    "**Inactive Peers**. If peer $i$ doesn’t download from anybody else, or if it assigns a zero score to all other peers, $c_{ij}$ from Equation $s_{ij} = sat(i, j) − unsat(i, j)$ will be undefined. In this case, we set $c_{ij} = p_j$ . \n",
    "\n",
    "So we redefine $c_{ij}$ as:\n",
    "\n",
    "$\n",
    "c_{ij}=\n",
    "\\begin{cases}\n",
    "\\dfrac{max(s_{ij},0)}{\\sum_{j} max(s_{ij},0)} & \\quad \\text{if $\\sum_{j} max(s_{ij},0) \\neq 0$ }\\\\ \n",
    "p_j & \\quad \\text{otherwise}\n",
    "\\end{cases}\n",
    "$\n",
    "\n",
    "That is, if peer $i$ doesn’t know anybody, or doesn’t trust anybody, he will choose to trust the pre-trusted peers.\n",
    "\n",
    "**Malicious Collectives**. In peer-to-peer networks, there is potential for malicious collectives to form. A malicious collective is a group of malicious peers who know each other, who give each other high local trust values and give all other peers low local trust values in an attempt to subvert the system and gain high global trust values.\n",
    "\n",
    "We address this issue by taking\n",
    "\n",
    "$\\overrightarrow{t}^{(k+1)} = (1-a) C^T \\overrightarrow{t}^{(k)} + a\\overrightarrow{p}$ \n",
    "\n",
    "where $a$ is some constant less than 1.\n",
    "\n",
    "This is equivalent to setting the opinion vector for all peers to be $\\overrightarrow{c_{ij}} = (1-a) C^T \\overrightarrow{t}^{(k)} + a\\overrightarrow{p}$ , breaking collectives by having each peer place at least some trust in the peers $P$ that are not part of a collective. Probabilistically, this is equivalent to saying that the agent that is crawling the network by the probabilistic model given by $\\overrightarrow{t}$ is less likely to get stuck crawling a malicious collective, because at each step, he has a certain probability of crawling to a pre-trusted peer.\n",
    "\n",
    "It should be emphasized that the pre-trusted peers are essential to this algorithm, as they guarantee convergence and break up malicious collectives. Therefore, the choice of pre-trusted peers is important. In particular, it is important that no pre-trusted peer be a member of a malicious collective. This would compromise the quality of the algorithm. To avoid this, the system may choose a very few number of pre-trusted peers (for example, the designers of the network)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a035816f-5f2d-44ef-82e9-6642d86a2d0c",
   "metadata": {},
   "source": [
    "### Modified EigenTrust\n",
    "\n",
    "Let's define s set of pre-trusted peers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab647f30-96a5-4490-9fe6-ace212f8ea89",
   "metadata": {},
   "outputs": [],
   "source": [
    "P = {0, 6, 11}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d510f68-1a90-4d3c-bb28-8b2b3f6410e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#nodelist, [\"#D2A254\" if x in P else \"#1f78b4\" for x in nodelist]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ccbaeb88-d4fe-409d-aaa6-e623e7f1e9f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G), nodelist=nodelist, with_labels=True, node_color=[\"#D2A254\" if x in P else \"#1f78b4\" for x in nodelist], font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c09412a0-ee1e-451b-a3ed-d34876dd7abf",
   "metadata": {},
   "outputs": [],
   "source": [
    "p = np.array([1/len(P) if x in P else 0 for x in nodelist])\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f55510a0-99b0-4278-975b-36c6c59a5c03",
   "metadata": {},
   "outputs": [],
   "source": [
    "tp = basic_eigen(p)\n",
    "tp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3414fd4a-c5e7-423a-9c3c-18cf4d23de53",
   "metadata": {},
   "outputs": [],
   "source": [
    "def modified_eigen(c, P, a = 0.999):    \n",
    "    def make_c_adj(ce):\n",
    "        li = np.sum(ce, axis=1, keepdims=True).flatten().tolist()\n",
    "        inactive = [idx for (idx, value) in enumerate(li) if np.isnan(value)]\n",
    "        if len(inactive)>0:            \n",
    "            for i in inactive:\n",
    "                ce[i] = p\n",
    "            return ce\n",
    "        else:\n",
    "            return ce\n",
    "                \n",
    "    nodelist = [x for x in range(c.shape[0])]\n",
    "    p_vec = np.array([1/len(P) if x in P else 0 for x in nodelist])\n",
    "    c_adj = make_c_adj(c)\n",
    "    counter = 0\n",
    "    rep = p_vec\n",
    "    epsilon = 0.0005    \n",
    "    while True:\n",
    "        t_vec = np.dot(c_adj.T,rep)\n",
    "        t_vec = (1 - a) * t_vec + a * p_vec\n",
    "        theta = np.abs(t_vec - rep)\n",
    "        rep = t_vec\n",
    "        if ((theta < epsilon).all()):\n",
    "            break\n",
    "        if counter >= 200: \n",
    "            break\n",
    "        counter += 1\n",
    "    return dict(t_vec=t_vec, counter=counter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6ce9dd3-a828-4239-8d9f-93446223b492",
   "metadata": {},
   "source": [
    "$\\overrightarrow{t}^{(k+1)} = (1-a) C^T \\overrightarrow{t}^{(k)} + a\\overrightarrow{p}$ \n",
    "\n",
    "where $a$ is some constant less than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52d68661-f1ab-40d9-8888-cec7e6a0940e",
   "metadata": {},
   "outputs": [],
   "source": [
    "tm = modified_eigen(c, P, 0)\n",
    "tm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d6cede1-9b35-4bd9-aaae-ff4476d6b6da",
   "metadata": {},
   "outputs": [],
   "source": [
    "tp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16ad5249-6c1c-4e72-87b9-0c72d7fda899",
   "metadata": {},
   "outputs": [],
   "source": [
    "te"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1d64dcf-8698-40ba-b9f5-4f8cfa2dcb8b",
   "metadata": {},
   "source": [
    "## Distributed EigenTrust\n",
    "\n",
    "Here, we present an algorithm where all peers in the network cooperate to compute and store the global trust vector, and the computation, storage, and message overhead for each peer are minimal.\n",
    "\n",
    "In a distributed environment, the first challenge that arises is how to store $C$ and $\\overrightarrow{t}$. In previous sections, we suggested that each peer could store its local trust vector $\\overrightarrow{c_i}$. Here, we also suggest that each peer store its own global trust value $t_i$.\n",
    "\n",
    "In fact, each peer can compute its own global trust value:\n",
    "\n",
    "$t_{i}^{(k+1)} = (1-a)(c_{1i}t_{1}^{(k)} + ... + c_{ni}t_{n}^{(k)}) + ap_i$\n",
    "\n",
    "Inspection will show that this is the component-wise version of\n",
    "$\\overrightarrow{t}^{(k+1)} = (1−a)C^T \\overrightarrow{t}^{(k)}+a\\overrightarrow{p}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c8864188-a299-48d2-bc1d-c7160d072423",
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.draw(G,pos=nx.spring_layout(G), with_labels=True, font_weight='bold')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f01fe355-d224-4000-950d-81e5646978a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "#i=12\n",
    "tabula_aggregate_trust_values(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb9c349-aec5-474e-81a6-98133a0dc743",
   "metadata": {},
   "source": [
    "#### $A_i$: set of peers which have downloaded files from peer $i$. These guys may have an opinion about $i$, but $i$ still do not know it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef8ddb95-ce4c-40a2-bdca-0f187ba16ead",
   "metadata": {},
   "outputs": [],
   "source": [
    "def A():\n",
    "    A=dict()\n",
    "    for i in range(c.shape[0]):    \n",
    "        li = c[i].flatten().tolist()\n",
    "        A[i]=[idx for (idx, value) in enumerate(li) if value>0]\n",
    "    return A\n",
    "A()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2351610-e129-45c4-a5a4-cf58bd83fb6d",
   "metadata": {},
   "source": [
    "#### $A$ is matrix of entire network, each line shows the interaction between the column peers $j$ with the line peer $i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bd7a9b95-b20f-4b52-8db7-fb5de1dfbecc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def A_matrix():\n",
    "    A = adjs*c\n",
    "    A = np.where(A>0,1,0)\n",
    "    return A\n",
    "A_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "979fadce-4828-4209-8369-1b9682285e49",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_matrix()[12]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a73567f-163c-4dab-826b-425f306c7ea4",
   "metadata": {},
   "source": [
    "#### $B_i$: set of peers from which peer $i$ has downloaded files, so peer $i$ might have opinions about all of them, but they still do not know it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b2a7c06-5fa3-4cf7-9989-2a65d1464ef3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def B():\n",
    "    B=dict()\n",
    "    for i in range(c.shape[0]):    \n",
    "        li = c.T[i].flatten().tolist()\n",
    "        B[i]=[idx for (idx, value) in enumerate(li) if value>0]\n",
    "    return B\n",
    "B()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "717eeab0-5206-4723-a219-d13dacfcae5d",
   "metadata": {},
   "source": [
    "#### B is a matrix of the entire network, whcih relates the relation of peer $i$ with those peers $j$ that he may have an opinion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f72f27da-7793-4f13-9b50-118d80bb7dd0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def B_matrix():\n",
    "    B = adjs*c.T\n",
    "    B = np.where(B>0,1,0)\n",
    "    return B\n",
    "B_matrix()[12]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e59c4e1-e169-4c4a-a3ee-cbeae6a475e1",
   "metadata": {},
   "source": [
    "#### Pre-trusted Peers\n",
    "\n",
    "Only the pre-trusted peers need to know their $p_i$. This means that pre-trusted peers may remain anonymous; nobody else needs to know that they are pre-trusted. Therefore, the pretrusted peers maintain anonymity as pre-trusted peers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1c76995-931c-41e6-8de7-b5143a84269f",
   "metadata": {},
   "outputs": [],
   "source": [
    "P, p"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61b9915e-f657-48c6-8f59-cc8c9892586c",
   "metadata": {},
   "source": [
    "### Algorithm:\n",
    "\n",
    "#### Important assumption\n",
    "\n",
    "- Each peer store its local trust vector $\\overrightarrow{c_i}$. \n",
    "- Each peer store its own global trust value $t_i$.\n",
    "\n",
    "Each peer $i$ do: \n",
    "\n",
    "1. Query all peers $j ∈ A_i$ for $t^{(0)}_j = p_j$ ;\n",
    "   \n",
    "   Filtre todos os amigos $j$ que conhecem $i$ e considere $t^{(0)}_j = p_j$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e38cd942-703b-439a-a0e2-226cc07c97d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "ti = np.zeros(p.shape)\n",
    "ci = np.zeros(c.shape)\n",
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43b55483-a7b2-4c8f-9043-42f0b4413989",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 0.5\n",
    "i = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4170ea9-dcec-4b5d-83aa-c2aae22eb248",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_matrix()[i], A()[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e163fc05-d0ba-4ae2-956f-f95696512bbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in A()[i]:\n",
    "    ti[j] = p[j]\n",
    "ti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8221c8a3-4b6b-44e4-a147-26cca51f7e64",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_old = ti[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "639ad63e-5531-41e7-b808-a34a2ad81cb7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# repeat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9aafcce-3d15-4a9f-a6ef-cb9357cf305b",
   "metadata": {},
   "outputs": [],
   "source": [
    "ci[i] = c[0]\n",
    "ci[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e9377af-4220-4599-b72a-8df920a5fe83",
   "metadata": {},
   "outputs": [],
   "source": [
    "ci.T[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "866dde49-6a98-4476-b701-537454997abc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute t^(k+1)\n",
    "ti[i] = (1 - a) * np.sum(ci.T[i] * ti[i]) + a * p[i]\n",
    "ti[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9545623e-aedb-458d-99c9-106322fa266b",
   "metadata": {},
   "outputs": [],
   "source": [
    "B_matrix()[i], B()[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b34624a-65d2-4a37-91aa-16aa46160f6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Send C_(ij)^(t(k+1)) to all peers j in B[i]\n",
    "for j in B()[i]:\n",
    "    \n",
    "    ci[j][i] = ci[i][j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87f7c1b3-c23e-4f42-99a0-df66e9fc333e",
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = np.abs(ti[i]-t_old)\n",
    "delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d59a3ae-3bb2-4237-a107-aa5abcb8bd77",
   "metadata": {},
   "outputs": [],
   "source": [
    "A_matrix()[i], A()[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71dcb89e-7a91-411f-951e-83c06a4b3acf",
   "metadata": {},
   "outputs": [],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bce4d9f3-6164-4308-a4c0-ebb5a2826eea",
   "metadata": {},
   "outputs": [],
   "source": [
    "ci"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08cc2b10-a6ee-4fa9-9e9e-629dce0c8859",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Wait for all peers j in A[i] to return  C_(ji)^(t(k+1))\n",
    "for j in A()[i]:\n",
    "    ti[j] = (1 - a) * np.sum(ci.T[j] * ti[j]) + a * p[j]\n",
    "    ci[i][i] = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12f68987-4642-4b3d-8a1e-6849c5b7c208",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7ca14127-c621-401c-9c82-84b6fdd6fe32",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01c5ddcd-e53a-4a9c-96f3-17c931c2047b",
   "metadata": {},
   "outputs": [],
   "source": [
    "A[0]*p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9bf2aaf9-29ad-4e22-8ad3-24820de01bf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c74e86e-972e-4b96-946e-05419179b818",
   "metadata": {},
   "outputs": [],
   "source": [
    "tnew = np.zeros(p.shape)\n",
    "tnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77ccd283-ac7c-4de8-bbdf-6bca57dbc84f",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d56c849a-224e-4847-83ad-e15fd6db6099",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[0]*B[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e3f5364-85b4-43b0-97f8-8bb52e04929e",
   "metadata": {},
   "outputs": [],
   "source": [
    "cnew = np.zeros(c.shape)\n",
    "cnew.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0893a06d-25b8-4c9e-be41-894dab9d81c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "cnew[0] = c[0]*B[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db33aef2-7460-4377-99a9-1ec8230ad44a",
   "metadata": {},
   "outputs": [],
   "source": [
    "cnew[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f3ca3456-8da9-4d58-92c3-a159db45a6ea",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "80a5a80c-41ee-495a-bc57-6c5374ecf083",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c06d0526-5f74-4bb6-bf34-bda7de061df2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "09d73306-c489-47cc-a6c0-4307a4a7a712",
   "metadata": {},
   "source": [
    "$t_i$ is a vector of the trust each $i$ has of its peers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2413065-2fea-4383-9463-568e51957549",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.zeros(c.shape)\n",
    "t # cada i vai calcular seu t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bcf1e322-aa81-4766-a13b-6647bfaf99d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "t= A * p\n",
    "t\n",
    "# Only peers j = {0,6, 11} knows their initial score\n",
    "# each peer compute and store it won version of the GLOBAl TRUST VECTOR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21f949d4-2155-49b7-956f-ccfc54f11130",
   "metadata": {},
   "source": [
    "Initially the vector $t$ comes from pre-trusted peers that $i$ is related with.\n",
    "In the case of peer $i=5$, because it is related to peer $11$, and it happens to be a pre-trusted, then $t^{0}_5$ contains trust only with $11$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21638116-1b47-4577-ac6e-09a425b64c9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(c.T[5], t[5].T) # this is a component wise version of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21515592-bb05-43d9-a78c-3458a7613e51",
   "metadata": {},
   "outputs": [],
   "source": [
    "tnew = np.dot(c.T, t[5].T)\n",
    "tnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0acbf815-7698-4549-bad2-cc99ca0f8534",
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = np.abs(tnew[5] - t[5][5])\n",
    "delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03703fa7-e89b-46bc-9b6c-04b98646ab6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "31c5f461-f093-4edd-abb4-1812f05cd690",
   "metadata": {},
   "outputs": [],
   "source": [
    "c.T[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bc3bbe2b-780d-49f9-9ec3-f3253bce6a75",
   "metadata": {},
   "outputs": [],
   "source": [
    "t[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a571cc73-9488-4fac-850a-71a521ced35f",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.sum(c.T[5] * t[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "643d46f2-8608-4df1-8fec-861019496760",
   "metadata": {},
   "outputs": [],
   "source": [
    "tnew"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "258aaec5-ea1b-40a6-ac00-de080eb4777a",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9656ab2-b33a-47b6-8e56-2fed8d6c75d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[9]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a19608ba-44e2-4289-b6a8-f0b47130aaf3",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[11]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99cf2b36-6461-4af0-a4f3-18e777dc23cc",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0092b58d-f32b-47e3-81cb-7bb3c7b5a18a",
   "metadata": {},
   "outputs": [],
   "source": [
    "A[5] * c[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c340e954-b2a3-4283-aeb3-b6512f5b74ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[5] * c.T[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57b94fdc-974c-4b5e-9f65-3eefe8424116",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "785cc6b1-e1c8-485f-9db9-328b2f1e3a95",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d6526a1-a0ec-4085-b37d-41566d2bdd8c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f0abeeaa-ba4a-441d-9e25-e375fb454332",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e421761c-3d0f-4cd7-aa4c-976ac05195db",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1324c994-0f9b-47fa-a08f-1dd5037de7f9",
   "metadata": {},
   "source": [
    "Now we transpose the $c_{ij}$ matrix, because the only info peer $i$ has is his trust experience with his direct peers $j$. At this stage $i$ does not know how much his accquaintances think of him."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e07fc68-1ca8-4ecb-9eab-75b0b7ecfd31",
   "metadata": {},
   "outputs": [],
   "source": [
    "c.T[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6fed64b-cd45-4953-bd0e-154ca3238878",
   "metadata": {},
   "outputs": [],
   "source": [
    "c.T[5].shape, tj[5].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "118a06ce-3e1e-4a9a-85c8-7ad13831d6f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "ti[5] = np.dot(c.T[5],tj[5])\n",
    "ti[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8fff9637-0c19-484b-a420-f00f16c37ca3",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81c78a1d-c83d-42ef-bd9e-3b9505046cd2",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0d90d6d-cb46-476b-8cd5-9dc484138be5",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[5]*c[5]*ti[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "63ee2e03-3e37-4ac8-adf2-46076f593585",
   "metadata": {},
   "outputs": [],
   "source": [
    "ti[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d1611fd-c044-4ea6-b75d-4f8d39fe9ea7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# to start with\n",
    "a = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77609ad8-ed8b-4ec1-a9aa-b79aa9c9c56e",
   "metadata": {},
   "source": [
    "Para computar a interação vamos agregar as confianças dos peers que temos confiança, está é a única infomação que cada peer possui, no caso $c.T[5]$ são os peers que 5 tem uma experiencia própria de confiança vezes a confiança de cada um deles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bf5cfbb8-f382-4efa-9ad6-7632cca1f37f",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(20):\n",
    "    np.dot(c.T[i],t.T[i])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "83f4b607-afdd-49c1-afe3-f987f8d7916e",
   "metadata": {},
   "outputs": [],
   "source": [
    "t1[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b44731a7-71bc-44aa-a592-1143f087cdef",
   "metadata": {},
   "outputs": [],
   "source": [
    "res = termo1 + termo2\n",
    "res[5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8df1c3c-606a-4037-bfde-1102ada49264",
   "metadata": {},
   "source": [
    "Uma vez computado o escore de confiança de meus peers, eu passo para eles. Da mesma forma no final eu também vou receber de meus peers uma nova informação do quanto eles confiam em mim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2e84e0a-8d45-4cc7-9483-f28c84615d53",
   "metadata": {},
   "outputs": [],
   "source": [
    "B[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1293d2b7-136c-423f-aea5-39ea35bee6b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[5]*res[5]*B[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b14d9a6a-047d-418c-87b3-464e9ba38cfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[5]*res[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cd10b12c-94f0-4c9c-9c4d-a8ab11668977",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.dot(c[5],res[5].T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b16ae5a5-cf5d-42d1-b744-bef403d0346a",
   "metadata": {},
   "source": [
    "In most P2P networks, each peer has limited interaction with other peers. There are two benefits to this. First, the computation \n",
    "$t_{i}^{(k+1)} = (1-a)(c_{1i}t_{1}^{(k)} + ... + c_{ni}t_{n}^{(k)}) + ap_i$\n",
    "is not intensive, since most $c_{ji}$ are zero. Second, the number of messages passed is small, since $A_i$ and $B_i$ are small. In the case where a network is full of heavily active peers, we can enforce these benefits by limiting the number of local trust values $c_{ij}$ that each peer can report."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ffcf0ff1-16d1-45df-a1ec-00b0391d9327",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbf2a6b7-0cfa-495e-ba10-6bda5ef5e0e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Summary\n",
    "t = A * p\n",
    "epoch = 0\n",
    "#print(dict(t_0=t, epoch=epoch))\n",
    "a = 0\n",
    "\n",
    "while True:\n",
    "    if epoch >= 10: \n",
    "        break\n",
    "    epoch += 1\n",
    "    termo1 = (1-a) * np.dot(c.T,t.T)\n",
    "    termo2 = a * p\n",
    "    t = termo1 + termo2\n",
    "print('Each peer calculates its version of global trust')\n",
    "\n",
    "print(dict(t_i=t, epoch=epoch))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce195b8c-31fc-40a4-b7aa-783c4fed9ee0",
   "metadata": {},
   "source": [
    "# New Version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "55505acb-ccf2-47da-8eaf-72078f8a9b48",
   "metadata": {},
   "outputs": [],
   "source": [
    "A()[5], B()[5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ae110825-b168-4965-a62d-ff8494cccbf4",
   "metadata": {},
   "outputs": [],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95a4f82b-4866-445c-80ae-9f8138997373",
   "metadata": {},
   "outputs": [],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4ce1b090-d0ed-4262-8bb0-35e4123966ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "ti = np.zeros((c.shape))\n",
    "ti.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87b49161-c199-46e2-9373-26db990c5d1a",
   "metadata": {},
   "outputs": [],
   "source": [
    "a=0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ececa2a8-a03b-4399-8a93-4c23d712fde8",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(20):\n",
    "    for j in A()[i]:\n",
    "        ti[i][j] = p[j]\n",
    "ti"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e621d2d-dd51-4447-b681-aa62aa5d9bd3",
   "metadata": {},
   "outputs": [],
   "source": [
    "ci = np.zeros((20,20,20))\n",
    "for w in range(20):\n",
    "    ci[w][w] = c[w]\n",
    "ci[0], ti[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9b82f8ca-70c8-428b-9e8c-1c977f52b5a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 0\n",
    "ti[i][i] = (1 - a) * np.dot(ci[i][i].T,ti[i]) + a * p[i]\n",
    "ti[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "53a24454-a812-41de-881a-3194bea3e5b3",
   "metadata": {},
   "outputs": [],
   "source": [
    "A()[i], B()[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "44461602-64c3-424e-9d64-8380db124e64",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in B()[i]:\n",
    "    ci[j][i][j] = ci[i][i][j]\n",
    "    ti[j][i] = ti[i][i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f99025ee-e2f8-465b-b6fa-eab277677cf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "w=13\n",
    "ci[w], ti[w]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6ff30176-f3ef-47d5-96ee-9e03bd33a46c",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in A()[i]:\n",
    "    ci[i][j][i] = ci[j][j][i]\n",
    "    ti[i][j] = ti[j][j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2597e93a-1525-4413-b07c-ad28b3a7ff56",
   "metadata": {},
   "outputs": [],
   "source": [
    "w=13\n",
    "ci[w], ti[w]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c4780c6-f378-42ff-9c1d-5cff2a926e31",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b226e71-035f-4305-8ab5-b24528bdd6c0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0cbcad4a-0992-40ea-abca-2daff83c1dd5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "12a8bd30-5ce1-4f1f-9440-0888c6398a21",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Summary\n",
    "\n",
    "epoch = 0\n",
    "for i in range(1):\n",
    "    print(f'{i=}')\n",
    "    t_old = (A * p)[0]\n",
    "    while True:\n",
    "        if epoch >= 5: \n",
    "            break\n",
    "        epoch += 1\n",
    "        print(f'\\t{epoch=}')\n",
    "        t_new = np.dot(c.T,t_old.T)\n",
    "        print(f'\\t\\t{t_new[0]=}')\n",
    "        delta = np.abs(t_new[0]-t_old[0])\n",
    "        print(f'\\t\\t{delta=}')\n",
    "        t_old = t_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a0ec0266-a857-4d86-a75c-361f04ce25ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "c.T[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4820ceb-719a-4741-88e5-6988b4c08311",
   "metadata": {},
   "outputs": [],
   "source": [
    "A[0] * p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f478c54c-29f8-46db-ba2e-43cf664dcd1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "640bea87-1d10-4d87-b0a0-c9afe0fad028",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0a85a54-3528-42b7-85be-f382945198ca",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be939749-a00b-444b-a992-6fc263e17a26",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5543657d-c935-46dd-9abc-9dafe9e9c3d5",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94cef0a9-f009-45a4-a49e-e69c0d9c671d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1cfb6b72-d61f-4b21-99b0-7f320287a4e5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def distributed_eigen(c, p, a = 0.999):               \n",
    "    counter = 0\n",
    "    rep = pi\n",
    "    t=np.zeros((len(p)))\n",
    "    for i in range(len(p)):\n",
    "        t[i] = np.dot(c[:][i].T,rep)\n",
    "    epsilon = 0.0005    \n",
    "    while True:\n",
    "        \n",
    "        ti = np.dot(ci.T,rep)\n",
    "        ti = (1 - a) * ti + a * pi\n",
    "        theta = np.abs(ti - rep)\n",
    "        rep = ti\n",
    "        if ((theta < epsilon).all()):\n",
    "            break\n",
    "        if counter >= 200: \n",
    "            break\n",
    "        counter += 1\n",
    "    return dict(t_vec=ti, counter=counter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "144b18a2-a7f4-4a8b-a00a-3d86cf23df4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.zeros((len(p)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c00f8534-8fb1-4f3b-9645-703b60a56601",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[:][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "396e5997-841a-4ab0-8b35-2e12f3a1817b",
   "metadata": {},
   "outputs": [],
   "source": [
    "c[:][0]*p[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "03069f4f-7ec0-4970-b7b6-44903dc5d09f",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(nodelist)):\n",
    "    print(distributed_eigen(c[i], p[i], 0),'\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a92e7a95-4f57-4b11-8c10-9d1868b0ee7e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c4dec28-e191-4011-8301-13178804e515",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3f54c803-cab6-49c9-9d40-13269e3fed33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f08a068f-2325-48de-81f7-680c06f13f31",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def distributed_eigentrust(adj_matrix, num_iterations=10, damping_factor=0.85):\n",
    "    \"\"\"\n",
    "    Performs the distributed Eigentrust algorithm on a given adjacency matrix.\n",
    "\n",
    "    Args:\n",
    "        adj_matrix (numpy.ndarray): The adjacency matrix of the trust network.\n",
    "        num_iterations (int): The number of iterations to run the algorithm for. Default is 10.\n",
    "        damping_factor (float): The damping factor for the PageRank algorithm. Default is 0.85.\n",
    "\n",
    "    Returns:\n",
    "        numpy.ndarray: A vector containing the Eigentrust values for each node in the trust network.\n",
    "    \"\"\"\n",
    "\n",
    "    # Get the number of nodes in the trust network\n",
    "    num_nodes = adj_matrix.shape[0]\n",
    "\n",
    "    # Initialize the trust vector with equal values for all nodes\n",
    "    trust_vec = np.ones(num_nodes) / num_nodes\n",
    "\n",
    "    # Compute the out-degree of each node in the trust network\n",
    "    out_degree = np.sum(adj_matrix, axis=1)\n",
    "\n",
    "    # Normalize the adjacency matrix to obtain the transition probability matrix\n",
    "    trans_prob_matrix = adj_matrix / out_degree[:, np.newaxis]\n",
    "\n",
    "    # Perform the Eigentrust algorithm for the specified number of iterations\n",
    "    for i in range(num_iterations):\n",
    "        # Compute the new trust vector using the PageRank algorithm\n",
    "        trust_vec = damping_factor * np.matmul(trans_prob_matrix, trust_vec) + \\\n",
    "                    (1 - damping_factor) / num_nodes\n",
    "\n",
    "        # Normalize the trust vector\n",
    "        trust_vec /= np.sum(trust_vec)\n",
    "\n",
    "    return trust_vec\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "28592463-3780-4680-a535-c49a51ca5dbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "distributed_eigentrust(adjs)"
   ]
  }
 ],
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