pagerank.ipynb

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   "source": [
    "import numpy as np\n",
    "\n",
    "def pagerank(M, eps = 1.0e-8, d = 0.85):\n",
    "    # Get number of vertices of the graph\n",
    "    N = M.shape[1]\n",
    "    \n",
    "    # Generate random array of dimension N and normalize it\n",
    "    v = np.random.rand(N, 1)\n",
    "    v = v / np.linalg.norm(v, 1)\n",
    "    \n",
    "    # Init score matrix\n",
    "    last_v = np.ones((N, 1))\n",
    "    \n",
    "    # Secured convergence formula\n",
    "    M_hat = ((1 - d) / N) * np.ones(M.shape) + d * M\n",
    "    \n",
    "    # Init step counter\n",
    "    steps = 1\n",
    "    \n",
    "    # Loop while the norm of two steps is greater than eps\n",
    "    while np.linalg.norm(v - last_v, 2) > eps:\n",
    "        last_v = v\n",
    "        v = np.matmul(M_hat, v)\n",
    "        \n",
    "        steps += 1\n",
    "       \n",
    "    print('Steps: {}'.format(steps))\n",
    "    print('Site #{} is the best with score {}'.format(np.argmax(v), np.max(v)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "sites_matrix = np.array(\n",
    "    [[0, 0, 0, 0, 1],\n",
    "     [0.5, 0, 0, 0, 0],\n",
    "     [0.5, 0, 0, 0, 0],\n",
    "     [0, 1, 0.5, 0, 0],\n",
    "     [0, 0, 0.5, 1, 0]]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Steps: 77\n",
      "Site #4 is the best with score 0.2637550314744842\n"
     ]
    }
   ],
   "source": [
    "pagerank(sites_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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