freemans_centrality.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c3928aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b32f120",
   "metadata": {},
   "source": [
    "### ADJACENCY MATRIX A:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d1f32c5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 0 1 0 0 0]\n",
      " [1 0 1 0 0 1 0 0]\n",
      " [0 1 0 1 0 0 1 0]\n",
      " [0 0 1 0 0 0 0 1]\n",
      " [1 0 0 0 0 1 0 0]\n",
      " [0 1 0 0 1 0 1 0]\n",
      " [0 0 1 0 0 1 0 1]\n",
      " [0 0 0 1 0 0 1 0]]\n"
     ]
    }
   ],
   "source": [
    "A = np.matrix('0,1,0,0,1,0,0,0;1,0,1,0,0,1,0,0;0,1,0,1,0,0,1,0;0,0,1,0,0,0,0,1;1,0,0,0,0,1,0,0;0,1,0,0,1,0,1,0;0,0,1,0,0,1,0,1;0,0,0,1,0,0,1,0')\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d5f4128",
   "metadata": {},
   "source": [
    "### Drawing graph from the Adjacency matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d0382d91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.from_numpy_matrix(A)  \n",
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9c0c3ea",
   "metadata": {},
   "source": [
    "## Betweenness Centrality of the graph G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0987a74e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 1.0833333333333335,\n",
       " 1: 5.916666666666667,\n",
       " 2: 5.916666666666667,\n",
       " 3: 1.0833333333333335,\n",
       " 4: 1.0833333333333335,\n",
       " 5: 5.916666666666667,\n",
       " 6: 5.916666666666666,\n",
       " 7: 1.0833333333333335}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_c=nx.betweenness_centrality(G, k=None, normalized=False, weight=None, endpoints=False, seed=None)\n",
    "b_c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53477f0f",
   "metadata": {},
   "source": [
    "## Closeness Centrality of the graph G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a90dc1d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.4375,\n",
       " 1: 0.5833333333333334,\n",
       " 2: 0.5833333333333334,\n",
       " 3: 0.4375,\n",
       " 4: 0.4375,\n",
       " 5: 0.5833333333333334,\n",
       " 6: 0.5833333333333334,\n",
       " 7: 0.4375}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_c=nx.closeness_centrality(G, u=None, distance=None, wf_improved=True)\n",
    "c_c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1718e535",
   "metadata": {},
   "source": [
    "## Degree Centrality of the graph G"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ed8e02c",
   "metadata": {},
   "source": [
    "### With networkx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "22744ba4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree Centalities for the graph G is: \n",
      " {0: 0.2857142857142857, 1: 0.42857142857142855, 2: 0.42857142857142855, 3: 0.2857142857142857, 4: 0.2857142857142857, 5: 0.42857142857142855, 6: 0.42857142857142855, 7: 0.2857142857142857}\n"
     ]
    }
   ],
   "source": [
    "d=nx.degree_centrality(G)\n",
    "print(\"Degree Centalities for the graph G is: \\n\",d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5db736a",
   "metadata": {},
   "source": [
    "### Without networkx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bd35ed6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a copy of Adjacency matrix:\n",
    "B = A.copy()\n",
    "\n",
    "def summ(graph, a):\n",
    "    sum_deg = 0\n",
    "    # Summing all columns in the row\n",
    "    for column in range(8):\n",
    "        sum_deg += graph[a,column]\n",
    "    return sum_deg\n",
    "\n",
    "def degCen(a):\n",
    "    sum_deg = summ(B, a)\n",
    "    # dividing the sum of the degree with the (n-1) nodes\n",
    "    deg_cen = (sum_deg/(8-1))\n",
    "    return deg_cen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "aedb8859",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree Centralities of the Graph G is: \n",
      " [0.2857142857142857, 0.42857142857142855, 0.42857142857142855, 0.2857142857142857, 0.2857142857142857, 0.42857142857142855, 0.42857142857142855, 0.2857142857142857]\n"
     ]
    }
   ],
   "source": [
    "d_c = [degCen(a) for a in range(8)]\n",
    "print(\"Degree Centralities of the Graph G is: \\n\", d_c)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "9d027d7f",
   "metadata": {},
   "source": [
    "## Freemans Centrality is given by\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4bb7378",
   "metadata": {},
   "source": [
    "**$ C_x=\\frac{\\sum_{i}\\left[{c_{cen}^\\ast-c}_{cen}(i)\\right]}{\\max g{\\sum_{i}\\left[{c_{cen}^\\ast-c}_{cen}(i)\\right]}} $**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6fef84d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum value of degree centrality is: 0.42857142857142855\n"
     ]
    }
   ],
   "source": [
    "d_max=max(d.values())\n",
    "print('Maximum value of degree centrality is:',d_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6d10adfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.14285714285714285,\n",
       " 0.0,\n",
       " 0.0,\n",
       " 0.14285714285714285,\n",
       " 0.14285714285714285,\n",
       " 0.0,\n",
       " 0.0,\n",
       " 0.14285714285714285]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values=[]\n",
    "for i in range(8):\n",
    "    s=d_max-d[i]\n",
    "    values.append(s)   \n",
    "values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "760afbe9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5714285714285714"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numerator=sum(values)\n",
    "numerator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4776f015",
   "metadata": {},
   "source": [
    "### Denominator is for a star graph with 8 vertices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "48348910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G1 = nx.star_graph(7)\n",
    "nx.draw(G1, node_color = 'green',node_size = 1000,with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3ad9ed09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 1.0,\n",
       " 1: 0.14285714285714285,\n",
       " 2: 0.14285714285714285,\n",
       " 3: 0.14285714285714285,\n",
       " 4: 0.14285714285714285,\n",
       " 5: 0.14285714285714285,\n",
       " 6: 0.14285714285714285,\n",
       " 7: 0.14285714285714285}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1=nx.degree_centrality(G1)\n",
    "d1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "de0f24aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d1_max=max(d1.values())\n",
    "d1_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e3c4b43c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572,\n",
       " 0.8571428571428572]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values1=[]\n",
    "for i in range(8):\n",
    "    s1=d1_max-d1[i]\n",
    "    values1.append(s1)   \n",
    "values1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0544d87a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.000000000000002"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "denominator=sum(values1)\n",
    "denominator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ea14b445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08163265306122448"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "freeman_centrality=numerator/denominator\n",
    "freeman_centrality"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}