Barabasi Albert model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = [1,1]  # int array since only degree matters for this model\n",
    "\n",
    "# start with two nodes connected to each other\n",
    "\n",
    "for i in range(20000):\n",
    "    total_degree = 2*(i+1)\n",
    "    weights = [n/total_degree for n in nodes] # node-wise probability dist. of adding new node\n",
    "    \n",
    "    \n",
    "    stacked_weights = np.cumsum(weights) # partitions unit interval for weighted RNG\n",
    "    p = np.random.random()\n",
    "    ind = None\n",
    "    \n",
    "    for j, weight in enumerate(stacked_weights):\n",
    "        if p < weight:\n",
    "            ind = j\n",
    "            break\n",
    "            \n",
    "    nodes[ind] += 1  # add new node to chosen index\n",
    "    nodes.append(1)  # new node added to list of nodes with degree 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([230, 105, 103, ...,   1,   1,   1])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ordered_nodes = np.flip(np.sort(nodes))\n",
    "ordered_nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set()\n",
    "\n",
    "fig, ax = plt.subplots((1), figsize=(8,10))\n",
    "ax.set(xscale=\"log\", yscale=\"log\")\n",
    "\n",
    "ax = sns.lineplot(range(len(nodes)), ordered_nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.693147</td>\n",
       "      <td>5.442418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.098612</td>\n",
       "      <td>4.663439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.386294</td>\n",
       "      <td>4.644391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.609438</td>\n",
       "      <td>4.574711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.791759</td>\n",
       "      <td>4.382027</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x    degree\n",
       "0  0.693147  5.442418\n",
       "1  1.098612  4.663439\n",
       "2  1.386294  4.644391\n",
       "3  1.609438  4.574711\n",
       "4  1.791759  4.382027"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_vals = np.array(range(1, len(nodes) + 1))\n",
    "\n",
    "paired_data = np.stack([x_vals, ordered_nodes]).transpose()\n",
    "paired_data = pd.DataFrame(data=paired_data, columns=[\"x\", \"degree\"]).apply(lambda x: np.log(x+1))\n",
    "\n",
    "paired_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots((1), figsize=(10,8))\n",
    "ax.set(xscale=\"log\", yscale=\"log\") # scatterplot seems to have trouble with this\n",
    "ax.set_xlim(0.65, 8)\n",
    "ax.set_ylim(0.65, 8)\n",
    "\n",
    "ax = sns.scatterplot(x=\"x\", y=\"degree\", data=paired_data)  # marker outlines cover up other markers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}