BA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Barabasi-Albert Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "from tqdm import tqdm\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from scipy.optimize import curve_fit\n",
    "from scipy.special import factorial\n",
    "from scipy.stats import poisson\n",
    "from scipy.optimize import minimize\n",
    "from scipy import stats\n",
    "from collections import deque\n",
    "import networkx as nx\n",
    "import math as m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Network Initialize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Target Mean Degree : 10\n"
     ]
    }
   ],
   "source": [
    "size_list = [1000, 5000, 10000, 20000]\n",
    "mean_degree = int(input(\"Target Mean Degree : \").strip())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BA Network Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BA:\n",
    "    def __init__(self, mean_degree, size_list=[]):\n",
    "        self.size = mean_degree + 1\n",
    "        self.mean_degree = mean_degree\n",
    "        self.size_list = size_list\n",
    "        self.degree = dict()\n",
    "        self.adjacent = dict()\n",
    "        self.pref = dict()\n",
    "        self.num_of_links = dict()\n",
    "        for item in self.size_list:\n",
    "            self.degree[item] = dict()\n",
    "            self.adjacent[item] = dict()\n",
    "            self.pref[item] = dict()\n",
    "            self.num_of_links[item] = 0    \n",
    "        self.largest_cluster = []\n",
    "    \n",
    "    @staticmethod\n",
    "    def power_law(x, a, b):\n",
    "        return b * np.power(x, a)\n",
    "    \n",
    "    @staticmethod\n",
    "    def log_binning(data, start, length):\n",
    "        maxbin = m.ceil(np.log10(max(data)))\n",
    "        hist, bins = np.histogram(data, bins=np.logspace(start, maxbin, num=length, endpoint=True, base=10.0))\n",
    "        bin_centers = (bins[1:] + bins[:-1]) * 0.5\n",
    "        delt = bins[1:] - bins[:-1]\n",
    "        # print(maxbin, delt, sum(hist))\n",
    "        hist = hist / delt / sum(hist)\n",
    "        return bin_centers, hist\n",
    "    \n",
    "    def generate(self):\n",
    "        ## Make Seed ##\n",
    "        self.size = self.mean_degree + 1\n",
    "        for size in self.size_list:\n",
    "            for node in range(self.mean_degree + 1):\n",
    "                self.adjacent[size][node] = [node2 for node2 in range(self.size) if node != node2]\n",
    "                self.degree[size][node] = self.mean_degree\n",
    "                self.num_of_links[size] += len(self.adjacent[size][node])\n",
    "                self.pref[size][node] = self.degree[size][node] / (self.num_of_links[size] / 2.0)\n",
    "\n",
    "        ## Generate BA ##\n",
    "        for size in self.size_list:\n",
    "            for self.size in tqdm(range(self.mean_degree + 1, size)):\n",
    "                nodes = [i for i in range(self.size)]\n",
    "                prob = np.array(list(self.pref[size].values())) / sum(list(self.pref[size].values()))\n",
    "                samp_nodes = np.random.choice(nodes, self.mean_degree, p=prob)\n",
    "                self.degree[size][self.size] = 0\n",
    "                self.pref[size][self.size] = 0\n",
    "\n",
    "                for node in samp_nodes:\n",
    "                    self.degree[size][node] += 1\n",
    "                    self.degree[size][self.size] += 1\n",
    "\n",
    "                    self.adjacent[size][node].append(self.size)\n",
    "                    if self.size in self.adjacent[size].keys():\n",
    "                        self.adjacent[size][self.size].append(node)\n",
    "                    else:\n",
    "                        self.adjacent[size][self.size] = [node]\n",
    "\n",
    "                    self.num_of_links[size] += 1\n",
    "                    self.pref[size][node] = self.degree[size][node] / (self.num_of_links[size] / 2.0)\n",
    "                    self.pref[size][self.size] = self.degree[size][self.size] / (self.num_of_links[size] / 2.0)\n",
    "    \n",
    "    def plot_degree_dist(self):\n",
    "        dat = sorted(self.degree.values(), reverse=False)\n",
    "        plt.figure(figsize=(10, 16))\n",
    "        sns.countplot(dat)\n",
    "        plt.show()\n",
    "    \n",
    "    def loglog_plot(self, cutoff):\n",
    "        fig = plt.figure(figsize=(10, 8), facecolor=(0.9, 0.9, 0.9))\n",
    "        plt.xscale('log')\n",
    "        plt.yscale('log')\n",
    "        plt.xlabel('degree')\n",
    "        plt.ylabel('distribution')\n",
    "        plt.xlim(10000, 1000000000)\n",
    "        plt.ylim(0.00001,100)\n",
    "        plt.grid()\n",
    "                                                   \n",
    "        for enum, size in enumerate(self.size_list):\n",
    "            enum += 1\n",
    "            dat = sorted(self.degree[size].values(), reverse=False)\n",
    "\n",
    "            x_bin, y_bin = self.log_binning(dat, 0, 30)\n",
    "            sum_y = sum(y_bin)\n",
    "            data = dict()\n",
    "            for x, y in zip(x_bin, y_bin):\n",
    "                data[x] = y\n",
    "\n",
    "            data0 = dict()\n",
    "\n",
    "            for item in dat:\n",
    "                if item in data0.keys():\n",
    "                    data0[item] += 1\n",
    "                else:\n",
    "                    data0[item] = 1\n",
    "\n",
    "            data_buf = sorted(data0.items(), key=lambda x:x[0], reverse=False)   \n",
    "            x0 = np.array(list(map(lambda x:x[0], data_buf)))\n",
    "            y0 = np.array(list(map(lambda x:x[1], data_buf)))\n",
    "            sum_y0 = sum(y0)\n",
    "            y0 = y0 / sum_y0\n",
    "\n",
    "            cum = dict()\n",
    "\n",
    "            for key, val in zip(x_bin, y_bin):\n",
    "                buf = x_bin[x_bin >= key]\n",
    "                for item in buf:\n",
    "                    if key in cum.keys():\n",
    "                        cum[key] += data[item]\n",
    "                    else:\n",
    "                        cum[key] = data[item]\n",
    "\n",
    "            x_2 = np.array(list(cum.keys()))\n",
    "            y_2 = np.array(list(cum.values()))\n",
    "            y_2 = y_2 / sum(y_2)\n",
    "\n",
    "\n",
    "            popt, pcov = curve_fit(self.power_law, xdata=x_2[cutoff:], ydata=y_2[cutoff:], method='dogbox')\n",
    "    \n",
    "            #plt.scatter(x_bin[9:] * size * 2, y_bin[9:], s=55.0, marker='o', color=(1.0 / enum,0.0,1.0 / enum), alpha=1.0, edgecolors=(0.0,0.0,0.0), label=\"BA Network, size=\" + str(size), zorder=2)\n",
    "            plt.scatter(x_2[cutoff:] * size * 2, y_2[cutoff:] * 10, s=55.0, marker='o', color=(0.0,1.0 / enum,1.0 / enum), alpha=1.0, edgecolors=(0.0,0.0,0.0), label=\"Size=\" + str(size), zorder=2)\n",
    "            #plt.scatter(x0[9:] * size * 2, y0[9:], s=55.0, marker='o', color=(1.0 / enum,1.0 / enum,0.0), alpha=1.0, edgecolors=(0.0,0.0,0.0), label=\"Raw BA Network , size=\" + str(size), zorder=2)\n",
    "            if size==max(self.size_list):\n",
    "                plt.scatter(x_2 * size * 2, self.power_law(x_2, *popt) * 100, s=55.0, marker='o', color=(1.0,1.0,1.0), alpha=1.0, edgecolors=(0.0,0.0,0.0), label=\"gamma=\"+str(-popt[0]), zorder=2)\n",
    "                plt.plot(x_2 * size * 2, self.power_law(x_2, *popt) * 100, c=(1.0,0.0,0.0), zorder=1)\n",
    "        \n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "        fig.savefig(\"./ba.png\")   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "ba = BA(mean_degree, size_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████| 989/989 [00:00<00:00, 2778.11it/s]\n",
      "100%|█████████████████████████████████████████████████████████████| 4989/4989 [00:05<00:00, 915.42it/s]\n",
      "100%|█████████████████████████████████████████████████████████████| 9989/9989 [00:20<00:00, 497.46it/s]\n",
      "100%|███████████████████████████████████████████████████████████| 19989/19989 [01:19<00:00, 251.13it/s]\n"
     ]
    }
   ],
   "source": [
    "ba.generate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ba.loglog_plot(cutoff=11)"
   ]
  },
  {
   "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}