{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# [Chapter 4](https://github.com/Ziaeemehr/netsci/blob/main/docs/examples/chap_04.ipynb)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### **THE SCALE-FREE PROPERTY**\n",
"\n",
"Code by : Abolfazl Ziaeemehr \n",
"- https://github.com/Ziaeemehr\n",
"\n",
"
"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# uncomment and run this line to install the package on colab\n",
"# !pip install \"git+https://github.com/Ziaeemehr/netsci.git\" -q"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from netsci.utils import generate_power_law_dist, generate_power_law_dist_bounded"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"LABELSIZE = 13\n",
"plt.rc('axes', labelsize=LABELSIZE)\n",
"plt.rc('axes', titlesize=LABELSIZE)\n",
"plt.rc('figure', titlesize=LABELSIZE)\n",
"plt.rc('legend', fontsize=LABELSIZE)\n",
"plt.rc('xtick', labelsize=LABELSIZE)\n",
"plt.rc('ytick', labelsize=LABELSIZE)\n",
"# set legend font size \n",
"plt.rc('legend', fontsize=10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Figure 4.4, Comparing Poisson and Powe-law Distributions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import poisson\n",
"\n",
"# Parameters\n",
"mean_poisson = 11\n",
"alpha_power_law = 2.1\n",
"x_values = np.arange(1, 1000)\n",
"\n",
"# Poisson Distribution\n",
"poisson_pmf = poisson.pmf(x_values, mean_poisson)\n",
"\n",
"# Power Law Distribution\n",
"power_law_pdf = x_values ** (-alpha_power_law)\n",
"# Normalize power-law PDF to make it a valid probability distribution\n",
"power_law_pdf /= np.sum(power_law_pdf)\n",
"\n",
"# Plotting\n",
"\n",
"fig, ax = plt.subplots(1,2, figsize=(12,4))\n",
"\n",
"ax[0].plot(x_values, poisson_pmf, label='Poisson Distribution (mean=11)')\n",
"ax[0].plot(x_values, power_law_pdf, label='Power Law Distribution (α=-2.1)')\n",
"ax[0].set_xlim([0,50])\n",
"ax[0].set_ylim([0,0.15])\n",
"ax[0].set_xlabel('x')\n",
"ax[0].set_ylabel(r'$p_k$')\n",
"fig.suptitle('Comparison of Poisson and Power Law Distributions')\n",
"ax[0].legend(frameon=False)\n",
"ax[1].loglog(x_values, poisson_pmf, label=\"poisson\")\n",
"ax[1].loglog(x_values, power_law_pdf, label=\"powerlaw\")\n",
"ax[1].set_ylim([1e-6, 1])\n",
"ax[1].set_xlabel('x')\n",
"ax[1].set_ylabel(r'$p_k$')\n",
"ax[1].legend(frameon=False);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### load sample graphs of the book"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['Collaboration', 'Internet', 'PowerGrid', 'Protein', 'PhoneCalls', 'Citation', 'Metabolic', 'Email', 'WWW', 'Actor']\n"
]
}
],
"source": [
"from netsci.utils import list_sample_graphs, load_sample_graph\n",
"from netsci.analysis import graph_info\n",
"\n",
"# on colab:\n",
"nets = ['Collaboration', 'Internet', 'PowerGrid', 'Protein', 'PhoneCalls', 'Citation', 'Metabolic', 'Email', 'WWW', 'Actor']\n",
"\n",
"# on local:\n",
"nets = list(list_sample_graphs().keys())\n",
"print(nets)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### On Google Colab only"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from google.colab import drive\n",
"import os\n",
"\n",
"# URL of the zip file to be downloaded\n",
"url = \"https://networksciencebook.com/translations/en/resources/networks.zip\"\n",
"# Mount Google Drive\n",
"drive.mount('/content/drive')\n",
"# Create the 'network_science' directory in MyDrive if it doesn't exist\n",
"network_science_dir = '/content/drive/MyDrive/network_science'\n",
"os.makedirs(network_science_dir, exist_ok=True)\n",
"# empty the directory\n",
"!rm -rf /content/drive/MyDrive/network_science/*\n",
"# Change directory to 'network_science'\n",
"os.chdir(network_science_dir)\n",
"# Download the zip file to the 'network_science' directory\n",
"!wget $url -O networks.zip\n",
"# Unzip the downloaded file in the 'network_science' directory\n",
"!unzip networks.zip\n",
"\n",
"json_file = \"https://raw.githubusercontent.com/Ziaeemehr/netsci/main/netsci/datasets/sample_graphs.json\"\n",
"# download json file\n",
"!wget $json_file -O sample_graphs.json"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Graph information\n",
"Directed : False\n",
"Number of nodes : 23133\n",
"Number of edges : 93439\n",
"Average degree : 8.0784\n",
"Connectivity : disconnected\n",
"Calculating best minimal value for power law fit\n",
" α = 1.410, σ = ± 0.037\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import powerlaw\n",
"from collections import Counter\n",
"from scipy.stats import poisson\n",
"\n",
"\n",
"G_collab = load_sample_graph(\"Collaboration\") # on colab: add colab_path=network_science_dir\n",
"graph_info(G_collab, quick=True)\n",
"degrees = list(dict(G_collab.degree()).values())\n",
"degree_count = Counter(degrees)\n",
"k, pk = zip(*degree_count.items())\n",
"\n",
"plt.figure(figsize=(6,4))\n",
"plt.loglog(k, pk, 'b.', label=r\"$k$\")\n",
"plt.xlabel(r\"$k$\")\n",
"plt.ylabel(\"pk\");\n",
"\n",
"fit = powerlaw.Fit(pk) # xmax=80\n",
"print(f\" α = {fit.power_law.alpha:6.3f}, σ = ± {fit.power_law.sigma:6.3f}\") # the exponent"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Generate the powerlaw distribution (bounded)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0;31mSignature:\u001b[0m \u001b[0mgenerate_power_law_dist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mxmin\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mDocstring:\u001b[0m\n",
"generate power law random numbers p(k) ~ x^(-a) for a>1\n",
"\n",
"Parameters\n",
"-----------\n",
"N:\n",
" is the number of random numbers\n",
"a:\n",
" is the exponent\n",
"xmin:\n",
" is the minimum value of distribution\n",
"\n",
"Returns\n",
"-----------\n",
"value: np.array\n",
" powerlaw distribution\n",
"\u001b[0;31mFile:\u001b[0m ~/git/workshops/network_science/netsci/netsci/utils.py\n",
"\u001b[0;31mType:\u001b[0m function"
]
}
],
"source": [
"generate_power_law_dist?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0;31mSignature:\u001b[0m\n",
"\u001b[0mgenerate_power_law_dist_bounded\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m \u001b[0mxmin\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m \u001b[0mxmax\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mfloat\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mint\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\n",
"\u001b[0;34m\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;31mDocstring:\u001b[0m\n",
"Generate a power law distribution of floats p(k) ~ x^(-a) for a>1\n",
"which is bounded by xmin and xmax\n",
"\n",
"parameters :\n",
" N: int\n",
" number of samples in powerlaw distribution (pwd).\n",
" a:\n",
" exponent of the pwd.\n",
" xmin:\n",
" min value in pwd.\n",
" xmax:\n",
" max value in pwd.\n",
"\u001b[0;31mFile:\u001b[0m ~/git/workshops/network_science/netsci/netsci/utils.py\n",
"\u001b[0;31mType:\u001b[0m function"
]
}
],
"source": [
"generate_power_law_dist_bounded?"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"plotting the powerlaw distributions"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def plot_distribution(vrs, N, a, xmin, ax, labelsize=10):\n",
"\n",
" # plotting the PDF estimated from variates\n",
" bin_min, bin_max = np.min(vrs), np.max(vrs)\n",
" bins = 10**(np.linspace(np.log10(bin_min), np.log10(bin_max), 100))\n",
" counts, edges = np.histogram(vrs, bins, density=True)\n",
" centers = (edges[1:] + edges[:-1])/2.\n",
"\n",
" # plotting the expected PDF\n",
" xs = np.linspace(bin_min, bin_max, N)\n",
" expected_pdf = [(a-1) * xmin**(a-1) * x**(-a) for x in xs] # according to eq. 4.12 network science barabasi 2016\n",
" ax.loglog(xs, expected_pdf, color='red', ls='--', label=r\"$x^{-\\gamma}$,\"+ r\"${\\gamma}$=\"+f\"{-a:.2f}\")\n",
" ax.loglog(centers, counts, 'k.', label='data')\n",
" ax.legend(fontsize=labelsize)\n",
" ax.set_xlabel(\"values\")\n",
" ax.set_ylabel(\"PDF\")\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1.000035809608483 74.39513593875918\n"
]
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(2)\n",
"\n",
"N = 10000\n",
"a = 3.0\n",
"xmin = 1\n",
"xmax = 100\n",
"\n",
"fig, ax = plt.subplots(1, figsize=(5,3))\n",
"x = generate_power_law_dist_bounded(N, a, xmin, xmax)\n",
"print (np.min(x), np.max(x))\n",
"plot_distribution(x, N, a, xmin, ax)\n"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Calculating best minimal value for power law fit\n",
"fit.power_law.alpha=np.float64(2.995340848455978)\n",
"fit.power_law.sigma=np.float64(0.02600579145725683)\n"
]
}
],
"source": [
"# find the exponent by fitting a power law by powerlaw package\n",
"\n",
"import powerlaw\n",
"fit = powerlaw.Fit(x) # xmax=50 we can constrain the max value for fitting\n",
"print(f\"{fit.power_law.alpha=}\") # the exponent\n",
"print(f\"{fit.power_law.sigma=}\") # standard error"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate descereted power law distribution"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from netsci.utils import generate_power_law_discrete\n",
"# Example usage\n",
"gamma = 2.5 # Power-law exponent\n",
"k_min = 1 # Minimum value of k\n",
"k_max = 1000 # Maximum value of k\n",
"size = 100000 # Number of samples\n",
"\n",
"samples = generate_power_law_discrete(size, gamma, k_min, k_max, seed=1)\n",
"fig, ax = plt.subplots(1, figsize=(6,4))\n",
"plot_distribution(samples, size, gamma, k_min, ax)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Table 4.1\n",
"loading with igraph"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"['Collaboration',\n",
" 'Internet',\n",
" 'PowerGrid',\n",
" 'Protein',\n",
" 'PhoneCalls',\n",
" 'Citation',\n",
" 'Metabolic',\n",
" 'Email',\n",
" 'WWW',\n",
" 'Actor']"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import os\n",
"import igraph as ig\n",
"from tqdm import tqdm\n",
"from netsci.utils import list_sample_graphs\n",
"from netsci.utils import get_sample_dataset_path\n",
"from netsci.utils import download_sample_dataset\n",
"from netsci.utils import load_sample_graphi\n",
"\n",
"# download_sample_dataset()\n",
"sample_graph_names = list(list_sample_graphs().keys()) # not on colab\n",
"sample_graph_names"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"processing graphs: 100%|██████████| 10/10 [00:40<00:00, 4.05s/it]\n"
]
}
],
"source": [
"# select the files in the path ending with .edgelist.txt\n",
"graphs = {}\n",
"\n",
"for name in tqdm(sample_graph_names, desc=\"processing graphs\"):\n",
" G = load_sample_graphi(name) # on colab: add colab_path=network_science_dir\n",
" directed = G.is_directed()\n",
" if directed:\n",
" in_degrees = G.degree(mode=\"in\")\n",
" out_degrees = G.degree(mode=\"out\")\n",
" in_degree_count = Counter(in_degrees) \n",
" out_degree_count = Counter(out_degrees)\n",
" in_k, in_pk = zip(*in_degree_count.items())\n",
" out_k, out_pk = zip(*out_degree_count.items())\n",
" graphs[name]={}\n",
" graphs[name]['in_k']=in_k\n",
" graphs[name]['in_pk']=in_pk\n",
" graphs[name]['out_k']=out_k\n",
" graphs[name]['out_pk']=out_pk\n",
" graphs[name]['directed']=True\n",
" else:\n",
" degrees = G.degree()\n",
" degree_count = Counter(degrees)\n",
" k, pk = zip(*degree_count.items())\n",
" graphs[name]={}\n",
" graphs[name]['k']=k\n",
" graphs[name]['pk']=pk\n",
" graphs[name]['directed']=False"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"Calculating best minimal value for power law fit\n",
"xmin progress: 99%\r"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def fit_powerlaw(k, pk, ax, label=None, label_inout=\"\"):\n",
" \n",
" fit = powerlaw.Fit(pk)\n",
" alpha = fit.power_law.alpha\n",
" sigma = fit.power_law.sigma\n",
" fit.plot_pdf(lw=2, ax=ax, marker='.', label='pdf ' + label_inout, ls='') \n",
" fit.power_law.plot_pdf(lw=2, ax=ax, ls='--', label='fit ' + label_inout+ f\"$\\gamma$={alpha:.2f}\" ) \n",
" # ax.text(0.1, 0.1, f\"α = {alpha:.2f}, σ = ± {sigma:.2f}\", transform=ax.transAxes)\n",
" ax.set_title(name)\n",
" ax.legend(frameon=False)\n",
" return alpha, sigma\n",
"\n",
"fig, ax = plt.subplots(2, 5, figsize=(12, 6))\n",
"ax = ax.ravel()\n",
"counter = 0\n",
"alpha_list = {}\n",
"for name, data in graphs.items():\n",
" if data['directed']:\n",
" alpha_in, sigma_in = fit_powerlaw(data['in_k'], data['in_pk'], ax[counter], label=name, label_inout=\"in\")\n",
" alpha_out, sigma_out = fit_powerlaw(data['out_k'], data['out_pk'], ax[counter], label=name, label_inout=\"out\")\n",
" else:\n",
" alpha, sigma = fit_powerlaw(data['k'], data['pk'], ax[counter], label=name)\n",
" alpha_list[name] = (alpha, sigma)\n",
" counter += 1\n",
"plt.tight_layout();\n",
"# ax.legend(frameon=False);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(np.float64(68.5327868852459), np.float64(189.61475409836066))"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# np.mean(graphs['www']['k']), np.mean(graphs['www']['pk'])\n",
"np.mean(graphs['collaboration']['k']), np.mean(graphs['collaboration']['pk'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Powerlaw package\n",
"\n",
"- Alstott, J., Bullmore, E. and Plenz, D., 2014. powerlaw: a Python package for analysis of heavy-tailed distributions. PloS one, 9(1), p.e85777.\n",
"\n",
" - probability density function (PDF), \n",
" - cumulative distribution function (CDF)\n",
" - complementary cumulative distribution (CCDF)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Calculating best minimal value for power law fit\n",
"xmin progress: 00%\r"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"fit.power_law.alpha=2.995340848455978\n",
"fit.power_law.sigma=0.02600579145725683\n",
"----------------------------------------------------------------------\n",
"(894.9727455051284, 5.263968413468816e-22)\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import powerlaw\n",
"fig, ax = plt.subplots(1, figsize=(6,4))\n",
"fit = powerlaw.Fit(x) # xmax=50\n",
"print(f\"{fit.power_law.alpha=}\")\n",
"print(f\"{fit.power_law.sigma=}\")\n",
"print(\"-\"*70)\n",
"print(fit.distribution_compare(\"power_law\", \"exponential\"))\n",
"\n",
"powerlaw.plot_pdf(x, linear_bins=0, color='k', marker='o', lw=1, ax=ax);"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, figsize=(6,4))\n",
"fit.plot_pdf(c='b', lw=2, marker=\"*\", label='pdf', ax=ax)\n",
"fit.power_law.plot_pdf(c='b', ax=ax, ls='--', label='fit pdf')\n",
"fit.plot_ccdf(c='r', ax=ax, ls=\"-\", label='ccdf')\n",
"fit.power_law.plot_ccdf(c='r', ax=ax, ls='--', label='fit ccdf')\n",
"ax.legend(frameon=False);\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"language_info": {
"name": "python"
}
},
"nbformat": 4,
"nbformat_minor": 2
}