{"id":85,"date":"2021-03-29T23:58:00","date_gmt":"2021-03-29T15:58:00","guid":{"rendered":"https:\/\/philip.twinight.co\/portfolio\/?p=85"},"modified":"2024-03-06T10:04:19","modified_gmt":"2024-03-06T02:04:19","slug":"analysis-of-node-degree-distributions-in-network-graphs-following-power-law-using-linear-regression","status":"publish","type":"post","link":"https:\/\/philip.twinight.co\/portfolio\/index.php\/2021\/03\/29\/analysis-of-node-degree-distributions-in-network-graphs-following-power-law-using-linear-regression\/","title":{"rendered":"Analysis of Node Degree Distributions in Network Graphs Following Power Law Using Linear Regression"},"content":{"rendered":"\n

This is an individual project of SDSC2004 – Data Visualization. I did the project in my year 1 2020\/21 Semester B.<\/p>\n\n\n\n

Project Requirement:<\/strong><\/p>\n\n\n\n

The Power Law degree distribution is an important finding in Network Science. Specifically, the Power Law says that in a real network, the distribution of nodes’ degrees roughly satisfies that \"y = cx^{-\alpha}\", where \"c\" and \"\alpha\" are two parameters that may vary over different networks, \"x\" indicates a given degree and \"y\" denotes the percentage of nodes whose degrees are \"x\".<\/p>\n\n\n\n

(1) Show that if \"y = cx^{-\alpha}\", \"\log y\" has a linear relationship with \"\log x\". (Hint: the linear relationship is \"\log y = c_1 \log x + c_2\", please find \"c_1\" and \"c_2\". You need to figure out how to use c and \"\alpha\" to represent \"c_1\" and \"c_2\". The base of \"\log x\" and \"\log y\" is e which means \"\log x = \ln x\").<\/p>\n\n\n\n

(2) Download the com-LiveJournal (https:\/\/snap.stanford.edu\/data\/com-LiveJournal.html<\/a>) dataset and the com-Friendster (https:\/\/snap.stanford.edu\/data\/com-Friendster.html<\/a>) dataset. Please download “Undirected XXXXXX network”. To verify if these two networks’ node degrees follow the Power Law, apply linear regression to fit the model \"\log y = c_1 \log x + c_2\". Report \"c_1\", \"c_2\", and the R-Squared value for the two datasets.
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n


Below is my code (not perfect answer for sure):<\/strong><\/p>\n\n\n

\nimport math\nfrom scipy import stats\n\n# Function to load data from a file\ndef load_data(filename):\n    # Open the file in read mode\n    file = open(filename, \"r\")\n    return file\n\n# Function to map each node ID to its degree\ndef get_node_id_to_degree(file):\n    node_id_to_degree = {}\n    # Read the file lines, skipping the header if present\n    lines = file.readlines()[4:]  # Adjust the number based on file header lines\n    for line in lines:\n        # Process lines with two integers representing nodes\n        if len(line.split()) == 2:\n            node1 = int(line.split()[0])\n            node2 = int(line.split()[1])\n            # Update the degree count for both nodes\n            add_to_dict(node1, node_id_to_degree)\n            add_to_dict(node2, node_id_to_degree)\n    return node_id_to_degree\n\n# Helper function to update degree count in a dictionary\ndef add_to_dict(key, dictionary):\n    # Increment the node's degree count or add it if not present\n    if key in dictionary:\n        dictionary[key] += 1\n    else:\n        dictionary[key] = 1\n\n# Function to map each degree to its frequency count\ndef get_degree_to_count(node_id_to_degree):\n    degree_to_count = {}\n    for node_id, degree in node_id_to_degree.items():\n        add_to_dict(degree, degree_to_count)\n    return degree_to_count\n\n# Function to generate the x and y values for linear regression\ndef generate_xy(degree_to_count):\n    x = []\n    y = []\n    # Calculate the total number of nodes\n    number_of_nodes = sum(degree_to_count.values())\n    for degree, count in degree_to_count.items():\n        # Apply logarithmic transformation for the Power Law distribution\n        x.append(math.log(degree))\n        y.append(math.log(count \/ number_of_nodes))\n    return x, y\n\n# Function to perform linear regression and return model parameters\ndef get_c1_c2_rsquared(x, y):\n    # Perform linear regression on log-log transformed data\n    slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)\n    return slope, intercept, r_value ** 2\n\n# Main block to execute the functions\nif __name__ == '__main__':\n    # Replace 'FileName.txt' with the actual file name\n    file = load_data(\"FileName.txt\")\n    node_id_to_degree = get_node_id_to_degree(file)\n    degree_to_count = get_degree_to_count(node_id_to_degree)\n    x_list, y_list = generate_xy(degree_to_count)\n    c1, c2, rsquared = get_c1_c2_rsquared(x_list, y_list)\n    \n    # Output the results\n    print(f\"c1 (slope): {c1}\")\n    print(f\"c2 (intercept): {c2}\")\n    print(f\"R-squared value: {rsquared}\")\n<\/pre><\/div>\n\n\n
Result: (cor. to 7 d.p.)<\/strong><\/p>\n\n\n\n
<\/td>c1<\/td>c2<\/td>R-Squared value<\/td><\/tr>
com-LiveJournal<\/td>-2.3955318<\/td>2.5449043<\/td>0.9232843<\/td><\/tr>
com-Friendster<\/td>-2.6347939<\/td>21.0607001<\/td>0.9194954<\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"
This is an individual project of SDSC2004 – Data Visualization. I did the project in my year 1 2020\/21 Semester B. Project Requirement: The Power Law degree distribution is an … Continue readingAnalysis of Node Degree Distributions in Network Graphs Following Power Law Using Linear Regression<\/span><\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":330,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[74,3],"tags":[11,13,15,14,12],"class_list":["post-85","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-network-science","category-proj","tag-2020-21-semester-b","tag-data-science","tag-data-visualization","tag-sdsc2004","tag-year-1"],"yoast_head":"\nAnalysis of Node Degree Distributions in Network Graphs Following Power Law Using Linear Regression - Philip\u2019s Data Science Diary<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/philip.twinight.co\/portfolio\/index.php\/2021\/03\/29\/analysis-of-node-degree-distributions-in-network-graphs-following-power-law-using-linear-regression\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analysis of Node Degree Distributions in Network Graphs Following Power Law Using Linear Regression - Philip\u2019s Data Science Diary\" \/>\n<meta property=\"og:description\" content=\"This is an individual project of SDSC2004 – Data Visualization. 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Graduated from City University of Hong Kong. Previously founded Twinight Limited as CTO, developing AI investment analytics and automated trading solutions. 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