Analysis of Node Degree Distributions in Network Graphs Following Power Law Using Linear Regression

import math
from scipy import stats

# Function to load data from a file
def load_data(filename):
    # Open the file in read mode
    file = open(filename, "r")
    return file

# Function to map each node ID to its degree
def get_node_id_to_degree(file):
    node_id_to_degree = {}
    # Read the file lines, skipping the header if present
    lines = file.readlines()[4:]  # Adjust the number based on file header lines
    for line in lines:
        # Process lines with two integers representing nodes
        if len(line.split()) == 2:
            node1 = int(line.split()[0])
            node2 = int(line.split()[1])
            # Update the degree count for both nodes
            add_to_dict(node1, node_id_to_degree)
            add_to_dict(node2, node_id_to_degree)
    return node_id_to_degree

# Helper function to update degree count in a dictionary
def add_to_dict(key, dictionary):
    # Increment the node's degree count or add it if not present
    if key in dictionary:
        dictionary[key] += 1
    else:
        dictionary[key] = 1

# Function to map each degree to its frequency count
def get_degree_to_count(node_id_to_degree):
    degree_to_count = {}
    for node_id, degree in node_id_to_degree.items():
        add_to_dict(degree, degree_to_count)
    return degree_to_count

# Function to generate the x and y values for linear regression
def generate_xy(degree_to_count):
    x = []
    y = []
    # Calculate the total number of nodes
    number_of_nodes = sum(degree_to_count.values())
    for degree, count in degree_to_count.items():
        # Apply logarithmic transformation for the Power Law distribution
        x.append(math.log(degree))
        y.append(math.log(count / number_of_nodes))
    return x, y

# Function to perform linear regression and return model parameters
def get_c1_c2_rsquared(x, y):
    # Perform linear regression on log-log transformed data
    slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)
    return slope, intercept, r_value ** 2

# Main block to execute the functions
if __name__ == '__main__':
    # Replace 'FileName.txt' with the actual file name
    file = load_data("FileName.txt")
    node_id_to_degree = get_node_id_to_degree(file)
    degree_to_count = get_degree_to_count(node_id_to_degree)
    x_list, y_list = generate_xy(degree_to_count)
    c1, c2, rsquared = get_c1_c2_rsquared(x_list, y_list)
    
    # Output the results
    print(f"c1 (slope): {c1}")
    print(f"c2 (intercept): {c2}")
    print(f"R-squared value: {rsquared}")