Generation of Small-World Networks: Algorithm Implementation and Source Code

This documentation focuses on the generation procedure of small-world networks, providing detailed explanations of specific algorithms, implementation methods, and source code. Small-world networks represent highly practical network models where the generation process involves introducing random factors into regular networks. The core algorithm operates through two primary phases: first generating a structured regular network, followed by random rewiring of selected edges to establish more complex inter-node connections. The implementation typically utilizes adjacency matrices or linked lists to represent network topology, with key functions including: - initialize_regular_network(): Creates initial ring lattice with k-nearest neighbors - random_rewire_edges(): Selects edges probabilistically and reconnects to random nodes - calculate_clustering_coefficient(): Measures local connectivity density - compute_average_path_length(): Evaluates global network efficiency This generation methodology finds extensive applications in social network analysis, information diffusion models, and complex system simulations. We provide detailed explanations of algorithm implementation techniques and demonstrate how source code facilitates this process through parameter customization (e.g., rewiring probability p, network size N) and modular function design. The accompanying code includes validation mechanisms to ensure the generated networks exhibit characteristic small-world properties: high clustering coefficients and short average path lengths. This resource aims to assist researchers and developers in understanding and implementing small-world network generation procedures for various scientific computing and network analysis applications.