Complex Network Generation Implementation in MATLAB Code

Complex network generation in MATLAB can be implemented through various models, with commonly used ones including random graphs (Erdős–Rényi model), small-world networks (Watts-Strogatz model), and scale-free networks (Barabási-Albert model). Each model has distinct characteristics suitable for different research requirements. The random graph model generates networks by specifying the number of nodes and connection probability, featuring simple structure and straightforward implementation using MATLAB's built-in functions like `sprand` for creating sparse adjacency matrices. Small-world networks begin with a regular lattice structure and introduce random rewiring, achieving both high clustering coefficients and short average path lengths through controlled parameter adjustments in the rewiring algorithm. Scale-free networks simulate the "rich-get-richer" phenomenon observed in real-world systems, where node degree distributions follow power-law patterns, implemented through preferential attachment algorithms that incrementally add nodes with connections biased toward high-degree existing nodes. MATLAB provides powerful matrix operations and visualization tools ideal for implementing these network models. Network structures are efficiently stored using adjacency matrices, with sparse matrix implementations optimizing both memory usage and computational efficiency through functions like `sparse`. After network generation, topological properties can be analyzed using metrics such as average degree calculated with `mean(sum(adjacency_matrix))`, clustering coefficients computed via `clustering_coefficient` algorithms, and path lengths determined using shortest-path functions like `graphshortestpath`. For beginners, starting with random graphs helps build fundamental understanding of network generation logic before progressing to more complex models, eventually enabling customized network analysis through MATLAB's flexible programming environment and specialized toolbox functions.