MATLAB Modeling of Small-World Networks: Formation Functions and Implementation

In this article, we explore complex networks and small-world networks through MATLAB modeling. Complex networks consist of numerous interconnected nodes that may exhibit diverse characteristics and connection patterns. In contrast, small-world networks represent a special class of complex networks where most nodes are connected by short paths while only a few nodes maintain longer-distance connections. We will examine the mathematical formation function governing small-world network evolution, which describes how network structures develop over time. Understanding this function helps illuminate network formation processes and provides guidance for network design and optimization.

Key implementation aspects include using MATLAB's graph theory functions to generate Watts-Strogatz models, where we start with a regular ring lattice and randomly rewire edges with probability p. The algorithm involves creating initial connections between nearest neighbors, then iterating through edges to potentially reconnect them to random nodes. Critical MATLAB functions include wattsstrogatz() for network generation and graph() for visualization and analysis. The implementation calculates characteristic path lengths and clustering coefficients to verify small-world properties, ensuring optimal network performance through parameter tuning of rewiring probability and network size.