MATLAB Implementation for Generating Small-World Networks

Small-world networks represent a special network model that bridges the gap between regular networks and random networks, characterized by high clustering coefficients and short average path lengths. In MATLAB, we can utilize built-in functions or custom algorithms to generate these networks. The core methodology for generating small-world networks typically follows the Watts-Strogatz model. This model begins by constructing a regular ring lattice network where each node connects to its nearest neighbors. The algorithm then rewires each edge with a specified probability, introducing randomness while preserving local connectivity. This rewiring mechanism allows the network to maintain high clustering characteristics while achieving the short-path properties of random networks. In MATLAB, the `wattsStrogatz` function provides direct implementation for small-world network generation. The function requires three key parameters: number of nodes (N), mean degree (K) specifying initial neighbors per node, and rewiring probability (beta). The function returns a graph object that can be analyzed using MATLAB's graph theory toolbox. For example: G = wattsStrogatz(N, K, beta) creates a network where higher beta values increase randomness while maintaining small-world properties. For customized implementations, developers can create algorithms that manually build the initial ring lattice using adjacency matrices and implement the rewiring process through random edge selection and connection updates. This approach allows for modifications like controlling rewiring constraints or adding weight distributions to edges. Small-world network models find extensive applications in studying complex systems including social networks, neural networks, and transportation systems. MATLAB's implementation is particularly valued for its efficiency and simplicity, making it ideal for both educational purposes in network science and research scenarios requiring rapid prototyping and analysis. The platform's built-in graph functions enable immediate computation of network metrics like clustering coefficients, path lengths, and degree distributions following network generation.