MATLAB Simulation Source Code for Small-World Network Model

The small-world network model is a complex network structure that lies between regular networks and random networks, characterized by high clustering coefficients and short average path lengths. This network model finds wide applications in various practical systems including social networks, neural networks, and the Internet. Implementing small-world network simulations in MATLAB typically involves the following key steps: Initial Regular Network Construction: First create a regular network, such as a ring lattice network, where each node connects to its nearest neighbors. In MATLAB implementation, this can be achieved using adjacency matrix creation with commands like `adjacency = zeros(N,N)` followed by connecting each node to k nearest neighbors through systematic indexing operations. Random Rewiring Process: According to a specified probability, randomly disconnect existing connections and reconnect them to other nodes in the network. This process is controlled by the "rewiring probability" parameter. MATLAB implementation typically uses `rand` function for probability checks and random node selection using `randi` or `randperm` functions. Higher rewiring probabilities make the network approach random network characteristics, while lower probabilities preserve more regular network features. Network Property Calculations: After simulation completion, it's essential to calculate the network's average path length and clustering coefficient to verify small-world characteristics. MATLAB's Graph Theory Toolbox provides functions like `distances` for path length calculations and `clustering_coef` or custom implementations using neighborhood connectivity analysis. The implementation in MATLAB can utilize matrix representations for network connectivity relationships, combined with graph theory functions (such as `graph` objects or sparse matrices using `sparse` function) to optimize computational efficiency. By adjusting network size (number of nodes), neighbor count, and rewiring probability, researchers can study the evolutionary characteristics of small-world networks under different parameters. This model holds significant value in social network analysis, information diffusion studies, and biological network modeling. The simulation implementation provides fundamental tools for further theoretical and applied research, with MATLAB code typically involving loop structures for rewiring operations and matrix manipulations for efficient network property computations.