Watts-Strogatz Small-World Network Simulation

This MATLAB code implements the Watts-Strogatz small-world network model. The algorithm begins by constructing a regular ring lattice where N nodes are arranged in a circle, with each node connected to its K/2 nearest neighbors on both sides (K must be an even number). This initial configuration represents a highly structured, regular graph. However, since real-world networks often exhibit random characteristics, we introduce randomness through a rewiring process. The core algorithm involves iterating through each edge and rewiring it with probability p. During rewiring, one endpoint of the edge remains fixed while the other endpoint is randomly reassigned to a different node in the network. The implementation includes crucial validation checks to ensure no self-loops (edges connecting a node to itself) and no duplicate edges between any pair of nodes. This rewiring process creates networks that balance regular local connectivity with random long-range connections, producing the characteristic small-world properties of high clustering coefficient and short average path length. The resulting model is particularly valuable for studying complex network behaviors, as it provides more realistic network structures compared to purely regular graphs, making it suitable for simulations in social networks, neural networks, and transportation systems. Key implementation details include: - Efficient adjacency matrix manipulation for edge management - Random number generation for probabilistic rewiring - Validation functions to maintain graph integrity - Parameter validation for N, K, and p values