Small-World Models in Complex Networks with MATLAB Implementation

In complex networks, small-world models refer to a class of graph structures that exist between completely random graphs and completely regular graphs. The NW model creates connections by randomly adding edges between nodes while maintaining a regular ring lattice structure. The SW model starts with a regular lattice and randomly rewires edges with a specified probability to introduce shortcuts. To facilitate deeper investigation of these models, we provide MATLAB implementation code that calculates degree distribution - a fundamental metric for analyzing network connectivity patterns. The code includes functions for generating both NW and SW networks, with parameters for network size, connection probability, and rewiring probability. Key algorithms implement edge randomization while preserving overall connectivity, and the degree distribution calculation uses efficient histogram-based methods to analyze node connectivity patterns. This resource includes practical code examples demonstrating how to generate small-world networks and analyze their structural properties, making it valuable for both learning and research applications in network science.