Generating Random Graphs for Complex Networks in MATLAB

In MATLAB, there are two primary strategies for generating random graphs for complex networks. These strategies include the Erdős-Rényi model and the Watts-Strogatz model. The Erdős-Rényi model operates as a random connection model, whose fundamental concept involves randomly establishing edges between n nodes with a connection probability p. This can be implemented using MATLAB's built-in functions like rand for probability comparisons and adjacency matrix construction. The Watts-Strogatz model, classified as a small-world network model, enhances global connectivity and local clustering by rewiring a small percentage of edges from a regular ring lattice structure. Its implementation typically involves creating an initial regular network followed by controlled edge rewiring using functions like circshift and random number generation. Therefore, when selecting a strategy for generating complex network random graphs, it's essential to choose the appropriate model based on specific requirements and research objectives, considering factors like desired network density, clustering coefficient, and average path length.