MATLAB Implementation for Random Network Generation

Implementing random network generation in MATLAB primarily relies on random graph models from graph theory, with the Erdős-Rényi model being the most commonly used. This model constructs random networks by specifying the number of nodes and the probability of edge formation, making it suitable for simulation studies, social network analysis, and related fields. The implementation approach typically involves the following steps: First, determine the total number of nodes in the network. Then, for each pair of nodes, decide whether to establish a connection based on a predetermined probability, generating the corresponding adjacency matrix. The adjacency matrix is a symmetric matrix where an element value of 1 indicates the presence of an edge connection, while 0 indicates no connection. For undirected graphs, it's essential to ensure matrix symmetry; for directed graphs, the existence of each edge can be determined independently. MATLAB's built-in functions can help simplify this process, such as using random number generation functions like rand or randn to determine edge existence. Key implementation commands include creating an n×n matrix with rand(n) and applying a threshold comparison (e.g., A = rand(n) < p) where p represents the connection probability. Additionally, by adjusting the probability parameter, you can control the sparsity of the network. The generated network can be further visualized using functions like graph or digraph and plot for intuitive structural display, or used for complex network research such as connectivity analysis and path finding using algorithms like shortestpath or graphconncomp. This implementation method is simple and flexible, suitable for rapidly constructing basic random networks, and can serve as a foundational module for more complex network models. The approach allows for easy modification of network density through probability adjustments and provides a framework for extending to weighted networks or incorporating additional constraints.