BA Scale-Free Networks, Random Graphs, WS Small-World Networks, NW Small-World Networks, Nearest-Neighbor Coupled Networks, Average Path Length, Degree Distribution, Clustering Coefficient

Complex network models serve as essential tools for studying various real-world systems such as social networks, the Internet, and biological networks. MATLAB provides robust computational capabilities to efficiently implement and analyze multiple classic network models.

BA scale-free networks model systems exhibiting power-law degree distributions, where a small number of nodes possess numerous connections while most nodes have only few links. The construction algorithm typically starts with a small initial set of nodes and expands the network through preferential attachment mechanisms. In MATLAB implementation, this involves dynamically adding nodes with probabilities proportional to existing nodes' degrees, often using cumulative sum functions for efficient sampling.

Random graph models (e.g., Erdős-Rényi model) assume completely random connections between nodes, resulting in Poisson degree distributions. In contrast, WS and NW small-world networks bridge regular and random networks: the WS model achieves small-world properties through random rewiring of regular lattice connections, while the NW model adds random edges to a regular structure. Both models produce networks with short average path lengths and high clustering coefficients. MATLAB implementations typically involve creating regular lattices first, then applying stochastic modifications using random number generators and adjacency matrix manipulations.

Nearest-neighbor coupled networks represent the most basic regular network model where each node connects only to a fixed number of adjacent nodes. When analyzing these networks, the average path length reflects information transmission efficiency, degree distribution describes network connectivity heterogeneity, and clustering coefficient measures the tightness of node neighborhoods. These metrics collectively form a quantitative analytical framework for network characterization. MATLAB provides built-in functions for calculating these metrics, such as graph distance algorithms for path length computation, degree distribution histograms, and local clustering coefficient calculations using triangular subgraphs.