Classic BA Scale-Free Network Model in Complex Networks

The BA (Barabási-Albert) model represents a fundamental scale-free network generation algorithm in complex network theory. This MATLAB implementation provides researchers with a robust framework for creating and analyzing scale-free networks through a preferential attachment mechanism where new nodes connect to existing nodes with probabilities proportional to their degrees. The code includes comprehensive functionality for network generation, degree distribution calculation, and visualization of network properties. Key algorithmic components implement the step-by-step network growth process: initial connected network formation, iterative node addition with weighted connection probabilities, and efficient adjacency matrix updates. The program features specialized functions for computing node degrees, degree distributions, and network metrics that facilitate the study of scale-free characteristics including power-law distribution validation. With its modular structure and detailed comments, this implementation serves as both a practical research tool and educational resource, accessible to researchers across experience levels while maintaining computational efficiency for large-scale network simulations. The codebase has been optimized for performance through vectorized operations and includes validation checks to ensure network integrity throughout the generation process.