BA Scale-Free Network Topology Generation Algorithm Implementation

This article presents a MATLAB implementation of the BA (Barabási-Albert) scale-free network topology generation algorithm. The BA model is a renowned network model characterized by two fundamental properties: growth and preferential attachment. The growth property indicates that the network expands over time by adding new nodes, while preferential attachment means new nodes are more likely to connect to existing highly-connected nodes, resulting in a highly heterogeneous degree distribution. We provide detailed implementation steps including node addition mechanisms, connection selection methods using probability-based linking, and network visualization techniques using MATLAB's graph plotting functions. The algorithm implementation involves initializing a connected seed network, iteratively adding new nodes with m connections, and selecting attachment targets based on degree probabilities using cumulative distribution functions. Additionally, we discuss parameter tuning strategies for generating diverse network topologies by adjusting parameters like initial network size (m0) and connection count per new node (m). The article covers evaluation methods for analyzing network properties including degree distribution analysis using log-log plots, clustering coefficient calculation, and average path length computation. Through this comprehensive guide, readers will gain deep insights into the BA model mechanics and master practical implementation techniques for generating and analyzing scale-free networks in research applications.