MATLAB Implementation of Complex Network Barabási-Albert (BA) Model

This MATLAB code implements the Barabási-Albert (BA) model for complex networks, returning the adjacency matrix representation of the generated network graph. The implementation strategically employs sparse matrix storage, which dramatically reduces memory consumption and enhances computational performance for large-scale networks. The core algorithm is based on the scale-free network model where nodes are incrementally added to the network following preferential attachment principles - new nodes connect to existing nodes with probability proportional to their current degree distribution. Key implementation features include: - Stepwise network growth through node addition and connection establishment - Degree-based preferential attachment mechanism using cumulative probability distributions - Sparse matrix optimization for efficient memory management in large networks - Calculation of network parameters including average degree and degree distribution The generated model serves as a valuable tool for exploring network structure evolution and analysis across various domains such as social networks, biological networks, and technological networks. Beyond the adjacency matrix output, the code provides additional network metrics including average degree, degree distribution statistics, and connectivity patterns. This implementation is particularly useful for researchers and practitioners conducting complex network analysis requiring scalable and memory-efficient computational approaches.