MATLAB Source Code for Classic Routing Algorithm in BA Networks

In complex network research, the Barabási-Albert (BA) scale-free network model serves as a foundational framework for understanding real-world network topology characteristics, with its routing algorithm implementation frequently used as a classic case study in network science education.

The typical routing algorithm for BA networks generally includes the following core logic: Network Generation: Dynamically constructs the network based on preferential attachment mechanism - newly added nodes connect to existing highly-connected nodes with higher probability, forming scale-free properties Shortest Path Calculation: Utilizes modified Dijkstra or Floyd algorithms to handle dynamically growing adjacency matrices, adapting to the evolving nature of BA networks Routing Performance Evaluation: Validates small-world characteristics through metrics like average path length and clustering coefficient

Key MATLAB implementation considerations require special attention: Employ sparse matrix storage for large-scale network adjacency relationships Use vectorized operations instead of loops to enhance computational efficiency during network growth Apply Monte Carlo simulations to reduce statistical errors introduced by random connections

This algorithm not only reveals routing patterns in real-world systems like internet and social networks, but can also be extended to study network robustness against attacks or information diffusion dynamics. Understanding its implementation logic represents a crucial step in mastering complex network topology analysis.