Betweenness Centrality in Complex Networks

In complex network theory, betweenness centrality is a crucial metric for quantifying node importance within a network. A node achieves high betweenness centrality when it frequently appears on the shortest paths between other node pairs in the network. MATLAB implementations typically employ graph theory algorithms such as Brandes' algorithm or Freeman's algorithm for efficient computation. The Brandes algorithm offers an optimized approach with O(nm) time complexity for unweighted networks (where n represents nodes and m represents edges), utilizing breadth-first search (BFS) to compute shortest paths. Key MATLAB functions include graph() for network representation, distances() for shortest path calculation, and centrality() functions for direct metric computation. For custom implementations, developers often use sparse matrices to handle large-scale networks efficiently. These algorithms provide fundamental insights into network topology and node relationships, forming the basis for advanced network analysis research. Practical implementation considerations include handling disconnected components through pairwise reachability checks and adapting algorithms for weighted networks using Dijkstra's algorithm variations.