Classic GN Algorithm Utilizing Edge Betweenness for Community Detection in Complex Networks

In complex networks, community detection algorithms represent a significant research domain. The GN (Girvan-Newman) algorithm stands as a classical approach that employs edge betweenness to identify community structures. Its core methodology involves iteratively removing edges with the highest betweenness centrality, thereby progressively partitioning the network into smaller communities until no further divisions can be made. Key implementation aspects include calculating edge betweenness using shortest-path algorithms, typically achieved through breadth-first search (BFS) with O(ne) complexity for sparse graphs. The algorithm maintains a modularity score to evaluate partition quality, with recomputation of betweenness after each edge removal requiring O(n²) operations. Beyond GN, other prominent community detection algorithms include the Louvain method (optimizing modularity through greedy aggregation) and spectral clustering (utilizing graph Laplacian eigenvectors). These algorithms find extensive applications in social network analysis and bioinformatics for uncovering latent community structures within networks.