GN Algorithm for Community Detection in Complex Networks

In this document, we provide a comprehensive overview of the GN (Girvan-Newman) algorithm for community detection in complex networks. The algorithm systematically partitions network nodes into distinct communities where intra-community connections are denser than inter-community links. This approach enables better understanding of network topology and finds practical applications in various domains including social network analysis and biological network studies. The implementation focuses on the algorithm's core mechanics: iterative removal of edges with highest betweenness centrality, followed by modularity computation to evaluate partition quality. Key functions include calculating edge betweenness using breadth-first search (BFS) and optimizing community structures through hierarchical clustering. Through this technical breakdown, we aim to help readers understand both the theoretical foundations and practical implementation of the GN algorithm for solving real-world network analysis problems. The code structure typically involves: 1. Network representation using adjacency lists or matrices 2. Betweenness centrality computation via shortest path algorithms 3. Modularity maximization through greedy optimization 4. Community assignment based on connected components after edge removal