A new fast algorithm for detecting community structure in networks is introduced by M. E. J. Newman. The algorithm is based on modularity, which measures the fraction of edges within communities minus the expected value if edges were randomly distributed. It operates by iteratively joining communities that result in the greatest increase in modularity, leading to a dendrogram that shows the order of community merges. The algorithm runs in time O((m + n)n) or O(n²) for sparse graphs, making it significantly faster than previous methods, which had a worst-case time of O(m²n) or O(n³). The new algorithm is tested on both computer-generated and real-world networks, including a collaboration network of over 50,000 physicists, and performs well, identifying community structures with high accuracy. It is particularly effective for large networks where previous methods were too slow. The algorithm is also applicable to weighted networks and can be used to analyze real-world networks such as the "karate club" network and the dolphin social network. It is shown to outperform the Girvan and Newman algorithm in some cases and is much faster, allowing for the analysis of large networks that were previously intractable. The algorithm is also used to analyze a network of physicists, revealing strong community structures corresponding to traditional research areas. The algorithm's speed allows for the analysis of very large networks, making it a valuable tool for understanding complex systems.A new fast algorithm for detecting community structure in networks is introduced by M. E. J. Newman. The algorithm is based on modularity, which measures the fraction of edges within communities minus the expected value if edges were randomly distributed. It operates by iteratively joining communities that result in the greatest increase in modularity, leading to a dendrogram that shows the order of community merges. The algorithm runs in time O((m + n)n) or O(n²) for sparse graphs, making it significantly faster than previous methods, which had a worst-case time of O(m²n) or O(n³). The new algorithm is tested on both computer-generated and real-world networks, including a collaboration network of over 50,000 physicists, and performs well, identifying community structures with high accuracy. It is particularly effective for large networks where previous methods were too slow. The algorithm is also applicable to weighted networks and can be used to analyze real-world networks such as the "karate club" network and the dolphin social network. It is shown to outperform the Girvan and Newman algorithm in some cases and is much faster, allowing for the analysis of large networks that were previously intractable. The algorithm is also used to analyze a network of physicists, revealing strong community structures corresponding to traditional research areas. The algorithm's speed allows for the analysis of very large networks, making it a valuable tool for understanding complex systems.