The paper introduces a new algorithm for detecting community structure in networks, which is significantly faster than previous methods. The algorithm, based on the concept of modularity, optimizes a quality function that measures the fraction of edges within communities. It operates by repeatedly joining communities that increase the modularity, resulting in a dendrogram that represents the hierarchy of communities. The algorithm has a worst-case time complexity of O((m + n)n) or O(n²) for sparse graphs, making it feasible to analyze networks with up to a million vertices. The authors demonstrate the algorithm's effectiveness through various examples, including computer-generated and real-world networks, such as a collaboration network of over 50,000 physicists. The results show that the new algorithm can identify community structures with high accuracy and speed, making it a valuable tool for studying large and complex networks.The paper introduces a new algorithm for detecting community structure in networks, which is significantly faster than previous methods. The algorithm, based on the concept of modularity, optimizes a quality function that measures the fraction of edges within communities. It operates by repeatedly joining communities that increase the modularity, resulting in a dendrogram that represents the hierarchy of communities. The algorithm has a worst-case time complexity of O((m + n)n) or O(n²) for sparse graphs, making it feasible to analyze networks with up to a million vertices. The authors demonstrate the algorithm's effectiveness through various examples, including computer-generated and real-world networks, such as a collaboration network of over 50,000 physicists. The results show that the new algorithm can identify community structures with high accuracy and speed, making it a valuable tool for studying large and complex networks.