The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ∼ n and d ∼ log n, in which case our algorithm runs in essentially linear time, O(n log 2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.
A fast community discovery algorithm in very large network was proposed with approximate linear time complexity O(nlog 2 n), where n is the number of nodes REF .
Finding community structure in very large networks
Phys. Rev. E 70, 066111 (2004)
Physics Medicine