2004/08/30 by Aaron Clauset, M. E. J. Newman, Cristopher Moore · 8 citations
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.70.066111
published as Phys. Rev. E 70, 066111 (2004)
arxiv created 2004/08/30 · arxiv updated 2009/12/01
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(m d 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 log2 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.