Abstract
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 vertices and edges is where is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with and , in which case our algorithm runs in essentially linear time, . 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 on-line 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 edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.
- Received 30 August 2004
DOI:https://doi.org/10.1103/PhysRevE.70.066111
©2004 American Physical Society