Exploring Local Community Structures in Large Networks

In this paper, we extend the concept of degree from single vertex to sub-graph, and present a formal definition of module/community in a network based on this extension. A new locally optimized algorithm is designed to find the module for a given source vertex in a network. Our analysis shows that the complexity of this algorithm is O(K²d) where K is the number of vertices to be explored in the sub-graph and d is the average degree of the vertices in the sub-graph. Based on this algorithm, we implement a JAVA tool, MoNet, for exploring local community structures in large networks. Using this tool to analyze a co-purchase network from Amazon shows that there are local community structures in this network. Further analyses on these local community structures demonstrate that media items are much easier to form compact local modules than book items do, indicating that recommending digital media items to customers based on co-purchasing information in the online store is more efficient than recommending books