Towards community detection in locally heterogeneous networks

Abstract

In recent years, the size of many social networks such as Facebook, MySpace, and LinkedIn has exploded at a rapid pace, because of its convenience in using the internet in order to connect geographically disparate users. This has lead to considerable interest in many graph-theoretical aspects of social networks such as the underlying communities, the graph diameter, and other structural information which can be used in order to mine useful information from the social network. The graph structure of social networks is influenced by the underlying social behavior, which can vary considerably over different groups of individuals. One of the disadvantages of existing schemes is that they attempt to determine global communities, which (implicitly) assume uniform behavior over the network. This is not very well suited to the differences in the underlying density in different regions of the social network. As a result, a global analysis over social community structure can result in either very small communities (in sparse regions), or communities which are too large and incoherent (in dense regions). In order to handle the challenge of local heterogeneity, we will explore a simple property of social networks, which we refer to as the local succinctness property. We will use this property in order to extract compressed descriptions of the underlying community representation of the social network with the use of a min-hash approach. We will show that this approach creates balanced communities across a heterogeneous network in an effective way. We apply the approach to a variety of data sets, and illustrate its effectiveness over competing techniques. Copyright © SIAM.