Overlapping communities in social networks

Identifying communities is essential for understanding the dynamics of a social network. The prevailing approach to the problem of community discovery is to partition the network into disjoint groups of members that exhibit a high degree of internal communication. This approach ignores the possibility that an individual may belong to two or more groups. Increasingly, researchers have begun to explore new methods which allow groups to overlap. One problem with existing approaches is that the definition of a community comes as the result of a particular algorithm. Such an approach to ”defining”communities has been extended to overlapping communities with some success. Our goals in this paper are twofold: first, to present an axiomatic approach to defining overlapping communities in terms of the properties a group should satisfy to be a community; and second, to justify the existence of overlapping in the structure of social communities experimentally using LiveJournal Blog data. Historically, the justification for overlapping groups has been primarily intuitive rather than quantitative. We present a heuristic algorithm which outputs a collection of communities that satisfy the required minimal properties and demonstrate that, in real-life social networks, a large number of individuals are members of communities which have non-trivial overlap with other communities.