Overlapping communities in social networks

Traditionally, methods to identify community structure in networks have focused on partitioning the vertex set into a number of disjoint groups. However, recently proposed methods have included mechanisms to account for possible overlap between communities. These approaches have taken a wide variety of forms, resulting in a lack of consensus as to what characteristics overlapping communities should have. Additionally, the application of algorithms which account for community overlap are often justified via intuitive rather than empirical arguments. In this text, each of the issues mentioned above is examined. From previous literature, a minimal set of axioms which overlapping communities should satisfy is presented. Additionally, a modification of a previously published algorithm, iterative scan, is introduced to ensure that these properties are met. Finally, the overlap between communities discovered in a large, real world communication network is examined. The analysis offers empirical justification tha...