Defining and Discovering Communities in Social Networks

The categorization of vertices in a network is a common task across a multitude of domains. Specifically, structural divisions into internally well connected sets have been shown to be useful in computer science, social science, and biology. In each of these areas, grouping vertices using structural boundaries helps one to understand the underlying processes of a network. Identifying such groupings is a non-trivial task, and a subject of intense research in recent years. In general, identifying groups of vertices in a network based on structural properties alone is known as community detection. Methods to identify such groups take a wide variety of approaches, mirroring the diversity in domains where an accurate view of structural communities is useful. Depending on the definition of a community used, one could discover groups which maximize a global quality function, contain a specific set of substructures, or satisfy a set of local criteria. Each of these definitions has resulted in a number of methods which aim to produce the “best” set of communities relative to the definition chosen. Rather than focusing on a number of features which differentiate these definitions and methods from each other, this text will focus on perhaps the most fundamental question in the field of community detection; should groups be disjoint or should they be allowed to overlap? In the past, the field of community detection has primarily focused on identifying a set of groups such that each vertex in the network is assigned to a single group. Such a requirement results in a set of disjoint groups covering the entire network. However, with the explosion of social network and on-line communication