LOCAL SEARCH FOR IDENTIFYING COMMUNITIES IN LARGE RANDOM GRAPHS

A community may be defined informally as a locally-dense subgraph, of a significant size, in a large, globally-sparse graph. Communities do not exist in the classical Erdos-Renyi random graph, but they do exist in graphs representing the Internet, the World Wide Web (WWW), and numerous social and biological networks. At least two different questions may be posed about the community structure in large graphs: (i) Given a graph, identify or extract all (i.e., sets of nodes that constitute) communities; and (ii) Given a node (or a small subset of seed nodes) in the graph identify the best community to which the given node(s) belong, if there exists such a community. Several algorithms have been proposed to solve the former problem, known as Community Discovery. The latter problem, known as Community Identification, has also been studied, but to a much smaller extent. Both the problem of community discovery and community identification have been shown to be NP-complete. In this paper, we will first discuss more precise graph-theoretic definitions of communities and their presence in the context of other non-Erdos-Renyi properties and then propose a taxonomy based on underlying solution strategies of existing algorithms for community structures. We will also present a fast, approximate, local-search heuristic for identifying the community to which a given node may belong using only the neighborhood information.