Efficient community identification in complex networks

Abstract

Complex networks are large, dynamic, random graphs modeled to replicate interactions among entities in real-world complex systems (e.g., the Internet, the World Wide Web, online social networks—Facebook, Twitter, etc., and the human connectome). These networks differ from the classical Erdos–Renyi random graphs in terms of network properties such as degree distribution, average distance and clustering. Existence of communities is one such property inherent to complex networks. A community may be defined informally as a locally dense subgraph, of a significant size, in a large globally sparse graph. Such communities are of interest in various disciplines, including graph theory, physics, statistics, sociology, biology, and linguistics. At least two different questions may be posed on the community structure in large networks: (1) given a network, detect or extract all (i.e., sets of nodes that constitute) communities, and (2) given a node in the network, identify the best community that the given node belongs to, if there exists one. 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 these problems have been shown to be NP-complete, and a number of approximate algorithms have been proposed in recent years. In this paper, we discuss the various community definitions in the literature and analyze the algorithms for identifying communities. We propose an alternative definition of a community based on the average degree of the induced subgraph. Also, we propose a novel algorithm to identify community in complex networks based on maximizing the average degree.