Defining and identifying cograph communities in complex networks

Abstract

Community or module detection is a fundamental problem in complex networks. Most of the traditional algorithms available focus only on vertices in a subgraph that are densely connected among themselves while being loosely connected to the vertices outside the subgraph, ignoring the topological structure of the community. However, in most cases one needs to make further analysis on the interior topological structure of communities to obtain various meaningful subgroups. We thus propose a novel community referred to as a cograph community, which has a well-understood structure. The well-understood structure of cographs and their corresponding cotree representation allows for an immediate identification of structurally-equivalent subgroups. We develop an algorithm called the Edge P 4 centrality-based divisive algorithm (EPCA) to detect these cograph communities; this algorithm is efficient, free of parameters and independent of additional measures mainly due to the novel local edge P 4 centrality measure. Further, we compare the EPCA with algorithms from the existing literature on synthetic, social and biological networks to show it has superior or competitive performance in accuracy. In addition to the computational advantages over other community-detection algorithms, the EPCA provides a simple means of discovering both dense and sparse subgroups based on structural equivalence or homogeneous roles which may otherwise go undetected by other algorithms which rely on edge density measures for finding subgroups.This approach has been used to attempt to detect structures such as the clique [5], quasi-clique [6,7], n-club, nclan, k-plex, etc [1] as the expected community or module structure in complex networks or to characterize the topological structures of communities based on statistical methods [8]. These algorithms can obtain specific graceful topological structures, but they suffer from prohibitive computational complexity due to the inherent combinatorial complexity of the prime graphs on large-scale practical complex networks. The familial groups in social networks proposed by Nastos and Gao [4] and their corresponding comparability tree arrangements of the groups are one example in which the structural definition of a community reveals much interior structure in the communities, but they also show that the computational problem of detecting these groups is NP-complete. It does, however, open new strategies for defining communities or modules by structural analyses.From the viewpoint of structural analyses, we consider not only the traditional macroscopic clustering property of communities being internally dense while being externally sparse but also the topological structure of the communities found. We propose a polynomial-time approach of network partitioning, called the EPCA, which detects connected cograph communities in a network. A graph (network) is a cograph when it excludes a specific subgraph configuration called a P 4 , defined in the next section. Cographs have attracted persistent attention lately...

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