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 P4 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 P4 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.
Highlights
As one hotspot and keystone of the research on complex networks, community or module detection has been heavily developed in the past few decades [1]
We first introduce edge P4 centrality and the approach Edge P4 centrality-based divisive algorithm (EPCA); we demonstrate the properties of cograph communities
We propose the novel cograph community and develop an approach (EPCA) for extracting cograph communities based on edge P4 centrality
Summary
As one hotspot and keystone of the research on complex networks, community or module detection has been heavily developed in the past few decades [1]. While a range of algorithms have been proposed to focus mainly on how to detect a cohesive group of vertices as a rough community, they primarily use the macroscopic property of communities, since they are internally edge-dense while being sparse outside and pay little attention to the interior topological structure The fact that these traditional algorithms do not reveal a specific structure in their detected communities means that extra work will have to be done in order to identify the important subgroups or modules within the community. Cographs have a unique cotree representation, which is efficiently constructed (an example is displayed in appendix A); this allows us to analyze the topological structure of our communities By this nontraditional structural analysis, we can obtain various meaningful subgroups within cograph communities which the traditional algorithms cannot detect since the sub-modules may be sparsely connected.
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