Quantifying and identifying the overlapping community structure in networks

TL;DR

This paper introduces a new metric for quantifying and identifying overlapping community structures in networks by leveraging maximal cliques and modularity optimization, validated on artificial and real-world networks.

Contribution

The paper proposes a novel metric and method for detecting overlapping communities by transforming the problem into modularity optimization on a maximal clique network.

Findings

Effective in identifying overlapping communities

Works well on artificial and real-world networks

Reproduces excellent results in word association networks

Abstract

It has been shown that the communities of complex networks often overlap with each other. However, there is no effective method to quantify the overlapping community structure. In this paper, we propose a metric to address this problem. Instead of assuming that one node can only belong to one community, our metric assumes that a maximal clique only belongs to one community. In this way, the overlaps between communities are allowed. To identify the overlapping community structure, we construct a maximal clique network from the original network, and prove that the optimization of our metric on the original network is equivalent to the optimization of Newman's modularity on the maximal clique network. Thus the overlapping community structure can be identified through partitioning the maximal clique network using any modularity optimization method. The effectiveness of our metric is demonstrated by extensive tests on both the artificial networks and the real world networks with known community structure. The application to the word association network also reproduces excellent results.