Detecting Hierarchical and Overlapping Network Communities Based on Opinion Dynamics

It is common for communities in real-world networks to possess hierarchical and overlapping structures, which make community detection even more challenging. In this paper, by investigating consensus process of the classical DeGroot model in opinion dynamics, we propose a novel method based on the cumulative opinion distance (COD) to discover hierarchical and overlapping communities. It is shown that this method is different from those classical algorithms relying on static fitness metrics that depict the inhomogeneous connectivity across the network. The proposed method is validated from two aspects. First, by estimating the eigenvectors of adjacency matrices, we investigate the detectability limit of our algorithms on random networks, which together with the results concerning the convergence speed of consensus guarantees the performance of our method theoretically. Second, experiments on both large scale real-world networks and artificial benchmarks show that our method is very effective and competitive on hierarchical modular graphs. In particular, it outperforms the state-of-the-art algorithms on overlapping community detection.