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.

中文翻译：

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基于意见动态的分层和重叠网络社区检测

现实世界网络中的社区通常具有层次结构和重叠结构，这使得社区检测更具挑战性。在本文中，通过研究意见动态中经典 DeGroot 模型的共识过程，我们提出了一种基于累积意见距离 (COD) 的新方法来发现分层和重叠社区。结果表明，该方法不同于那些依赖静态适应度指标的经典算法，这些指标描述了整个网络的非均匀连通性。从两个方面验证了所提出的方法。首先，通过估计邻接矩阵的特征向量，我们研究了我们的算法在随机网络上的可检测性极限，这与关于共识收敛速度的结果一起保证了我们方法的理论上的性能。其次，大规模真实世界网络和人工基准的实验表明，我们的方法在分层模块化图上非常有效且具有竞争力。特别是，它在重叠社区检测方面优于最先进的算法。