FACH: Fast algorithm for detecting cohesive hierarchies of communities in large networks

Vertices in a real-world social network can be grouped into densely connected communities that are sparsely connected to other groups. Moreover, these communities can be partitioned into successively more cohesive communities. Despite an ever-growing pile of research on hierarchical community detection, existing methods suffer from either inefficiency or inappropriate modeling. Yet, some cut-based approaches have shown to be effective in finding communities without hierarchies. In this paper, we study the hierarchical community detection problem in large networks and show that it is NP-hard. We then propose an efficient algorithm based on edgecuts to identify the hierarchy of communities. Since communities at lower levels of the hierarchy are denser than the higher levels, we leverage a fast network sparsification technique to enhance the running time of the algorithm. We further propose a randomized approximation algorithm for information centrality of networks. We finally evaluate the performance of the proposed algorithms by conducting extensive experiments using real datasets. Our experimental results show that the proposed algorithms are promising and outperform the state-of-the-art algorithms by several orders of magnitude.