Hierarchical community detection based on multi degrees of distance space and submodularity optimization

Abstract

Detecting hierarchical community is crucial to analyze complex networks. In this paper, we propose a model for Hierarchical Community Detection based on Multi Degrees of distance space and submodularity function optimization (MD-HCD). First, an original network is divided into many communities under one degree of distance space. Then each community in original network is regarded as a super node, so those super nodes and corresponding edges construct a quotient network. And the same method is used to identify communities in quotient network. During hierarchical process, target function holds the property of submodularity, so that a result with [1, − 1/e] approximation is guaranteed. Experiments reveal the benefits of the multi degree of distance space. The proposed method generally detects a hierarchical community structure that includes three layers and has a stable performance in terms of modularity compared with many other main stream algorithms.