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Network module (community) structure has been a hot research topic in recent years. Many methods have been proposed for module detection and identification. Hierarchical structure of modules is shown to exist in many networks such as biological networks and social networks. Compared to the partitional module identification methods, less research is done on the inference of hierarchical modular structure. In this paper, we propose a method for constructing the hierarchical modular structure based on the stochastic block model. Statistical tests are applied to test the hierarchical relations between different modules. We give both artificial networks and real data examples to illustrate the performance of our approach. Application of the proposed method to yeast gene coexpression network shows that it does have a hierarchical modular structure with the modules on different levels corresponding to different gene functions.

Hierarchical Modular Structure Identification with Its Applications in Gene Coexpression Networks