The subgraph that we do not mark with the module corresponds to the combined module M1, M2, M3, M4, M7, M8. Here the modules M6, M9 and other modules are parallel to each other, which is consistent with our results. M3 and M7 belong to a large category, which is ��branched chain family amino acid metabolic process”. This large category is different from the most enriched category for selleck products the combined module M3 and M7. This may come from the fact that since M7 is very small, it does not cover a large part of its enriched category. M1 and M4 are parallel to each other which is also consistent with our analysis. All these results show that our proposed method can explain some of the hierarchical structure of the GO categories. Due to the network size, we did not handle all the genes of yeast.

This may be a reason why some of our computational results are not consistent with the GO function tree map.Figure 6Tree map of the enriched GO categories in yeast gene coexpression network.4. ConclusionModule identification problem has attracted much attention from different fields and it continues being a hot research topic. How to determine the number of modules in a modular network has been an open problem during the study of module identification methods. This problem may come from the hierarchical structure of modular networks. The different numbers correspond to the different levels of the hierarchical structure and they may be all reasonable. In this paper, we proposed a method for constructing the hierarchical modular structure of networks.

With statistical tests, we can identify both the parallel modules and the hierarchical structure. According to different cutoffs of the hierarchical tree, different numbers of modules can be identified. This may solve the problem of the number of network modules to some extent. Several examples are given to demonstrate the efficiency of our method. Application of this method to gene coexpression networks shows that there are hierarchical modules in yeast gene coexpression network. On different levels of such networks, the genes in the module belong to different gene functions most. Thus studying the gene function through constructing the hierarchical modular structure instead of specifying the number of modules should perform better. Application of such algorithms to other kinds of networks may also contribute GSK-3 to other research fields.Acknowledgments This work was supported in part by NSFC Grants 10901042, 10971075, and 91130032. The primary version of this paper has appeared in IEEE ISB 2012.