A New Approach for Discovering and Quantifying Hierarchical Structure of Complex Networks

Biological robustness has been understood in many different ways. One of them is based on analysis of topological structures such as modularity, and hierarchy. While modularity has been studied in various areas intensively, only a few methods have been proposed to study hierarchical structure of networks. In this paper we propose a new algorithm to discover and quantify hierarchical structure of complex networks. This new algorithm identifies nodes on the top layer of hierarchical structure based on betweenness calculation among links, and groups the rest of nodes according to the distance from nodes on the top layer in order to locate them in different layers. The rearranged structure is quantified to represent the strength of hierarchy structure. In addition, we show the difference between hierarchy and modularity that have been regarded as similar properties.