Extracting hierarchical organization of complex networks by dynamics towards synchronization

Based on the dynamics towards synchronization in hierarchical networks, we present an efficient method for extracting hierarchical organization in complex network. In the synchronization process, hierarchical structures corresponding to well defined communities of nodes emerge in different time scales, ordered in a hierarchical way. Thus, a new strategy for quantifying the dissimilarity between a pair of nodes in networks is introduced according to their time scales of synchronization. Then, using such a dissimilarity measure in conjunction with a hierarchical clustering method, our extracting method is proposed. The performance of our approach is tested on a set of computer generated and real-world networks with known hierarchical organization. The results demonstrate that our method enables us to offer insight into the complex networks with a multi-scale description. In addition, using a criterion of modularity, the method can also accurately find community structures in complex networks.