GRAPH THEORY AND COMPLEX NETWORKS

In the past ten years,the fast development of complex network theory has provided a good support for the study of complexity and complex systems,since they describe clearly the important characteristics of complex systems,and show bright prospects in theory and applications.This paper presents mainly the application of graph theory to complex networks,especially to the synchronization problem of complex networks First,its application to the estimations of smallest nonzero,largest eigenvalues and synchronizability index of certain graphs are commented,followed by the effects of subgraph and graph eigenvector in the estimation of synchronizability index.Furthermore,the complexity between the relationships of synchronizability and network structural parameters are discussed via two simple graphs,and the effects of complementary graph, edge-addition and graph operation on the synchronization of complex networks are elaborated.Finally,some possible development directions in complex networks are predicted from the viewpoint of graph and control theory.