Due to the complexity of the interactions among the nodes of the complex networks,the properties of the networkmodules,to a large extent,remain unknown or unexplored.In this paper,we introduce the spatial correlation ...Due to the complexity of the interactions among the nodes of the complex networks,the properties of the networkmodules,to a large extent,remain unknown or unexplored.In this paper,we introduce the spatial correlation function Grs to describe the correlations among the modules of the weighted networks.In order to test the proposedmethod,we use ourmethod to analyze and discuss themodular structures of the ER random networks,scale-free networks and the Chinese railway network.Rigorous analysis of the existing data shows that the spatial correlation function Grs is suitable for describing the correlations among different networkmodules.Remarkably,we find that different networks display different correlations,especially,the correlation function Grs with different networks meets different degree distribution,such as the linear and exponential distributions.展开更多
基金Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0605the National Natural Science Foundation of China under Grant Nos.60634010 and 60776829+1 种基金New Century Excellent Talents in University under Grant No.NCET-06-0074the Key Project of Chinese Ministry of Education under Grant No.107007.
文摘Due to the complexity of the interactions among the nodes of the complex networks,the properties of the networkmodules,to a large extent,remain unknown or unexplored.In this paper,we introduce the spatial correlation function Grs to describe the correlations among the modules of the weighted networks.In order to test the proposedmethod,we use ourmethod to analyze and discuss themodular structures of the ER random networks,scale-free networks and the Chinese railway network.Rigorous analysis of the existing data shows that the spatial correlation function Grs is suitable for describing the correlations among different networkmodules.Remarkably,we find that different networks display different correlations,especially,the correlation function Grs with different networks meets different degree distribution,such as the linear and exponential distributions.