复杂网络的特征谱及其应用  

Spectra of Complex Networks and Its Applications

作　　者：赵永毅 史定华[1] 

机构地区：[1]上海大学数学系,上海200444

出　　处：《复杂系统与复杂性科学》2006年第1期1-12,共12页Complex Systems and Complexity Science

基　　金：国家863计划(2002AA234021)

摘　　要：网络的特征谱与网络的拓扑密切相关,通过研究特征谱可以更好地了解网络的结构涌现和动力学特性。本文总结了近年来在网络特征谱方面的研究进展,首先介绍了3类重要网络模型邻接矩阵的特征谱密度和网络结构的关系及其在网络中心性和二分性中的应用,接着介绍了谱序列中存在的标度不变性和结构涌现,然后介绍了网络Laplacian矩阵的特征谱与网络同步之间的关系以及在分析网络社团结构中的应用,最后指出了进一步研究的方向。The spectra of networks are closely related to their topology, based on the spectra, we will have a good understanding of their structure emergence and dynamic behavior. In this paper, a review on the recent studies of the spectra of complex networks has been presented. First, we introduce relations between the spectral density and the structure of the three important network models and the applications in the centrality and bipartivity. Next, we describe the scaling invariance property of the spectral series and the structure emergence. Then, we discuss the applications of the Laplacian spectra in the network synchronization and the community in networks. Finally, we point out some problems and directions for further investigation.

关 键 词：复杂网络 特征谱 网络结构 谱序列 网络同步 

分 类 号：N94[自然科学总论—系统科学] TP39[自动化与计算机技术—计算机应用技术]