复杂网络的拉普拉斯和无符号拉普拉斯特征谱分析  

Analysis of Spectra of Laplacian and Signless Laplacian Metrices in Complex Networks

作　　者：李发旭[1] 卫良[2] 

机构地区：[1]青海师范大学计算机学院,青海西宁810008 [2]青海师范大学数学与统计学院,青海西宁810008

出　　处：《青海师范大学学报（自然科学版）》2016年第4期20-26,共7页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：教育部春晖计划项目(Z2015058)资助

摘　　要：复杂网络的特征谱与网络的拓扑结构密切相关,通过研究特征谱可以更好地了解网络的拓扑性质和动力学行为.本文总结了复杂网络特征谱方面的研究成果,首先介绍了三类典型的复杂网络模型邻接矩阵、拉普拉斯矩阵和无符号拉普拉斯矩阵的特征谱与网络结构和网络同步之间的关系,然后通过仿真分析研究了ER随机网络、WS小世界网络和BA无标度网络模型的邻接矩阵、拉普拉斯矩阵和无符号拉普拉斯矩阵的谱半径与网络规模和连边概率之间的关系.The spectra of networks are closely related to their topology, based on the spectra, we will have a good understanding of topological properties and dynamic behavior of networks. In this paper, a review on the recent studies of the spectra of complex networks has been presented. First, we discuss the relations between the spectra and synchronization of Adjacency, Laplacian and Signless Laplacian matrices. Next, through theory-guided extensive numerical simulations, we investigate the relations between spectral radius and size and probability of above three matrices for typical complex networks models, namely the ER random--graph networks, the WS small--world networks, the BA scale-free networks.

关 键 词：复杂网络 特征谱 网络结构 拉普拉斯矩阵 无符号拉普拉斯矩阵 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]