有向社团网络的Laplace特征值谱和同步能力的分析研究  

On Laplace Spectra and Synchronizability of Directed Community Networks

作　　者：涂壕 黄金珠 赵雪漪 黄苗苗 TU-Hao;HUANG Jin-zhu;ZHAO Xue-yi;HUANG Miao-miao(School of Maths and Computer Science,Hanjiang Normal University,Shiyan 442000,China;Yunyang Middle School,Shiyan 442000,China)

机构地区：[1]汉江师范学院数学与计算机科学学院,湖北十堰442000 [2]十堰市郧阳中学,湖北十堰442000

出　　处：《汉江师范学院学报》2023年第3期13-17,共5页Journal of Hanjiang Normal University

基　　金：湖北省高等学校优秀中青年科技创新团队计划:超网络的动力学及控制(项目编号:T2022035);应用数学湖北省重点实验室(湖北大学)开放基金资助(项目编号:HBAM202003)。

摘　　要：网络的Laplace矩阵的特征值谱中包含了网络拓扑结构的丰富信息,在研究网络动力学行为上发挥着重要的作用.现实中网络很多都具有社团结构,甚至还是有向的.以两种典型的有向环状相连的社团网络为例,旨在研究社团个数和社团内节点数的增加对单边和两边相连的有向社团网络的Laplace特征值谱、同步能力和社团显著度的影响.并且,基于主稳定函数方法讨论两种不同的环状有向社团网络的同步能力随着网络规模增大时的变化趋势.The spectrum of Laplace matrix of a work contains a great deal of information about the network structure and plays a fundamental role in the dynamical behavior of the network. There are lots of real networks that have directed community structure. This paper investigates the Laplace spectra, synchronizability and community modularity of two typical directed ring community networks and explores the effect of them in increasing the number of communities or the number of nodes in each community. Based on the master stability function approach, the synchronizability of two different circular directed community networks is discussed with the increase of network size.

关 键 词：有向社团网络 LAPLACE特征值 社团结构 同步能力 

分 类 号：O233[理学—运筹学与控制论] O157.5[理学—数学]