Does the eigenratio synchronizability of λ2/λN represent the a complex network？  

作　　者：段志生 陈关荣 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems,Department of Mechanics and Aerospace Engineering,College of Engineering,Peking University,Beijing 100871,China [2]Department of Electronic Engineering,City University of Hong Kong,Hong Kong,SAR,China

出　　处：《Chinese Physics B》2012年第8期103-107,共5页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China （Grant Nos. 60974078 and 10832006）.

摘　　要：In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.In the study of complex networks, it is commonly believed that the eigenratio λ2/λN of the Laplacian matrix of a network represents the network synchronizability, especially for symmetric networks. This paper gives two counterexamples to show that this is not true for the case where the network has a disconnected synchronized region. Consequently, a simple answer is presented to the question of when the eigenratio λ2/λN does represent the network synchronizability.

关 键 词：SYNCHRONIZABILITY synchronized region Laplacian eigenratio complex network 

分 类 号：O157.5[理学—数学] O231[理学—基础数学]