Does the eigenratio λ2/λN represent the synchronizability of a complex network?
Duan Zhi-Sheng (段志生)a, Chen Guan-Rong (陈关荣)b
a State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China; b Department of Electronic Engineering, City University of Hong Kong, Hong Kong, SAR, China
Abstract 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.
Duan Zhi-Sheng (段志生), Chen Guan-Rong (陈关荣) Does the eigenratio λ2/λN represent the synchronizability of a complex network? 2012 Chin. Phys. B 21 080506
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