中国物理B ›› 2012, Vol. 21 ›› Issue (8): 80506-080506.doi: 10.1088/1674-1056/21/8/080506

• GENERAL • 上一篇    下一篇

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

段志生a, 陈关荣b   

  1. 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
  • 收稿日期:2011-10-02 修回日期:2011-11-02 出版日期:2012-07-01 发布日期:2012-07-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 60974078 and 10832006).

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   

  1. 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
  • Received:2011-10-02 Revised:2011-11-02 Online:2012-07-01 Published:2012-07-01
  • Contact: Duan Zhi-Sheng, Chen Guan-Rong E-mail:duanzs@pku.edu.cn; eegchen@cityu.edu.hk
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 60974078 and 10832006).

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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.

关键词: synchronizability, synchronized region, Laplacian eigenratio, complex network

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.

Key words: synchronizability, synchronized region, Laplacian eigenratio, complex network

中图分类号:  (Synchronization; coupled oscillators)

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