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

doi:10.1088/1674-1056/21/8/080506

Abstract In the study of complex networks, it is commonly believed that the eigenratio λ₂/λ_N 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/λ_N does represent the network synchronizability.

Keywords: synchronizability synchronized region Laplacian eigenratio complex network

Received: 02 October 2011
Revised: 02 November 2011
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	02.10.Ox	(Combinatorics; graph theory)

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

Corresponding Authors: Duan Zhi-Sheng, Chen Guan-Rong
E-mail: duanzs@pku.edu.cn; eegchen@cityu.edu.hk

Cite this article:

Duan Zhi-Sheng (段志生), Chen Guan-Rong (陈关荣) Does the eigenratio λ₂/λ_N represent the synchronizability of a complex network? 2012 Chin. Phys. B 21 080506

[1]	Barahona M and Pecora L M 2002 Phys. Rev. Lett. 89 054101
[2]	Boccaletti S, Latora V, Moreno Y, Chavez M and Hwang D U 2006 Phys. Rep. 424 175
[3]	Kocarev L and Amato P 2005 Chaos 15 024101
[4]	Li C P and Xu C X 2009 Chaos 19 013106
[5]	Motter A E, Zhou C S and Kurths J 2005 Europhys. Lett. 69 334
[6]	Sorrentino F, di Bernardo M, Garofalo F and Chen G R 2007 Phys. Rev. E 75 046103
[7]	Wang X G, Guan S G, Lai Y C, Li B W and Lai C H 2009 Europhys. Lett. 88 28001
[8]	Zhou C S and Kurths J 2006 Phys. Rev. Lett. 96 164102
[9]	Zhang G, Zhang W and Liu Z R 2010 Chin. Phys. Lett. 27 030504
[10]	Jin X Z and Yang G H 2010 Chin. Phys. B 19 080508
[11]	Zheng H Q and Jing Y W 2010 Chin. Phys. B 20 060504
[12]	Li H Q, Liao X F and Huang H Y 2011 Acta Phys. Sin. 60 020512 (in Chinese)
[13]	Duan Z S, Chen G R and Huang L 2008 Phys. Lett. A 372 3741
[14]	Pecora L M and Carroll T L 1998 Phys. Rev. Lett. 80 2109
[15]	Duan Z S, Chen G R and Huang L 2009 IEEE Trans. Auto. Control 54 845
[16]	Liu C, Duan Z S, Chen G R and Huang L Physica A 386 531
[17]	Belykh I V, Lange E and Hasler M 2005 Phys. Rev. Lett. 94 188101
[18]	Zhan C J, Chen G R and Yeung L F 2010 Physica A 389 1779
[19]	Zhao M, Wang B H, Yan G, Yang H J and Bai W J 2006 Physica A 371 773
[20]	Wang S J, Wu Z X, Dong H R and Chen G R 2011 Chin. Phys. B 20 048903
[21]	Comellas F and Gago S 2007 J. Phys. A: Math. Theor. 40 4483
[22]	Duan Z S, Liu C and Chen G R 2008 Physica D 237 1006
[23]	Duan Z S, Wang W X, Liu C and Chen G R 2009 Chin. Phys. B 18 3122
[24]	Kim D H and Motter A E 2007 Phys. Rev. Lett. 98 248701
[25]	McGraw P N and Menzinger M 2007 Phys. Rev. E 75 027104
[26]	Motter A E 2007 New. J. Phys. 9 182
[27]	Chen G R and Duan Z S 2008 Chaos 18 037102
[28]	Wang J Z, Duan Z S and Huang L 2006 Phys. Lett. A 351 143
[29]	Duan Z S, Chen G R and Huang L 2007 Phys. Rev. E 76 056103
[30]	Li Z K, Duan Z S, Chen G R and Huang L 2010 IEEE Trans. Circ. Syst. I 57 213

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

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