Eur. Phys. J. B 63, 515-520 (2008)
https://doi.org/10.1140/epjb/e2008-00258-x

Consensus on de Bruijn graphs

¹ Department of Electronic Science and Technology, University of Science and Technology of China, Hefei, Anhui, 230026, P.R. China
² Centre for Chaos and Complex Networks and Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P.R. China

Corresponding authors: ^a platoy@mail.ustc.edu.cn - ^b zqfu@ustc.edu.cn - ^c eegchen@cityu.edu.hk

Received: 20 November 2007
Revised: 27 April 2008
Published online: 10 July 2008

Abstract

We study the consensus dynamics with or without time-delays on directed and undirected de Bruijn graphs. Our results show that consensus on an undirected de Bruijn graph has a lower converging speed and larger time-delay tolerance in comparison with that on an undirected scale-free network. Although there is not much difference between the eigenvalue ratios of the two undirected networks, we found that their dynamical properties are remarkably different; consequently, it is seemingly more informative to consider the second smallest and the largest eigenvalues separately rather than considering their ratio in the study of synchronization of a coupled oscillators network. Moreover, our study on directed de Bruijn graphs reveals that properly setting directions on edges can improve the converging speed and time-delay tolerance simultaneously.