Consensus on de Bruijn graphs
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
Revised: 27 April 2008
Published online: 10 July 2008
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.
PACS: 89.75.-k – Complex systems / 05.45.Xt – Synchronization; coupled oscillators
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008