Consensus on de Bruijn graphs

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.

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Correspondence to G. Yan.

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Yan, G., Fu, Z.Q. & Chen, G. Consensus on de Bruijn graphs. Eur. Phys. J. B 63, 515–520 (2008). https://doi.org/10.1140/epjb/e2008-00258-x

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PACS

  • 89.75.-k Complex systems
  • 05.45.Xt Synchronization; coupled oscillators