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Optimal synchronizability of networks

Author

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  • B. Wang
  • T. Zhou
  • Z. L. Xiu
  • B. J. Kim

Abstract

We numerically investigate how to enhance synchronizability of coupled identical oscillators in complex networks with research focus on the roles of the high level of clustering for a given heterogeneity in the degree distribution. By using the edge-exchange method with the fixed degree sequence, we first directly maximize synchronizability measured by the eigenratio of the coupling matrix, through the use of the so-called memory tabu search algorithm developed in applied mathematics. The resulting optimal network, which turns out to be weakly disassortative, is observed to exhibit a small modularity. More importantly, it is clearly revealed that the optimally synchronizable network for a given degree sequence shows a very low level of clustering, containing much fewer small-size loops than the original network. We then use the clustering coefficient as an object function to be reduced during the edge exchanges, and find it a very efficient way to enhance synchronizability. We thus conclude that under the condition of a given degree heterogeneity, the clustering plays a very important role in the network synchronization. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • B. Wang & T. Zhou & Z. L. Xiu & B. J. Kim, 2007. "Optimal synchronizability of networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(1), pages 89-95, November.
    • Handle: RePEc:spr:eurphb:v:60:y:2007:i:1:p:89-95
    DOI: 10.1140/epjb/e2007-00324-y
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    Cited by:

    1. Qin, Ying-Mei & Che, Yan-Qiu & Zhao, Jia, 2018. "Effects of degree distributions on signal propagation in noisy feedforward neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 763-774.
    2. Yang, Yong & Tu, Lilan & Li, Kuanyang & Guo, Tianjiao, 2019. "Optimized inter-structure for enhancing the synchronizability of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 310-318.

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