Emergence of loop structure in scale-free networks and dynamical consequences

Xiaojuan Ma, Liang Huang, Ying-Cheng Lai, Zhigang Zheng

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Previous work has revealed that the synchronizability of a scale-free network tends to be suppressed when its clustering coefficient is increased. We present a theory to explain this phenomenon. Our proposition is that, as the network becomes more strongly clustered, topological loop structure can emerge, generating a set of eigenvalues that are close to zero. As a result, the dynamics of synchronization tends to be dominated by the loop structure. As the clustering coefficient is increased, the size of the dominant loop increases, leading to continuous degradation of the network synchronizability. We provide analysis and numerical evidence to support the proposition and we speculate that the loop structure can provide a platform for controlling dynamical processes on scale-free networks with high clustering coefficients.

Original languageEnglish (US)
Article number056106
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - May 14 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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