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On the role of hubs in the coherence of unicyclic and bicyclic networks

Author

Listed:
  • Ling Zhou

    (Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R. China)

  • Xiangdong Li

    (��School of Information Technology, Zhejiang Yuying College of Vocational Technology, Hangzhou 310018, P. R. China)

  • Weigang Sun

    (Department of Mathematics, School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, P. R. China)

Abstract

In this paper, we aim to study the role of hubs in the network coherence quantified by the Laplacian spectra and choose two families of unicyclic and bicyclic networks with the same network size as our network models. In order to investigate the influence of adding links on the coherence, we construct four types of bicyclic networks with the same average degree. Using the network’s regular structures and matrix theories, we obtain analytical solutions of the coherences regarding the degrees of hub nodes. Based on these exact results for the coherence, the network with one hub displays higher coherence compared to the network with two hubs. We then obtain exact relations for the coherences of the bicyclic networks with the same average degree and show that different adding links and hub’s positions are responsible for distinct performance of the consensus algorithms. Finally, we show that the coherence and average path length behave in a linear way meaning that smaller average path length results in better coherence.

Suggested Citation

  • Ling Zhou & Xiangdong Li & Weigang Sun, 2023. "On the role of hubs in the coherence of unicyclic and bicyclic networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(11), pages 1-12, November.
    • Handle: RePEc:wsi:ijmpcx:v:34:y:2023:i:11:n:s0129183123501437
    DOI: 10.1142/S0129183123501437
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