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Robustness of regular ring lattices based on natural connectivity

Author

Listed:
  • J. Wu
  • M. Barahona
  • Y.-J. Tan
  • H.-Z. Deng

Abstract

It has been recently proposed that natural connectivity can be used to efficiently characterise the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this article, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalised Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with K monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices.

Suggested Citation

  • J. Wu & M. Barahona & Y.-J. Tan & H.-Z. Deng, 2011. "Robustness of regular ring lattices based on natural connectivity," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1085-1092.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:7:p:1085-1092
    DOI: 10.1080/00207721003605468
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    Cited by:

    1. Pavón-Domínguez, Pablo & Moreno-Pulido, Soledad, 2022. "Sandbox fixed-mass algorithm for multifractal unweighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Jichao Li & Yuejin Tan & Kewei Yang & Xiaoke Zhang & Bingfeng Ge, 2017. "Structural robustness of combat networks of weapon system-of-systems based on the operation loop," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 659-674, February.
    3. Peng, Guan-sheng & Wu, Jun, 2016. "Optimal network topology for structural robustness based on natural connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 212-220.
    4. Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    5. Bo Jiao & Yuan-ping Nie & Jian-mai Shi & Gang Lu & Ying Zhou & Jing Du, 2016. "Accurately and quickly calculating the weighted spectral distribution," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(1), pages 231-243, May.

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