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A small-world network derived from the deterministic uniform recursive tree

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  • Lu, Zhe-Ming
  • Guo, Shi-Ze

Abstract

As the deterministic version of the uniform recursive tree (URT), the deterministic uniform recursive tree (DURT) has been intensively studied by Zhang et al. (2008) [21]. They gave several important properties of DURT, including its topological characteristics and spectral properties. Although DURT shows a logarithmic scaling with the size of the network, DURT is not a small-world network since its clustering coefficient is zero. In this paper, we propose a new deterministic small-world network by adding some edges with a simple rule in each DURT iteration, and then give the analytic solutions to several topological characteristics of the model proposed.

Suggested Citation

  • Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:87-92
    DOI: 10.1016/j.physa.2011.08.002
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    References listed on IDEAS

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    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
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    Cited by:

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    4. Lu, Zhe-Ming & Su, Yu-Xin & Guo, Shi-Ze, 2013. "Deterministic scale-free small-world networks of arbitrary order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3555-3562.
    5. Wang, Jianrong & Wang, Jianping & Li, Lei & Yang, Bo, 2018. "A novel relay selection strategy based on deterministic small world model on CCN," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 559-568.
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    8. Huanshen Jia & Guona Hu & Haixing Zhao, 2014. "Topological Properties of a 3-Regular Small World Network," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-4, April.

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