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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. "Renormalization Group Analysis of the Small-World Network Model," Working Papers 99-04-029, Santa Fe Institute.
    2. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
    3. Comellas, Francesc & Sampels, Michael, 2002. "Deterministic small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 231-235.
    4. Zhang, Zhongzhi & Rong, Lili & Guo, Chonghui, 2006. "A deterministic small-world network created by edge iterations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 567-572.
    5. 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.
    6. Chandra, Anjan Kumar & Dasgupta, Subinay, 2005. "A small world network of prime numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 436-446.
    7. Zhongzhi Zhang & Shuigeng Zhou & Yi Qi & Jihong Guan, 2008. "Topologies and Laplacian spectra of a deterministic uniform recursive tree," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(4), pages 507-513, June.
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    Cited by:

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