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Topological Properties of a 3-Regular Small World Network

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  • Huanshen Jia
  • Guona Hu
  • Haixing Zhao

Abstract

Complex networks have seen much interest from all research fields and have found many potential applications in a variety of areas including natural, social, biological, and engineering technology. The deterministic models for complex networks play an indispensable role in the field of network model. The construction of a network model in a deterministic way not only has important theoretical significance, but also has potential application value. In this paper, we present a class of 3-regular network model with small world phenomenon. We determine its relevant topological characteristics, such as diameter and clustering coefficient. We also give a calculation method of number of spanning trees in the 3-regular network and derive the number and entropy of spanning trees, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnddns:160740
    DOI: 10.1155/2014/160740
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    References listed on IDEAS

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    1. Szabó, Gábor J. & Alava, Mikko & Kertész, János, 2003. "Geometry of minimum spanning trees on scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 31-36.
    2. 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.
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