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Incompatibility networks as models of scale-free small-world graphs


  • Zhongzhi Zhang


  • Shuigeng Zhou


  • Tao Zou
  • Lichao Chen
  • Jihong Guan


We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • Zhongzhi Zhang & Shuigeng Zhou & Tao Zou & Lichao Chen & Jihong Guan, 2007. "Incompatibility networks as models of scale-free small-world graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(2), pages 259-264, November.
  • Handle: RePEc:spr:eurphb:v:60:y:2007:i:2:p:259-264
    DOI: 10.1140/epjb/e2007-00344-7

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    Cited by:

    1. Chen, Renxia & Fu, Xinchu & Wu, Qingchu, 2012. "On topological properties of the octahedral Koch network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 880-886.
    2. Knor, Martin & Škrekovski, Riste, 2013. "Deterministic self-similar models of complex networks based on very symmetric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4629-4637.


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