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Properties of a new small-world network with spatially biased random shortcuts

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  • Matsuzawa, Ryo
  • Tanimoto, Jun
  • Fukuda, Eriko

Abstract

This paper introduces a small-world (SW) network with a power-law distance distribution that differs from conventional models in that it uses completely random shortcuts. By incorporating spatial constraints, we analyze the divergence of the proposed model from conventional models in terms of fundamental network properties such as clustering coefficient, average path length, and degree distribution. We find that when the spatial constraint more strongly prohibits a long shortcut, the clustering coefficient is improved and the average path length increases. We also analyze the spatial prisoner’s dilemma (SPD) games played on our new SW network in order to understand its dynamical characteristics. Depending on the basis graph, i.e., whether it is a one-dimensional ring or a two-dimensional lattice, and the parameter controlling the prohibition of long-distance shortcuts, the emergent results can vastly differ.

Suggested Citation

  • Matsuzawa, Ryo & Tanimoto, Jun & Fukuda, Eriko, 2017. "Properties of a new small-world network with spatially biased random shortcuts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 408-415.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:408-415
    DOI: 10.1016/j.physa.2017.05.031
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    References listed on IDEAS

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    1. Jon M. Kleinberg, 2000. "Navigation in a small world," Nature, Nature, vol. 406(6798), pages 845-845, August.
    2. Fukuda, Eriko & Kokubo, Satoshi & Tanimoto, Jun & Wang, Zhen & Hagishima, Aya & Ikegaya, Naoki, 2014. "Risk assessment for infectious disease and its impact on voluntary vaccination behavior in social networks," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 1-9.
    3. Shao, Feng-jing & Sui, Yi & Zhou, Yong-hong & Sun, Ren-cheng, 2016. "Complex network model of the Treatise on Cold Damage Disorders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 152-161.
    4. Naoki Masuda & Issei Kurahashi & Hiroko Onari, 2013. "Suicide Ideation of Individuals in Online Social Networks," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-8, April.
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

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    3. Tatsukawa, Yuichi & Arefin, Md. Rajib & Utsumi, Shinobu & Kuga, Kazuki & Tanimoto, Jun, 2022. "Stochasticity of disease spreading derived from the microscopic simulation approach for various physical contact networks," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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