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Comments on “Scale-free networks without growth”

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  • Zhong, Weicai
  • Liu, Jing

Abstract

In [Y.-B. Xie, T. Zhou, B.-H. Wang, Scale-free networks without growth, Physica A 387 (2008) 1683–1688], a nongrowing scale-free network model has been introduced, which shows that the degree distribution of the model varies from the power-law form to the Poisson form as the free parameter α increases, and indicates that the growth may not be necessary for a scale-free network structure to emerge. However, the model implicitly assumes that self-loops and multiple-links are allowed in the model and counted in the degree distribution. In many real-life networks, such an assumption may not be reasonable. We showed here that the degree distribution of the emergent network does not obey a power-law form if self-loops and multiple-links are allowed in the model but not counted in the degree distribution. We also observed the same result when self-loops and multiple-links are not allowed in the model. Furthermore, we showed that the effect of self-loops and multiple-links on the degree distribution weakens as α increases and even becomes negligible when α is sufficiently large.

Suggested Citation

  • Zhong, Weicai & Liu, Jing, 2012. "Comments on “Scale-free networks without growth”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2163-2165.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:5:p:2163-2165
    DOI: 10.1016/j.physa.2011.10.025
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    References listed on IDEAS

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    1. Lü, Linyuan & Zhou, Tao, 2011. "Link prediction in complex networks: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1150-1170.
    2. Hu, Bo & Jiang, Xin-Yu & Ding, Jun-Feng & Xie, Yan-Bo & Wang, Bing-Hong, 2005. "A weighted network model for interpersonal relationship evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 576-594.
    3. Xie, Yan-Bo & Zhou, Tao & Wang, Bing-Hong, 2008. "Scale-free networks without growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(7), pages 1683-1688.
    4. Xu, Xin-Jian & Hu, Xiao-Ming & Zhang, Li-Jie, 2011. "Network evolution by nonlinear preferential rewiring of edges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2429-2434.
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    Cited by:

    1. in ’t Veld, Daan & van Lelyveld, Iman, 2014. "Finding the core: Network structure in interbank markets," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 27-40.

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