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A general geometric growth model for pseudofractal scale-free web

Author

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  • Zhang, Zhongzhi
  • Rong, Lili
  • Zhou, Shuigeng

Abstract

We propose a general geometric growth model for pseudofractal scale-free web (PSW), which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks: degree distribution, second moment of degree distribution, degree correlations, distribution of clustering coefficient, as well as the diameter, which are partially determined by the parameters. Analytical results show that the resulting networks are disassortative and follow power-law degree distributions with a more general degree exponent tuned from 2 to 1+ln3ln2; the clustering coefficient of each individual node is inversely proportional to its degree and the average clustering coefficient of all nodes approaches to a large nonzero value in the infinite network order; the diameter grows logarithmically with the number of network nodes. All these reveal that the networks described by our model have small-world effect and scale-free topology.

Suggested Citation

  • Zhang, Zhongzhi & Rong, Lili & Zhou, Shuigeng, 2007. "A general geometric growth model for pseudofractal scale-free web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 329-339.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:329-339
    DOI: 10.1016/j.physa.2006.11.006
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    Citations

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    Cited by:

    1. Sun, Lina & Huang, Ning & Li, Ruiying & Bai, Yanan, 2019. "A new fractal reliability model for networks with node fractal growth and no-loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 699-707.
    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.
    3. Xie, Pinchen & Zhang, Zhongzhi & Comellas, Francesc, 2016. "On the spectrum of the normalized Laplacian of iterated triangulations of graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1123-1129.

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