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A unified model for Sierpinski networks with scale-free scaling and small-world effect

Author

Listed:
  • Guan, Jihong
  • Wu, Yuewen
  • Zhang, Zhongzhi
  • Zhou, Shuigeng
  • Wu, Yonghui

Abstract

In this paper, we propose an evolving Sierpinski gasket, based on which we establish a model of evolutionary Sierpinski networks (ESNs) that unifies deterministic Sierpinski network [Z.Z. Zhang, S.G. Zhou, T. Zou, L.C. Chen, J.H. Guan, Eur. Phys. J. B 60 (2007) 259] and random Sierpinski network [Z.Z. Zhang, S.G. Zhou, Z. Su, T. Zou, J.H. Guan, Eur. Phys. J. B 65 (2008) 141] to the same framework. We suggest an iterative algorithm generating the ESNs. On the basis of the algorithm, some relevant properties of presented networks are calculated or predicted analytically. Analytical solution shows that the networks under consideration follow a power-law degree distribution, with the distribution exponent continuously tuned in a wide range. The obtained accurate expression of clustering coefficient, together with the prediction of average path length reveals that the ESNs possess small-world effect. All our theoretical results are successfully contrasted by numerical simulations. Moreover, the evolutionary prisoner’s dilemma game is also studied on some limitations of the ESNs, i.e., deterministic Sierpinski network and random Sierpinski network.

Suggested Citation

  • Guan, Jihong & Wu, Yuewen & Zhang, Zhongzhi & Zhou, Shuigeng & Wu, Yonghui, 2009. "A unified model for Sierpinski networks with scale-free scaling and small-world effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2571-2578.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:12:p:2571-2578
    DOI: 10.1016/j.physa.2009.03.005
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    Citations

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    Cited by:

    1. Le, Anbo & Gao, Fei & Xi, Lifeng & Yin, Shuhua, 2015. "Complex networks modeled on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 646-657.
    2. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    3. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    4. Wang, Songjing & Xi, Lifeng & Xu, Hui & Wang, Lihong, 2017. "Scale-free and small-world properties of Sierpinski networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 690-700.
    5. Chen, Jin & Le, Anbo & Wang, Qin & Xi, Lifeng, 2016. "A small-world and scale-free network generated by Sierpinski Pentagon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 126-135.
    6. He, Jia & Xue, Yumei, 2018. "Scale-free and small-world properties of hollow cube networks," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 11-15.
    7. Ye, Dandan & Dai, Meifeng & Sun, Yu & Su, Weiyi, 2017. "Average weighted receiving time on the non-homogeneous double-weighted fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 390-402.
    8. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    9. Rasul Kochkarov, 2021. "Research of NP-Complete Problems in the Class of Prefractal Graphs," Mathematics, MDPI, vol. 9(21), pages 1-20, October.
    10. Lu, Zhe-Ming & Su, Yu-Xin & Guo, Shi-Ze, 2013. "Deterministic scale-free small-world networks of arbitrary order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3555-3562.

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