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A deterministic small-world network created by edge iterations

Author

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  • Zhang, Zhongzhi
  • Rong, Lili
  • Guo, Chonghui

Abstract

Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.

Suggested Citation

  • Zhang, Zhongzhi & Rong, Lili & Guo, Chonghui, 2006. "A deterministic small-world network created by edge iterations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 567-572.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:567-572
    DOI: 10.1016/j.physa.2005.08.020
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    Citations

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    Cited by:

    1. Zhang, Jingyuan & Yan, Weigen, 2020. "Counting spanning trees of a type of generalized Farey graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    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. Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    4. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    5. Sun, Daoqiang & Li, Long & Liu, Kai & Wang, Hua & Yang, Yu, 2022. "Enumeration of subtrees of planar two-tree networks," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    6. 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.
    7. De Bona, Anderson Andrei & de Oliveira Rosa, Marcelo & Ono Fonseca, Keiko Verônica & Lüders, Ricardo, 2021. "A reduced model for complex network analysis of public transportation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    8. Feng, Qunqiang & Li, Xing & Hu, Zhishui, 2023. "Asymptotic degree distribution in a homogeneous evolving network model," Statistics & Probability Letters, Elsevier, vol. 193(C).

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