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A New Random Rewiring Method To Transform Fractal Networks Into Small-World Networks

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  • JIAN-HUI LI

    (National Center for Applied Mathematics in Hunan, Xiangtan University, Hunan 411105, P. R. China†Key Laboratory of Intelligent Computing and Information, Processing of Ministry of Education, Xiangtan University, Hunan 411105, P. R. China)

  • ZU-GUO YU

    (National Center for Applied Mathematics in Hunan, Xiangtan University, Hunan 411105, P. R. China†Key Laboratory of Intelligent Computing and Information, Processing of Ministry of Education, Xiangtan University, Hunan 411105, P. R. China)

  • VO V. ANH

    (��School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia)

  • JIN-LONG LIU

    (National Center for Applied Mathematics in Hunan, Xiangtan University, Hunan 411105, P. R. China†Key Laboratory of Intelligent Computing and Information, Processing of Ministry of Education, Xiangtan University, Hunan 411105, P. R. China)

  • AN-QI PENG

    (National Center for Applied Mathematics in Hunan, Xiangtan University, Hunan 411105, P. R. China†Key Laboratory of Intelligent Computing and Information, Processing of Ministry of Education, Xiangtan University, Hunan 411105, P. R. China)

Abstract

The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method also retains the tree structure of tree graphs. Our method can transform many different types of fractal networks into small-world networks while the degree distribution and connectivity of these networks remain unchanged, demonstrating the generality of small-world networks. In addition, the method also works for other types of complex networks. The rewiring method proposed in this paper can be used in a broader range of applications of network analysis.

Suggested Citation

  • Jian-Hui Li & Zu-Guo Yu & Vo V. Anh & Jin-Long Liu & An-Qi Peng, 2023. "A New Random Rewiring Method To Transform Fractal Networks Into Small-World Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-15.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500895
    DOI: 10.1142/S0218348X23500895
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