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Average Fermat Distance Of A Pseudo-Fractal Hierarchical Scale-Free Network

Author

Listed:
  • LULU PENG

    (School of Mathematical Science, Beihang University, Beijing 100083, P. R. China)

  • CHENG ZENG

    (School of Mathematical Science, Beihang University, Beijing 100083, P. R. China)

  • DIRONG CHEN

    (School of Mathematical Science, Beihang University, Beijing 100083, P. R. China)

  • YUMEI XUE

    (School of Mathematical Science, Beihang University, Beijing 100083, P. R. China)

  • ZIXUAN ZHAO

    (School of Mathematical Science, Beihang University, Beijing 100083, P. R. China)

Abstract

Fermat point of a triangle is the point with the minimal total distance from the three vertices in a triangle. In this paper, we discuss the average Fermat distance for a class of hierarchical networks. First, the unweighted hierarchical scale-free network is established in an iterative way. Applying the recursive method, we deduce the analytical expression of average Fermat distance and average geodesic distance. Then we reveal the linear relation of the leading terms for average Fermat distance and average geodesic distance. Finally, we obtain the small-world property of the hierarchical scale-free network, which indicates that average Fermat distance can be a valuable index of small-word property.

Suggested Citation

  • Lulu Peng & Cheng Zeng & Dirong Chen & Yumei Xue & Zixuan Zhao, 2023. "Average Fermat Distance Of A Pseudo-Fractal Hierarchical Scale-Free Network," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:01:n:s0218348x23500135
    DOI: 10.1142/S0218348X23500135
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