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Hausdorff Dimension Of A Family Of Networks

Author

Listed:
  • QINGCHENG ZENG

    (School of Mathematics and Statistics, Ningbo University, 315211 Ningbo, P. R. China)

  • LIFENG XI

    (School of Mathematics and Statistics, Ningbo University, 315211 Ningbo, P. R. China)

Abstract

For a family of networks {Gn}n≥1, we define the Hausdorff dimension of {Gn}n≥1 inspired by the Frostman’s characteristics of potential for Hausdorff dimension of fractals on Euclidean spaces. We prove that our Hausdorff dimension of the touching networks is log m/log N. Our definition is quite different from the fractal dimension defined for real-world networks.

Suggested Citation

  • Qingcheng Zeng & Lifeng Xi, 2023. "Hausdorff Dimension Of A Family Of Networks," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:01:n:s0218348x23500160
    DOI: 10.1142/S0218348X23500160
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