HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS

Qingcheng Zeng () and Lifeng Xi
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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

FRACTALS (fractals), 2023, vol. 31, issue 01, 1-10

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.

Keywords: Fractal Network; Dimension; Touching Networks (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500160

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