Theoretical analysis defines local Hausdorff dimension in fractal networks, indicating properties and generalizations.
In this paper, we define the local Hausdorff dimension on fractal networks inspired by the idea of α-potential at a point x∈Rd. We prove some basic properties of the local Hausdorff dimension and then obtain the local Hausdorff dimension of some networks. We also discuss a more generalized dimension definition, namely the subset Hausdorff dimension.
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Zeng et al. (2026) studied this question.
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