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.
Zeng et al. (Wed,) studied this question.