HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS

For a family of networks {G(n)}n >= 1, we define the Hausdorff dimension of {G(n)}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.

Automated summary

We define the Hausdorff dimension of the family of networks {G(n)}n ≥ 1, inspired by Frostman's characteristics of potential for the Hausdorff dimension of fractals in Euclidean spaces. We prove that the Hausdorff dimension of the touching networks is log m/log N. Our definition is distinct from the fractal dimension defined for real-world networks.