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HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS
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For a family of networks [Formula: see text], we define the Hausdorff dimension of [Formula: see text] 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 [Formula: see text] Our definition is quite different from the fractal dimension defined for real-world networks.
Title: HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS
Description:
For a family of networks [Formula: see text], we define the Hausdorff dimension of [Formula: see text] 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 [Formula: see text] Our definition is quite different from the fractal dimension defined for real-world networks.
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