HAUSDORFF DIMENSION OF A FAMILY OF NETWORKS
Qingcheng Zeng, Lifeng Xi
Abstract
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.
Topics & Concepts
Hausdorff dimensionMathematicsPacking dimensionEffective dimensionUrysohn and completely Hausdorff spacesDimension functionDimension (graph theory)Minkowski–Bouligand dimensionEuclidean geometryFractal dimensionFractal dimension on networksHausdorff measureHausdorff spaceFractalInductive dimensionPure mathematicsDiscrete mathematicsCombinatoricsFractal analysisMathematical analysisGeometryComplex Network Analysis TechniquesMathematical Dynamics and FractalsTheoretical and Computational Physics