title: Scale-free networks embedded in fractal space.
abstract: The impact of an inhomogeneous arrangement of nodes in space on a network organization cannot be neglected in most real-world scale-free networks. Here we propose a model for a geographical network with nodes embedded in a fractal space in which we can tune the network heterogeneity by varying the strength of the spatial embedding. When the nodes in such networks have power-law distributed intrinsic weights, the networks are scale-free with the degree distribution exponent decreasing with increasing fractal dimension if the spatial embedding is strong enough, while the weakly embedded networks are still scale-free but the degree exponent is equal to γ = 2 regardless of the fractal dimension. We show that this phenomenon is related to the transition from a noncompact to compact phase of the network and that this transition accompanies a drastic change of the network efficiency. We test our analytically derived predictions on the real-world example of networks describing the soil porous architecture.
authors.affiliation: Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan.
authors.forename: K
authors.initials: K
authors.lastname: Yakubo
authors.forename: D
authors.initials: D
authors.lastname: Korošak
mesh_terms: D017709:Fractals; D016062:Porosity; D012987:Soil / Q000737:chemistry; D014057:Tomography, X-Ray Computed
chemical_list: D012987:Soil