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Effective dimensions and percolation in hierarchically structured scale-free networks

Victor M. Eguiluz·Emilio Hernandez-Garcia·Oreste Piro·Konstantin Klemm
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Abstract

We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial character of this network that displays scale-free connectivity among other features, it turns out to be approximately one-dimensional. The dimensional characterization is in agreement with the results on statistics of site percolation and other dynamical processes implemented on such a network.

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Victor M. Eguiluz, Emilio Hernandez-Garcia, Oreste Piro, Konstantin Klemm. 2003-02-25. Effective dimensions and percolation in hierarchically structured scale-free networks. https://doi.org/10.1103/physreve.68.055102

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