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Effective dimensions and percolation in hierarchicaly structured scale-free networks

Eguíluz, Víctor M.; Hernández-García, Emilio; Piro, Oreste; Klemm, Konstantin
Physical Review E 68, 055102 (1-4) (2003)

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.