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Self-similarity of complex networks and hidden metric spaces
M. Serrano, D. Krioukov, and M. Boguñá, "Self-similarity of complex networks and hidden metric spaces", Physical Review Letters, vol. 100, no. 078701, Feb 2008.
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Self-similarity of complex networks and hidden metric spaces

Mirian Ángeles Serrano3
Dmitri Krioukov1
Marián Boguñá2

CAIDA, San Diego Supercomputer Center, University of California San Diego


Departament de Física Fonamental, Universitat de Barcelona


Institute of Theoretical Physics, LBS, SB, EPFL

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Keywords: routing, topology
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