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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
1

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

2

Departament de Física Fonamental, Universitat de Barcelona

3

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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