Thursday, May 22, 2008

Self-similarity of complex networks and hidden metric spaces

Self-similarity of complex networks and hidden metric spaces





Abstract for "Self-similarity of complex networks and hidden metric
spaces" authored by M. Ángeles Serrano, Dmitri Krioukov, and Marián
Boguñá. Published in Physical Review Letters in 2008.


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Self-similarity of complex networks and hidden metric spaces


Published in Physical Review Letters in 2008.





M. Ángeles Serrano

Institute of Theoretical Physics, LBS, SB, EPFL,

1015 Lausanne, Switzerland




Dmitri Krioukov

Cooperative Association for Internet Data Analysis - CAIDA

San Diego Supercomputer Center,

University of California, San Diego




Marián Boguñá

Departament de Física Fonamental,

Universitat de Barcelona, Martí i Franquès 1,

08028 Barcelona, Spain





We demonstrate that the self-similarity of some scale-free networks with respect to a simple degreethresholding
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.





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