2007/10/31 by M. Angeles Serrano, Dmitri Krioukov, Marian Boguna · 2 citations
Physics and Astronomy · Computer Science · #cond-mat.dis-nn #cs.NI #physics.soc-ph
paper · pdf · doi:10.1103/physrevlett.100.078701
published as Physical Review Letters 100, 078701 (2008)
arxiv created 2008/02/20 · arxiv updated 2009/12/01
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.