Self-similarity of complex networks and hidden metric spaces

By Ángeles Serrano, Dmitri V. Krioukov, Marián Boguñá. Physical Review Letters, 2007

314 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/97c599caff3fb98ccf9a335e86759b259db3c85a

Citations in the corpus

• Growing Homophilic Networks Are Natural Navigable Small Worlds (2015, unknown): “The hierarchical self-similarity property is found in many real-life networks[31, 55, 56].”