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Self-similarity of complex networks and hidden metric spaces
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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.
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SERRANO MORAL, Ma. Ángeles (María Ángeles), KRIOUKOV, Dmitri and BOGUÑÁ, Marián. Self-similarity of complex networks and hidden metric spaces. Physical Review Letters. 2008. Vol. 100, num. 7, pags. 078701-1-078701-4. ISSN 0031-9007. [consulted: 20 of August of 2026]. Available at: https://hdl.handle.net/2445/13287