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2022-10-06

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cc-by (c) Kolk, Jasper van der et al., 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/198264

A geometry-induced topological phase transition in random graphs

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https://doi.org/10.1038/s42005-022-01023-w

Abstract

Clustering - the tendency for neighbors of nodes to be connected - quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase transition, separating a phase with finite clustering from a regime where clustering vanishes in the thermodynamic limit. We prove this geometric-to-nongeometric phase transition to be topological in nature, with anomalous features such as diverging entropy as well as atypical finite size scaling behavior of clustering. Moreover, a slow decay of clustering in the nongeometric phase implies that some real networks with relatively high levels of clustering may be better described in this regime.

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Física estadística, Percolació (Física estadística)

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Statistical physics, Percolation (Statistical physics)

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Articles publicats en revistes (Física de la Matèria Condensada)

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KOLK, Jasper Eibertus van der, SERRANO MORAL, Ma. Ángeles (María Ángeles) and BOGUÑÁ, Marián. A geometry-induced topological phase transition in random graphs. Communications Physics. 2022. Vol. 5, num. 245. ISSN 2399-3650. [consulted: 12 of August of 2026]. Available at: https://hdl.handle.net/2445/198264

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