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A geometry-induced topological phase transition in random graphs

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Serrano Moral, Ma. Ángeles (María Ángeles)

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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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Communications Physics, 2022, vol. 5, num. 245

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cc-by (c) Kolk, Jasper van der et al., 2022

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Articles publicats en revistes (Física de la Matèria Condensada)

# metadata.dc.title[].value
A geometry-induced topological phase transition in random graphs