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A geometry-induced topological phase transition in random graphs

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 نشر من قبل Jasper Van Der Kolk
 تاريخ النشر 2021
  مجال البحث فيزياء
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Clustering $unicode{x2013}$ the tendency for neighbors of nodes to be connected $unicode{x2013}$ quantifies the coupling of a complex network to its underlying 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 atypical features such as diverging free energy and entropy as well as anomalous finite size scaling behavior. 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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