English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Due to their conceptual and mathematical simplicity, Erd\"os-R\'enyi orclassical random graphs remain as a fundamental paradigm to model complexinteracting systems in several areas. Although condensation phenomena have beenwidely considered in complex network theory, the condensation of degrees hashitherto eluded a careful study. Here we show that the degree statistics of theclassical random graph model undergoes a first-order phase transition between aPoisson-like distribution and a condensed phase, the latter characterized by alarge fraction of nodes having degrees in a limited sector of theirconfiguration space. The mechanism underlying the first-order transition isdiscussed in light of standard concepts in statistical physics. We uncover thephase diagram characterizing the ensemble space of the model and we evaluatethe rate function governing the probability to observe a condensed state, whichshows that condensation of degrees is a rare statistical event akin to similarcondensation phenomena recently observed in several other systems. Monte Carlosimulations confirm the exactness of our theoretical results.

Condensation of degrees emerging through a first-order phase transition in classical random graphs