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

  title={Condensation of degrees emerging through a first-order phase transition in classical random graphs.},
  author={Fernando Lucas Metz and Isaac P'erez Castillo},
  journal={Physical review. E},
  volume={100 1-1},
Due to their conceptual and mathematical simplicity, Erdös-Rényi or classical random graphs remain as a fundamental paradigm to model complex interacting systems in several areas. Although condensation phenomena have been widely considered in complex network theory, the condensation of degrees has hitherto eluded a careful study. Here we show that the degree statistics of the classical random graph model undergoes a first-order phase transition between a Poisson-like distribution and a… 

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