The European Physical Journal Special Topics

, Volume 226, Issue 4, pp 567–579 | Cite as

Large-deviation properties of the largest 2-core component for random graphs

  • Alexander K. HartmannEmail author
Regular Article
Part of the following topical collections:
  1. Recent Advances in Phase Transitions and Critical Phenomena


Distributions of the size of the largest component of the 2-core for Erdos-Rényi (ER) random graphs with finite connectivity c and a finite number N of nodes are studied. The distributions are obtained basically over the full range of the support, with probabilities down to values as small as 10−320. This is achieved by using an artificial finite-temperature (Boltzmann) ensemble. The distributions for the 2-core resemble roughly the results obtained previously for the largest components of the full ER random graphs, but they are shifted to much smaller probabilities (c ≤ 1) or to smaller sizes (c > 1). The numerical data is compatible with a convergence of the rate function to a limiting shape, i.e., the large-deviations principle apparently holds.


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© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Institut für Physik, Carl von Ossietzky Universität OldenburgOldenburgGermany

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