Large-deviation properties of the largest biconnected component for random graphs
Institut für Physik, Universität Oldenburg,
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Received in final form: 30 January 2019
Published online: 3 April 2019
We study the size of the largest biconnected components in sparse Erdős–Rényi graphs with finite connectivity and Barabási–Albert graphs with non-integer mean degree. Using a statistical-mechanics inspired Monte Carlo approach we obtain numerically the distributions for different sets of parameters over almost their whole support, especially down to the rare-event tails with probabilities far less than 10−100. This enables us to observe a qualitative difference in the behavior of the size of the largest biconnected component and the largest 2-core in the region of very small components, which is unreachable using simple sampling methods. Also, we observe a convergence to a rate function even for small sizes, which is a hint that the large deviation principle holds for these distributions.
Key words: Statistical and Nonlinear Physics
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2019