Large-deviation properties of the largest biconnected component for random graphs

Hendrik Schawe () and Alexander K. Hartmann
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Hendrik Schawe: Institut für Physik, Universität Oldenburg
Alexander K. Hartmann: Institut für Physik, Universität Oldenburg

The European Physical Journal B: Condensed Matter and Complex Systems, 2019, vol. 92, issue 4, 1-9

Abstract: Abstract 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. Graphical abstract

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1140/epjb/e2019-90667-y

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