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arXiv · 1811.04816

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

Hendrik Schawe·Alexander K. Hartmann
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Abstract

We study the size of the largest biconnected components in sparse Erd\H{o}s-R\'enyi graphs with finite connectivity and Barab\'asi-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.

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Hendrik Schawe, Alexander K. Hartmann. 2018-11-12. Large-deviation properties of the largest biconnected component for random graphs. https://doi.org/10.1140/epjb%2Fe2019-90667-y

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