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

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  • Hendrik Schawe

    (Institut für Physik, Universität Oldenburg)

  • Alexander K. Hartmann

    (Institut für Physik, Universität Oldenburg)

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

Suggested Citation

  • Hendrik Schawe & Alexander K. Hartmann, 2019. "Large-deviation properties of the largest biconnected component for random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(4), pages 1-9, April.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:4:d:10.1140_epjb_e2019-90667-y
    DOI: 10.1140/epjb/e2019-90667-y
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    Keywords

    Statistical and Nonlinear Physics;

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