Upper Bounds for the Largest Component in Critical Inhomogeneous Random Graphs

Umberto De Ambroggio, Angelica Pachon

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    Abstract

    We consider the Norros-Reittu random graph NRn(w), where edges are present independently but edge probabilities are moderated by vertex weights, and use probabilistic arguments based on martingales to analyse the order of the maximal component in this model when considered at criticality. In particular, we obtain stronger upper bounds (with respect to those available in the literature) for the probability of observing an unusually large maximal cluster, and simplify the arguments needed to derive polynomial upper bounds for the probability of observing an unusually small largest component.
    Original languageEnglish
    Article number20-49
    Pages (from-to)1315-1358
    JournalAlea
    VolumeXX
    Issue number2
    DOIs
    Publication statusPublished - Nov 2023

    Keywords

    • 60C05
    • 05C05
    • 05C80

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