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2021 On the largest component of subcritical random hyperbolic graphs
Roland Diel, Dieter Mitsche
Author Affiliations +
Electron. Commun. Probab. 26: 1-14 (2021). DOI: 10.1214/21-ECP380

Abstract

We consider the random hyperbolic graph model introduced by [KPK+10] and then formalized by [GPP12]. We show that, in the subcritical case α>1, the size of the largest component is asymptotically almost surely n1(2α)+o(1), thus strengthening a result of [BFM15] which gave only an upper bound of n1α+o(1).

Funding Statement

Roland Diel has been partially supported by grant GrHyDy ANR-20-CE40-0002. Dieter Mitsche has been partially supported by grant GrHyDy ANR-20-CE40-0002 and by IDEXLYON of Université de Lyon (Programme Investissements d’Avenir ANR16-IDEX-0005).

Acknowledgments

The authors would like to thank Antoine Barrier for providing Figure 1 and the anonymous referees for their many valuable comments which helped to significantly improve the clarity of the paper.

Citation

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Roland Diel. Dieter Mitsche. "On the largest component of subcritical random hyperbolic graphs." Electron. Commun. Probab. 26 1 - 14, 2021. https://doi.org/10.1214/21-ECP380

Information

Received: 2 March 2020; Accepted: 5 February 2021; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.1214/21-ECP380

Subjects:
Primary: 05C80, 05C82, 60D05

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