On the largest component of subcritical random hyperbolic graphs

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 n^{1/(2α)+o(1)} , thus strengthening a result of [BFM15] which gave only an upper bound of n^{1/α+o(1)}.

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Bibliographic Details
Published inElectronic communications in probability Vol. 26; no. none; pp. 1 - 14
Main Authors Diel, Roland, Mitsche, Dieter
Format Journal Article
LanguageEnglish
Published Institute of Mathematical Statistics (IMS) 01.01.2021
Subjects
Mathematics
Probability
Random hyperbolic graphs
Graph theory
Geometric probability
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Summary: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 n^{1/(2α)+o(1)} , thus strengthening a result of [BFM15] which gave only an upper bound of n^{1/α+o(1)}.
ISSN:1083-589X
1083-589X
DOI:10.1214/21-ECP380