On the largest component of subcritical random hyperbolic graphs

Abstract

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