On the second largest component of random hyperbolic graphs
Abstract
We show that in the random hyperbolic graph model as formalized by Gugelmann et al. in the most interesting range of $\frac12 < \alpha < 1$ the size of the second largest component is $\Theta((\log n)^{1/(1\alpha)})$, thus answering a question of Bode et al. We also show that for $\alpha=\frac12$ with constant probability the corresponding size is $\Theta(\log n)$, whereas for $\alpha=1$ it is $\Omega(n^{b})$ for some $b > 0$.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 DOI:
 10.48550/arXiv.1712.02828
 arXiv:
 arXiv:1712.02828
 Bibcode:
 2017arXiv171202828K
 Keywords:

 Mathematics  Probability;
 Mathematics  Combinatorics
 EPrint:
 22 pages