On the giant component of hyperbolic random graphs

Abstract

The theory of geometric random graphs was initiated by Gilbert [2] already in 1961 in the context of what is called continuum percolation. In 1972, Hafner [4] focused on the typical properties of large but finite random geometric graphs. Here N points are sampled within a certain region of ℝd following a certain distribution and any two of them are joined when their Euclidean distance is smaller than some threshold which, in general, is a function of N. In the last two decades, this class of random graphs has been studied extensively — see the monograph of Penrose [6].