On the hyperbolicity of random graphs

Abstract

Let G=(V,E) be a connected graph with the usual (graph) distance metric d:V×V→ℕ∪{0}. Introduced by Gromov, G is δ-hyperbolic if for every four vertices u,v,x,y∈V, the two largest values of the three sums d(u,v)+d(x,y), d(u,x)+d(v,y), d(u,y)+d(v,x) differ by at most 2δ. In this paper, we determine precisely the value of this hyperbolicity for most binomial random graphs.