On the hyperbolicity of random graphs

Abstract

Let $G=(V,E)$ be a connected graph with the usual (graph) distance metric $d:V\times V\to N\cup \{0\}$. Introduced by Gromov, $G$ is $\delta$-hyperbolic if for every four vertices $u,v,x,y\in V$, 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 $2\delta$. In this paper, we determinate the value of this hyperbolicity for most binomial random graphs.

20 pages

References in corpus (1)

• Navigability of Complex Networks