  In this work we prove that the giant component of the Erd\"os--Renyi random
graph $G(n,c/n)$ for c a constant greater than 1 (sparse regime), is not Gromov
$\delta$-hyperbolic for any positive $\delta$ with probability tending to one
as $n\to\infty$. As a corollary we provide an alternative proof that the giant
component of $G(n,c/n)$ when c>1 has zero spectral gap almost surely as
$n\to\infty$.
