  We consider the adjacency matrix of the ensemble of Erd\H{o}s-R\'enyi random
graphs which consists of graphs on $N$ vertices in which each edge occurs
independently with probability $p$. We prove that in the regime $pN \gg 1$
these matrices exhibit bulk universality in the sense that both the averaged
$n$-point correlation functions and distribution of a single eigenvalue gap
coincide with those of the GOE. Our methods extend to a class of random
matrices which includes sparse ensembles whose entries have different
variances.
