  We consider a class of sparse random matrices, which includes the adjacency
matrix of Erd\H{o}s-R\'enyi graphs $\mathcal G(N,p)$ for $p \in
[N^{\varepsilon-1},N^{-\varepsilon}]$. We identify the joint limiting
distributions of the eigenvalues away from 0 and the spectral edges. Our result
indicates that unlike Wigner matrices, the eigenvalues of sparse matrices
satisfy central limit theorems with normalization $N\sqrt{p}$. In addition, the
eigenvalues fluctuate simultaneously: the correlation of two eigenvalues of the
same/different sign is asymptotically 1/-1. We also prove CLTs for the
eigenvalue counting function and trace of the resolvent at mesoscopic scales.
