  We consider the adjacency matrices of sparse random graphs from the Chung-Lu
model, where edges are added independently between the $N$ vertices with
varying probabilities $p_{ij}$. The rank of the matrix $(p_{ij})$ is some fixed
positive integer. We prove that the distribution of eigenvalues is given by the
solution of a functional self-consistent equation. We prove a local law down to
the optimal scale and prove bulk universality. The results are parallel to
\cite{Erdos2013b} and \cite{Landon2015}.
