  Recently, Laplacian matrices of graphs are studied as density matrices in
quantum mechanics. We continue this study and give conditions for separability
of generalized Laplacian matrices of weighted graphs with unit trace. In
particular, we show that the Peres-Horodecki positive partial transpose
separability condition is necessary and sufficient for separability in
${\mathbb C}^2\otimes {\mathbb C}^q$. In addition, we present a sufficient
condition for separability of generalized Laplacian matrices and diagonally
dominant nonnegative matrices.
