  We study the sets of inertias achieved by Laplacian matrices of weighted
signed graphs. First we characterize signed graphs with a unique Laplacian
inertia. Then we show that there is a sufficiently small perturbation of the
nonzero weights on the edges of any connected weighted signed graph so that all
eigenvalues of its Laplacian matrix are simple. Next, we give upper bounds on
the number of possible Laplacian inertias for signed graphs with a fixed
flexibility $\tau$ (a combinatorial parameter of signed graphs), and show that
these bounds are sharp for an infinite family of signed graphs. Finally, we
provide upper bounds for the number of possible Laplacian inertias of signed
graphs in terms of the number of vertices.
