  Signed graphs have appeared in a broad variety of applications, ranging from
social networks to biological networks, from distributed control and
computation to power systems. In this paper, we investigate spectral properties
of signed Laplacians for undirected signed graphs. We find conditions on the
negative weights under which a signed Laplacian is positive semidefinite via
the Kron reduction and multiport network theory. For signed Laplacians that are
indefinite, we characterize their inertias with the same framework.
Furthermore, we build connections between signed Laplacians, generalized
M-matrices, and eventually exponentially positive matrices.
