2020/09/08 by Wei Chen, Dan Wang, Ji Liu +5 · 1 citation
Engineering · Computer Science · #eess.SY #cs.SY
paper · pdf · doi:10.1109/tac.2020.3008300
online publication in IEEE Transactions on Automatic Control
arxiv created 2020/09/08 · arxiv updated 2020/09/09
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.