On Spectral Properties of Signed Laplacians with Connections to Eventual Positivity

Wei Chen, Dan Wang, Ji Liu, Yongxin Chen, Sei Zhen Khong, Tamer Basar, Karl H. Johansson, Li Qiu

Research output: Contribution to journalArticlepeer-review


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 article, 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.

Original languageEnglish (US)
Article number9137633
Pages (from-to)2177-2190
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number5
StatePublished - May 2021


  • Kron reduction
  • eventual positivity
  • n-port network
  • signed Laplacians
  • spectral properties

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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