# On Spectral Properties of Signed Laplacians with Connections to Eventual Positivity

arXiv: https://arxiv.org/abs/2009.03581 · HTML: https://mlsanity.com/paper/2009.03581/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [A Method for Handling Negative Similarities in Explainable Graph Spectral Clustering of Text Documents -- Extended Version](https://mlsanity.com/paper/2504.12360/) (2025)

## Abstract (arXiv)

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.