On the spectrum of the net Laplacian matrix of a signed graph

Abstract

Given a signed graph G, let Ag, and D±g be its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of G is defined to be Ng = D±g - Ag. In this paper we give some spectral properties of Ng. We also point out some advantages and some disadvantages of using the net Laplacian matrix instead of the standard Laplacian matrix in study of signed graphs.