A Geometric Property of the Laplacian matrix of a Connected Nonsingular Mixed Graph

Abstract

In this paper, we give a geometric interpretation of the Laplacian matrix of a connected nonsingular mixed graph which generalizes the results of M. Fiedler (M. Fiedler, Geometry of the Laplacian, Linear Algebra Appl., 2005, 403: 409–413). In addition, the relations of geometric properties between a connected (singular or nonsingular) mixed graph, and all its resigned graphs will be characterized.