| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4598438 | Linear Algebra and its Applications | 2016 | 9 Pages |
Abstract
We introduce the concept of general complex weighted directed graphs where each edge is assigned a complex number. Necessary and sufficient conditions for the Laplacian matrix to be singular/nonsingular are derived. Our results give the relationship between the Laplacian matrix and the structure of its corresponding directed graph. Compared with the existing results, our main contribution is that our results are established without the restriction that the adjacency matrix is Hermitian.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jiu-Gang Dong, Lin Lin,