A new kind of Hermitian matrices for digraphs

Abstract

In an earlier work, the author together with Guo [Hermitian adjacency matrix of digraphs and mixed graphs, J. Graph Theory 85 (2017) 217-248] introduced the Hermitian adjacency matrix of directed (and partially directed) graphs. However, it appears that a more natural Hermitian matrix exists, and it is the purpose of this note to bring this new Hermitian matrix to the attention of researchers in algebraic graph theory.

Linear Algebra Appl. (2019), in press. arXiv admin note: text overlap with arXiv:1505.01321