  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.
