  We propose a quantum walk defined by digraphs (mixed graphs). This is like
Grover walk that is perturbed by a certain complex-valued function defined by
digraphs. The discriminant of this quantum walk is a matrix that is a certain
normalization of generalized Hermitian adjacency matrices. Furthermore, we give
definitions of the positive and negative supports of the transfer matrix, and
clarify explicit formulas of their supports of the square. In addition, we give
tables by computer on the identification of digraphs by their eigenvalues.
