Complex adjacency spectra of digraphs

Abstract

In this article, we consider only those (simple) digraphs which satisfy the property that if (Formula presented.) is an edge of a digraph, then (Formula presented.) is not an edge of it. A new matrix representation of a digraph is considered and the matrix is named as the complex adjacency matrix. The eigenvalues and the eigenvectors of the complex adjacency matrices of cycle digraphs and directed trees are obtained and it is shown that not only the eigenvalues of these matrices but also the eigenvectors provide a lot of information about the structure of these digraphs. � 2019 Informa UK Limited, trading as Taylor & Francis Group.