Hermitian Adjacency Matrices of Mixed Graphs

TL;DR

This paper introduces the concept of monographs to unify existing Hermitian adjacency matrices of mixed graphs, providing new insights into their spectral properties and cospectrality issues.

Contribution

It presents a new unified framework for Hermitian adjacency matrices of mixed graphs and explores cospectrality, advancing the theoretical understanding of their spectral characteristics.

Findings

Unified previous work on Hermitian adjacency matrices

Introduced the concept of monographs for mixed graphs

Analyzed cospectrality properties

Abstract

The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of digraphs or mixed graphs. In this work we unify previous work and offer a new perspective on the subject by introducing the concept of monographs. Moreover, we consider questions of cospectrality.