Minors of Hermitian (quasi-) Laplacian matrix of a mixed graph
Deepak Sarma
TL;DR
This paper derives general formulas for all minors of the Hermitian (quasi-) Laplacian matrix in mixed graphs, extending previous determinant results to a broader set of matrix minors.
Contribution
It introduces new general expressions for all minors of the Hermitian (quasi-) Laplacian matrix of mixed graphs, expanding on prior determinant formulas.
Findings
Derived formulas for all minors of Hermitian (quasi-) Laplacian matrices.
Extended previous determinant results to minors.
Provides tools for spectral analysis of mixed graphs.
Abstract
A mixed graph is obtained from an unoriented graph by orienting a subset of its edges. Yu, Liu, and Qu in 2017 have established the expression for the determinant of Hermitian (quasi-) Laplacian matrix of a mixed graph. Here we find general expressions for all minors of Hermitian (quasi-) Laplacian matrix of mixed graphs.
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