A mixed graph \(M_{G}\) is the graph obtained from an unoriented simple graph G by giving directions to some edges of G, where G is often called the underlying graph of \(M_{G}\) . In this paper, we discuss the determinants of two classes of incidence matrices of the second kind of rootless mixed trees and unicyclic mixed graphs. Applying these results, we characterize the explicit expressions of various minors for Hermitian (quasi-)Laplacian matrix of the second kind of \(M_{G}\) . Moreover, we give two sufficient conditions that the module of any cofactor of Hermitian (quasi-)Laplacian matrix of the second kind of the mixed graph \(M_{G}\) is equal to the number of spanning trees of the underlying graph G.
