The spectral distribution of random mixed graphs

Let G be a mixed graph with n vertices, H(G) the Hermitian adjacency matrix of G, and λ1(G),λ2(G),…,λn(G) the eigenvalues of H(G). The Hermitian energy of G is defined as EH(G)=∑i=1n|λi(G)|. In this paper we characterize the limiting spectral distribution of the Hermitian adjacency matrices of random mixed graphs, and as an application, we give an estimation of the Hermitian energy for almost all mixed graphs.