The spectra of random mixed graphs

A mixed graph is a that can be obtained from simple undirected by replacing some of the edges arcs in precisely one two possible directions. The Hermitian adjacency matrix G order n n×n H(G)=(hij), where hij=−hji=i (with i=−1) if there exists an arc vi to vj (but no vi), hij=hji=1 edge (and arcs) between and vj, hij=hji=0 otherwise (if are neither joined nor arc). Let λ1(G),λ2(G),…,λn(G) eigenvalues H(G). k-th spectral moment defined as sk(H(G))=∑i=1nλik(G), k≥0 integer. In this paper, we deal with asymptotic behavior spectrum random graphs. We will present prove separation result largest remaining matrix, application, estimate moments