An upper bound for the largest singular value of extended mixed graphs

An extended mixed graph contains edges declared to be either positive, or negative, or oriented from one end to the other. They unify concepts of mixed graphs, signed graphs, oriented graphs and ordinary graphs. We demonstrate a method that establishes an upper bound for the largest singular value of the corresponding adjacency matrix in a bit general setting allowing the existence of loops at vertices. An upper bound for the largest singular value of the Laplacian matrix is extracted. The obtained bounds remain valid for the largest modulus of the corresponding eigenvalues, and cover the aforementioned particular structures.