In this paper, we consider digraphs with possible loops and the particular case of oriented graphs, i.e. loopless digraphs with at most one oriented edge between every pair of vertices. We provide an upper bound for the largest singular value of the skew Laplacian matrix of an oriented graph, the largest singular value of the skew adjacency matrix of an oriented graph and the largest singular value of the adjacency matrix of a digraph. These bounds are expressed in terms of certain parameters related to vertex degrees. We also consider some bounds for the sums of squares of singular values. As an application, for the skew (Laplacian) adjacency matrix of an oriented graph and the adjacency matrix of a digraph, we derive some upper bounds for the spectral radius and the sums of squares of moduli of eigenvalues.

在本文中，我们考虑具有可能循环的有向图和有向图的特殊情况，即无环有向图在每对顶点之间最多有一个有向边。我们提供了有向图的倾斜拉普拉斯矩阵的最大奇异值，有向图的倾斜邻接矩阵的最大奇异值和有向图的邻接矩阵的最大奇异值。这些边界用与顶点度有关的某些参数表示。我们还考虑了奇异值平方和的一些界限。作为应用，对于有向图的偏斜（Laplacian）邻接矩阵和有向图的邻接矩阵，我们导出了谱半径和特征值模平方和的一些上限。