学术翻译：这意味着加权邻接矩阵ABC和D有以下性质如存在特征值1使得SDFG成立其中S和D分别是F和G的左特征向量。

This implies that the weighted adjacency matrices A, B, C, and D have the following properties: there exists an eigenvalue of 1 such that S, D, F, and G hold, where S and D are the left eigenvectors of F and G respectively.