ABSTRACT Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.

中文翻译：

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使用具有附加对角线权重的邻接矩阵的主特征向量来组成中心性度量并识别有向图的领结结构

摘要 邻接矩阵的主特征向量通常被用作图或有向图的中心性度量。然而，以前对有向图的类主特征向量度量通常只考虑其邻接子矩阵具有最大特征值的强连通分量。在本文中，对于有向图中的每个强连通分量，我们为其在邻接矩阵中的成员节点的对角元素添加权重，使得修改后的矩阵将具有新的唯一最大特征值和相应的主特征向量。因此，我们使用基于不同强连通分量的修改矩阵的新主特征向量，不仅可以构成中心性度量，还可以识别有向图的领结结构。