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The non-negative spectrum of a digraph. (English) Zbl 1441.05132

Summary: Given the adjacency matrix \(A\) of a digraph, the eigenvalues of the matrix \(AA^T\) constitute the so-called non-negative spectrum of this digraph. We investigate the relation between the structure of digraphs and their non-negative spectra and associated eigenvectors. In particular, it turns out that the non-negative spectrum of a digraph can be derived from the traditional (adjacency) spectrum of certain undirected bipartite graphs.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments
15A18 Eigenvalues, singular values, and eigenvectors
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