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On spectral hypergraph theory of the adjacency tensor. (English) Zbl 1298.05206

Summary: We study both \(H\) and \(E/Z\)-eigenvalues of the adjacency tensor of a uniform multi-hypergraph and give conditions for which the largest positive \(H\) or \(Z\)-eigenvalue corresponds to a strictly positive eigenvector. We also investigate when the \(E\)-spectrum of the adjacency tensor is symmetric.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C65 Hypergraphs
15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus

Software:

CoCoA
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Full Text: DOI arXiv

References:

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