On Spectral Hypergraph Theory of the Adjacency Tensor

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.

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 30; no. 5; pp. 1233 - 1248
Main Authors: Pearson, Kelly J., Zhang, Tan
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.09.2014
Springer Nature B.V
Subjects:
Combinatorial analysis
Combinatorics
Eigenvectors
Engineering Design
Graph theory
Graphs
Mathematical analysis
Mathematics
Mathematics and Statistics
Original Paper
Spectra
Tensors
Hypergraph
05C65
Spectral theory of hypergraph
05C50
Adjacency tensor
15A69
15A18
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Description
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.
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-013-1340-x