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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| Vydané v: | Graphs and combinatorics Ročník 30; číslo 5; s. 1233 - 1248 |
|---|---|
| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Tokyo
Springer Japan
01.09.2014
Springer Nature B.V |
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| ISSN: | 0911-0119, 1435-5914 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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.[PUBLICATION ABSTRACT] 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. 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. |
| Author | Zhang, Tan Pearson, Kelly J. |
| Author_xml | – sequence: 1 givenname: Kelly J. surname: Pearson fullname: Pearson, Kelly J. email: kpearson@murraystate.edu organization: Department of Mathematics and Statistics, Murray State University – sequence: 2 givenname: Tan surname: Zhang fullname: Zhang, Tan organization: Department of Mathematics and Statistics, Murray State University |
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| References_xml | – reference: HuS.A note on the positive eigenvector of nonnegative tensorsOptim. Lett.20137351953110.1007/s11590-011-0436-61268.901043022788 – reference: ChangK.C.PearsonK.ZhangT.On eigenvalue problems of real symmetric tensorsJ. Math. Anal. Appl.200935041642210.1016/j.jmaa.2008.09.0671157.150062476927 – reference: QiL.ZhangL.Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensorNumer. Linear Algebra Appl.201219583084110.1002/nla.8221274.651292979814 – reference: FriedlandS.GaubertS.HanL.Perron-Frobenius theorem for nonnegative multilinear forms and extensionsLinear Algebra Appl.2013438273874910.1016/j.laa.2011.02.0421261.150392996365 – reference: Lim, L.H.: Singular values and eigenvalues of tensors. A variational approach. 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| Snippet | 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... 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... |
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| SubjectTerms | Combinatorial analysis Combinatorics Eigenvectors Engineering Design Graph theory Graphs Mathematical analysis Mathematics Mathematics and Statistics Original Paper Spectra Tensors |
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| Title | On Spectral Hypergraph Theory of the Adjacency Tensor |
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