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Spectral theory of weighted hypergraphs via tensors

Spectral theory of weighted hypergraphs via tensors
Spectral theory of weighted hypergraphs via tensors

One way to study a hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper, we study how properties of weighted hypergraphs are reflected on eigenvalues and eigenvectors of their associated tensors. We also show how to efficiently compute eigenvalues with some techniques from numerical algebraic geometry.

05C50, 05C65, Spectral hypergraph theory, eigenvalues, tensors, weighted hypergraphs
Galuppi, Francesco
3d871687-6322-46d5-9bad-5ab935117c19
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Venturello, Lorenzo
5bccff00-e8ac-4409-86ef-cb8fef3acb4a
Galuppi, Francesco
3d871687-6322-46d5-9bad-5ab935117c19
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Venturello, Lorenzo
5bccff00-e8ac-4409-86ef-cb8fef3acb4a

Galuppi, Francesco, Mulas, Raffaella and Venturello, Lorenzo (2022) Spectral theory of weighted hypergraphs via tensors. Linear and Multilinear Algebra. (doi:10.1080/03081087.2022.2030659).

Record type: Article

Abstract

One way to study a hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper, we study how properties of weighted hypergraphs are reflected on eigenvalues and eigenvectors of their associated tensors. We also show how to efficiently compute eigenvalues with some techniques from numerical algebraic geometry.

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More information

Submitted date: 1 June 2021
Accepted/In Press date: 27 December 2021
e-pub ahead of print date: 1 February 2022
Additional Information: Publisher Copyright: © 2022 Informa UK Limited, trading as Taylor & Francis Group.
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Keywords: 05C50, 05C65, Spectral hypergraph theory, eigenvalues, tensors, weighted hypergraphs

Identifiers

Local EPrints ID: 450165
URI: http://eprints.soton.ac.uk/id/eprint/450165
DOI: doi:10.1080/03081087.2022.2030659
PURE UUID: 4f5cb6fd-5b27-4aed-9984-8c750c26b5ab

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Date deposited: 14 Jul 2021 16:43
Last modified: 16 Mar 2024 12:43

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Contributors

Author: Francesco Galuppi
Author: Raffaella Mulas
Author: Lorenzo Venturello

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