Interlacing results for hypergraphs
Interlacing results for hypergraphs
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can be inferred from the spectrum, i.e. the multiset of the eigenvalues, of an operator associated to a hypergraph. It is expected that a small perturbation of a hypergraph, such as the removal of a few vertices or edges, does not lead to a major change of the eigenvalues. In particular, it is expected that the eigenvalues of the original hypergraph interlace the eigenvalues of the perturbed hypergraph. Here we work on hypergraphs where, in addition, each vertex–edge incidence is given a real number, and we prove interlacing results for the adjacency matrix, the Kirchoff Laplacian and the normalized Laplacian. Tightness of the inequalities is also shown.
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Mulas, Raffaella
1ceeaad9-da27-4bb3-bd5b-4f0c7ec422e5
Mulas, Raffaella
(2021)
Interlacing results for hypergraphs.
In Proceedings of Blockchain in Kyoto 2021.
vol. 36,
10 pp
.
(In Press)
(doi:10.7566/JPSCP.36.011007).
Record type:
Conference or Workshop Item
(Paper)
Abstract
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can be inferred from the spectrum, i.e. the multiset of the eigenvalues, of an operator associated to a hypergraph. It is expected that a small perturbation of a hypergraph, such as the removal of a few vertices or edges, does not lead to a major change of the eigenvalues. In particular, it is expected that the eigenvalues of the original hypergraph interlace the eigenvalues of the perturbed hypergraph. Here we work on hypergraphs where, in addition, each vertex–edge incidence is given a real number, and we prove interlacing results for the adjacency matrix, the Kirchoff Laplacian and the normalized Laplacian. Tightness of the inequalities is also shown.
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jpscp.36.011007
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Submitted date: 31 March 2021
Accepted/In Press date: 8 June 2021
Venue - Dates:
Blockchain in Kyoto, Graduate School of Advanced Integrated Studies in Human Survivability, Kyoto, Japan, 2021-02-17 - 2021-02-18
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Local EPrints ID: 452304
URI: http://eprints.soton.ac.uk/id/eprint/452304
PURE UUID: 00dae5c2-9db6-4a77-b5b4-6664002503d9
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Date deposited: 06 Dec 2021 17:35
Last modified: 16 Mar 2024 15:02
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Author:
Raffaella Mulas
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