Symmetries of Hypergraphs and Some Invariant Subspaces of Matrices Associated with Hypergraphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908482595192832 |
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| author | Banerjee, Anirban Parui, Samiron |
| author_facet | Banerjee, Anirban Parui, Samiron |
| contents | Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph.
A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a given symmetry within a hypergraph, we investigate a collection of matrices that encapsulate information about the symmetry. Our investigation reveals that certain structural symmetries in a hypergraph manifest observable effects on the eigenvalues and eigenvectors of designated matrices associated with the hypergraph.
We identify specific matrices where the invariance is a consequence of symmetries present in the hypergraph. These invariant subspaces elucidate analogous behaviours observed in certain clusters of vertices during random walks and other dynamical processes on the hypergraph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_08314 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Symmetries of Hypergraphs and Some Invariant Subspaces of Matrices Associated with Hypergraphs Banerjee, Anirban Parui, Samiron Combinatorics Dynamical Systems 05C65, 34D06, 05C50, 05C69, 05C07, 05C82 Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a given symmetry within a hypergraph, we investigate a collection of matrices that encapsulate information about the symmetry. Our investigation reveals that certain structural symmetries in a hypergraph manifest observable effects on the eigenvalues and eigenvectors of designated matrices associated with the hypergraph. We identify specific matrices where the invariance is a consequence of symmetries present in the hypergraph. These invariant subspaces elucidate analogous behaviours observed in certain clusters of vertices during random walks and other dynamical processes on the hypergraph. |
| title | Symmetries of Hypergraphs and Some Invariant Subspaces of Matrices Associated with Hypergraphs |
| topic | Combinatorics Dynamical Systems 05C65, 34D06, 05C50, 05C69, 05C07, 05C82 |
| url | https://arxiv.org/abs/2212.08314 |