Symmetries of Hypergraphs and Some Invariant Subspaces of Matrices Associated with Hypergraphs
| Autor: | Banerjee, Anirban, Parui, Samiron |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 invariant subspaces of these specific matrices as 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. Comment: The article is updated. Some new result added and title is changed now |
| Databáze: | arXiv |
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