Symmetries of hypergraphs and some invariant subspaces of matrices associated with hypergraphs

• Published in: Linear algebra and its applications Vol. 726; pp. 328 - 358
• Main Authors: Banerjee, Anirban, Parui, Samiron
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2025
• Subjects: Eigenvalues and eigenvectors of hypergraph matrices; Hypergraphs; Hypergraphs and linear algebra; Invariant subspaces of hypergraph matrices; Symmetries in hypergraphs; secondary; Symmetries in hypergraphs; Eigenvalues and eigenvectors of hypergraph matrices; Invariant subspaces of hypergraph matrices; Hypergraphs; Hypergraphs and linear algebra; primary
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2025.07.030

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.