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arXiv · 2405.01364

Spectral decomposition of hypergraph automorphism compatible matrices

Anirban Banerjee·Samiron Parui
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Abstract

This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented by \( f \), within the hypergraph. First, we explore rotation, a specific kind of automorphism and find that the spectrum of any matrix compatible with a rotation can be decomposed into the spectra of smaller matrices associated with that rotation. We show that the spectrum of any \(f\)-compatible matrix can be decomposed into the spectra of smaller matrices associated with the component rotations comprising \( f \). Further, we study a hypergraph symmetry termed unit-automorphism, which induces bijections on the hyperedges, though not necessarily on the vertex set. We show that unit automorphisms also lead to the spectral decomposition of compatible matrices.

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Anirban Banerjee, Samiron Parui. 2024-05-02. Spectral decomposition of hypergraph automorphism compatible matrices. https://arxiv.org/abs/2405.01364

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