论文标题
与超图相关的矩阵的超图和一些不变子空间的对称性
Symmetries of Hypergraphs and Some Invariant Subspaces of Matrices Associated with Hypergraphs
论文作者
论文摘要
在这里，超图的结构对称性通过超图的顶点集的等效关系表示。 与超图相关的基质可能无法反映特定的结构对称性。在超图内给定的对称性的上下文中，我们研究了矩阵的集合，这些矩阵封装了有关对称性的信息。我们的研究表明，在超图表中，某些结构对称性对与超图相关的指定矩阵的特征值和特征向量显然可观察到。 我们确定特定的矩阵，其中不变性是超图中存在的对称性的结果。这些不变子空间阐明了在随机步行和超图上的其他动力学过程中在某些顶点中观察到的类似行为。
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.
