论文标题
使用入射矩阵的空空间及其转置的无效空间研究
A Study of Hypergraph Using Null Spaces of the Incidence Matrix and its Transpose
论文作者
论文摘要
在这项研究中，我们探索了超图的子结构，该超图导致我们在超图的入射矩阵中线性依赖的行（或列）。 这些子结构与各种超图矩阵的光谱密切相关，包括无价的拉普拉斯，邻接，laplacian和HyperGraph的发射率图的邻接矩阵。这些超图矩阵的特定特征向量可以表征这些子结构。我们表明，属于HyperGraph的入射率图的邻接矩阵零空间的向量提供了对这些子结构的独特描述。此外，我们说明这些子结构表现出固有的相似性和冗余，在随机步行过程中表现出类似的行为和超图中心的相似值。
In this study, we explore the substructures of a hypergraph that lead us to linearly dependent rows (or columns) in the incidence matrix of the hypergraph. These substructures are closely related to the spectra of various hypergraph matrices, including the signless Laplacian, adjacency, Laplacian, and adjacency matrices of the hypergraph's incidence graph. Specific eigenvectors of these hypergraph matrices serve to characterize these substructures. We show that vectors belonging to the nullspace of the adjacency matrix of the hypergraph's incidence graph provide a distinctive description of these substructures. Additionally, we illustrate that these substructures exhibit inherent similarities and redundancies, which manifest in analogous behaviours during random walks and similar values of hypergraph centralities.
