论文标题
复杂单元超图的光谱
Spectra of Complex Unit Hypergraphs
论文作者
论文摘要
复杂的单元超图是一个超图，其中每个顶点边缘的发病率都具有复杂的单元标记。我们定义了复杂单位超图的邻接，发病率，Kirchoff Laplacian和归一化的Laplacian，并研究其中的每一个。还发现了邻接，基尔乔夫·拉普拉斯（Kirchoff Laplacian）和标准化拉普拉斯（Laplacian）的特征值边界。复杂的单元超图自然会概括几种超图结构，例如方向的超图，其中顶点 - 边缘的发病率标记为$+1 $或$ -1 $，以及普通的超图。复杂的单元超图还概括了其图形类似物，即复杂的单位增益图，签名图和普通图。
A complex unit hypergraph is a hypergraph where each vertex-edge incidence is given a complex unit label. We define the adjacency, incidence, Kirchoff Laplacian and normalized Laplacian of a complex unit hypergraph and study each of them. Eigenvalue bounds for the adjacency, Kirchoff Laplacian and normalized Laplacian are also found. Complex unit hypergraphs naturally generalize several hypergraphic structures such as oriented hypergraphs, where vertex-edge incidences are labelled as either $+1$ or $-1$, as well as ordinary hypergraphs. Complex unit hypergraphs also generalize their graphic analogues, which are complex unit gain graphs, signed graphs, and ordinary graphs.
