论文标题
拉普拉斯操作员的光谱理论在定向超图上
Spectral Theory of Laplace Operators on Oriented Hypergraphs
论文作者
论文摘要
显示了针对定向超图的归一化拉普拉斯的几种新光谱特性。讨论了特征值$ 1 $和重复顶点的情况；建立了两个Courant Nodal域定理；引入了绑定特征值的新数量。特别是，cheeger常数已概括，并表明可以将经典的脸颊边界推广到某些类别的超图；结果表明，用于研究地位的几何量从下面界定了最大的特征值，并且可以将着色概念概括并用于证明霍夫曼样结合。最后，讨论了笛卡尔式超图产品的非均衡性拉普拉斯元素的光谱。
Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue $1$ and the case of duplicate vertices are discussed; two Courant nodal domain theorems are established; new quantities that bound the eigenvalues are introduced. In particular, the Cheeger constant is generalized and it is shown that the classical Cheeger bounds can be generalized for some classes of hypergraphs; it is shown that a geometric quantity used to study zonotopes bounds the largest eigenvalue from below, and that the notion of coloring number can be generalized and used for proving a Hoffman-like bound. Finally, the spectrum of the unnormalized Laplacian for Cartesian products of hypergraphs is discussed.
