超图的谱研究

Survey on Spectral Theory of Hypergraphs

本文简要介绍超图的矩阵谱与张量谱理论的近期主要成果,给出了超图的各种矩阵表示,以及各种矩阵谱与超图参数之间的关系。介绍了张量的概念,以及用k阶张量表示k-一致超图的三种方式,定义张量的H-特征值和Z-特征值,用两种特征值描述超图的性质。

In this paper, we present some main recent results on spectral theory of matrix and tensor of hypergraphs.First, we represent hypergraphs by various matrices, and give the relation between some spectrum of matrices and the parameters of hy-pergraphs.Second, we introduce the concept of tensor and three representations of k-uniform hypergraph by a k-order tensor, define H-eigenvalues and Z-eigenvalues of the tensor, and characterize some properties of hypergraph using above two eigenval-ues.In addition, we list some classical references.