非负张量与超图的主特征向量（英文）

Principal eigenvectors of nonnegative tensors and hypergraphs

非负弱不可约张量的谱半径是它的正特征值,该正特征值对应的单位正特征向量称为张量的主特征向量;张量的主特征向量的最大分量与最小分量的比值称为张量的主比率。给出非负弱不可约张量主比率和主特征向量分量的一些界;由于连通一致超图的无符号拉普拉斯张量是非负弱不可约张量,得到连通一致超图的符号拉普拉斯张量的主特征向量的分量和主比率的一些界。

The spectral radius of a nonnegative weakly irreducible tensor A is a positive eigenvalue,its corresponding unit positive eigenvector is called the principal eigenvector of A. The principal ratio of A is the ratio of the maximum entry and minimum entry of principal eigenvector. Some bounds on the principal ratio and the entries of principal eigenvector of a nonnegative weakly irreducible tensor are presented.Since the signless Laplacian tensor of a connected uniform hypergraph is weakly irreducible,some bounds on the principal ratio and the principal eigenvector of the signless Laplacian tensor of a connected uniform hypergraph can be obtained.