Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415981 | Linear Algebra and its Applications | 2016 | 17 Pages |
Abstract
Let A(H) be the adjacency tensor of r-uniform hypergraph H. If H is connected, the unique positive eigenvector x=(x1,x2,â¯,xn)T with âxâr=1 corresponding to spectral radius Ï(H) is called the principal eigenvector of H. The maximum and minimum entries of x are denoted by xmax and xmin, respectively. In this paper, we investigate the bounds of xmax and xmin in the principal eigenvector of H. Meanwhile, we also obtain some bounds of the ratio xi/xj for i, jâ[n] as well as the principal ratio γ(H)=xmax/xmin of H. As an application of these results we finally give an estimate of the gap of spectral radii between H and its proper sub-hypergraph Hâ².
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lele Liu, Liying Kang, Xiying Yuan,