On the principal eigenvectors of general hypergraphs.

Let G be a connected general hypergraph of order n with rank r. The unique positive eigenvector x with -n i=1 x r i = 1 corresponding to the spectral radius ρ(G) is called the principal eigenvector of G. In this paper, the relation between each entry of the principal eigenvector of G and the vertex degree associated with this entry is presented. And some bounds for the extreme entries of the principal eigenvector are obtained. As applications, we give some bounds of the spectral radius of G. [ABSTRACT FROM AUTHOR]