Principal eigenvectors and spectral radii of uniform hypergraphs

In this paper, some inequalities among the principal eigenvector, spectral radius and vertex degrees of a connected uniform hypergraph are established. Necessary and sufficient conditions of equalities holding are presented, which are related to the regularity of a hypergraph. Furthermore, we present some bounds on the spectral radius for a connected irregular uniform hypergraph in terms of some parameters, such as principal ratio, maximum degree, diameter, and the number of vertices and edges.