Some properties of the spectral radius for general hypergraphs

In this paper, the adjacency tensor of a general hypergraph is investigated. We study the Perron–Frobenius theorem for the general hypergraphs and obtain some relevant results based on it. In particular, the techniques of weighted incidence matrix and moving edge are extended to general hypergraphs for determining the structure with the maximum spectral radius. A nearly m  -uniform supertree is both connected and acyclic, in which each edge contains either m−1m−1 or m vertices. To begin with, the structures obtaining the maximum spectral radius in two classes of nearly uniform supertrees are determined, where one class is with given number of edges and the other is with given number of vertices.