Characterizations of the spectral radius of nonnegative weakly irreducible tensors via digraph

摘要

For a nonnegative weakly irreducible tensor $\mathcal{A}$, we give somecharacterizations of the spectral radius of $\mathcal{A}$, by using the digraphof tensors. As applications, some bounds on the spectral radius of theadjacency tensor and the signless Laplacian tensor of the $k$-uniformhypergraphs are shown.