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

TL;DR

This paper characterizes the spectral radius of nonnegative weakly irreducible tensors using digraphs and provides bounds for related tensors in hypergraphs.

Contribution

It introduces new characterizations of the spectral radius of such tensors through digraph analysis, extending understanding in tensor spectral theory.

Findings

Characterizations of spectral radius via tensor digraphs

Bounds on spectral radius of adjacency tensors in hypergraphs

Bounds on spectral radius of signless Laplacian tensors in hypergraphs

Abstract

For a nonnegative weakly irreducible tensor $\mathcal{A}$, we give some characterizations of the spectral radius of $\mathcal{A}$, by using the digraph of tensors. As applications, some bounds on the spectral radius of the adjacency tensor and the signless Laplacian tensor of the $k$-uniform hypergraphs are shown.