Principal eigenvectors of general hypergraphs

TL;DR

This paper investigates the properties of the principal eigenvector of hypergraphs, providing bounds and inequalities related to its entries based on spectral and degree parameters.

Contribution

It introduces new bounds and inequalities for the principal eigenvector of hypergraphs, connecting spectral radius with degree-based parameters.

Findings

Bounds for the extreme entries of the principal eigenvector.

Inequalities involving ratios and differences of eigenvector entries.

Relations between spectral radius and degree parameters.

Abstract

In this paper we obtain bounds for the extreme entries of the principal eigenvector of hypergraphs; these bounds are computed using the spectral radius and some classical parameters such as maximum and minimum degrees. We also study inequalities involving the ratio and difference between the two extreme entries of this vector.