A lower bound on the entries of the principal eigenvector of a graph

TL;DR

This paper establishes a lower bound on the individual entries of the principal eigenvector for non-regular connected graphs, providing insights into eigenvector localization.

Contribution

It introduces a novel lower bound on the entries of the principal eigenvector specific to non-regular connected graphs.

Findings

Provides a new lower bound for eigenvector entries

Enhances understanding of eigenvector localization in graphs

Applicable to non-regular connected graphs

Abstract

We obtain a lower bound on each entry of the principal eigenvector of a non-regular connected graph.