Cheeger-like inequalities for the largest eigenvalue of the graph Laplace Operator

TL;DR

This paper introduces a new Cheeger-like constant for graphs and establishes inequalities that relate this constant to the largest eigenvalue of the normalized Laplace operator, enhancing understanding of spectral graph properties.

Contribution

The paper proposes a novel Cheeger-like constant and derives bounds for the largest eigenvalue of the normalized Laplace operator using this constant.

Findings

New Cheeger-like constant for graphs introduced

Derived inequalities bounding the largest eigenvalue

Enhanced spectral graph analysis methods

Abstract

We define a new Cheeger-like constant for graphs and we use it for proving Cheeger-like inequalities that bound the largest eigenvalue of the normalized Laplace operator.