Cheeger inequalities for unbounded graph Laplacians

TL;DR

This paper introduces a new isoperimetric constant for graphs using intrinsic metrics and proves a Cheeger-type inequality for the spectrum's lower bound, applicable even with unbounded vertex degrees.

Contribution

It presents a novel isoperimetric constant based on intrinsic metrics and establishes a Cheeger inequality for unbounded graph Laplacians.

Findings

New isoperimetric constant for graphs using intrinsic metrics

Cheeger inequality applicable to graphs with unbounded degrees

Spectral bounds derived for unbounded graph Laplacians

Abstract

We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate for the bottom of the spectrum which is nontrivial even if the vertex degrees are unbounded.