Exact alignment recovery for correlated Erd\H{o}s-R\'enyi graphs

TL;DR

This paper establishes the precise information-theoretic conditions under which one can perfectly recover the vertex correspondence between two correlated Erdős-Rényi graphs, regardless of computational constraints.

Contribution

It determines the exact threshold for perfect vertex alignment recovery in correlated ER graphs, advancing understanding of graph matching limits.

Findings

Identifies the information-theoretic threshold for exact recovery

Provides conditions under which perfect alignment is possible

Advances theoretical understanding of graph matching in ER models

Abstract

We consider the problem of perfectly recovering the vertex correspondence between two correlated Erd\H{o}s-R\'enyi (ER) graphs on the same vertex set. The correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. We determine the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources.