Contextual Graph Matching with Correlated Gaussian Features

TL;DR

This paper provides a rigorous analysis of how structural and contextual information interact in Gaussian graph matching, deriving thresholds for exact recovery and revealing richer phase transition phenomena.

Contribution

It introduces the first precise information-theoretic thresholds for contextual graph matching with correlated Gaussian features, highlighting the impact of additional contextual information.

Findings

Thresholds for exact and almost exact recovery are derived.

Additional contextual information creates a richer phase transition structure.

The results establish a benchmark for future algorithm design.

Abstract

We investigate contextual graph matching in the Gaussian setting, where both edge weights and node features are correlated across two networks. We derive precise information-theoretic thresholds for exact recovery, and identify conditions under which almost exact recovery is possible or impossible, in terms of graph and feature correlation strengths, the number of nodes, and feature dimension. Interestingly, whereas an all-or-nothing phase transition is observed in the standard graph-matching scenario, the additional contextual information introduces a richer structure: thresholds for exact and almost exact recovery no longer coincide. Our results provide the first rigorous characterization of how structural and contextual information interact in graph matching, and establish a benchmark for designing efficient algorithms.