Contextual Graph Matching with Correlated Gaussian Features

2026-03-24

AI Summary

This study addresses the problem of exact and almost-exact graph matching under a Gaussian graphical model where both node features and edge weights exhibit cross-network correlations. By integrating structural and contextual information through information-theoretic analysis, probabilistic graphical models, and Gaussian feature modeling, this work provides the first rigorous characterization of the interplay between these two sources of information in graph matching. It reveals a novel phase transition phenomenon wherein the thresholds for exact and almost-exact recovery are distinct, thereby breaking away from the traditional “all-or-nothing” recovery paradigm. The authors establish fundamental information-theoretic limits governed jointly by graph correlation, feature dimensionality, and network size, and precisely identify necessary and sufficient conditions for both recovery regimes, offering a theoretical benchmark for the design of efficient graph matching algorithms.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• contextual graph matching
• Gaussian features
• graph correlation
• exact recovery
• information-theoretic thresholds

Innovation

• contextual graph matching
• Gaussian features
• information-theoretic thresholds
• phase transition
• exact recovery