Attributed Network Alignment: Statistical Limits and Efficient Algorithm

TL;DR

This paper investigates the limits and algorithms for recovering hidden vertex correspondences in correlated graphs with node features, introducing a new model and a quadratic programming-based algorithm with theoretical guarantees.

Contribution

It introduces the featured correlated Gaussian Wigner model and proposes QPAlign, a quadratic programming algorithm with proven theoretical guarantees for graph alignment.

Findings

Characterized information-theoretic thresholds for recovery.

Proposed QPAlign algorithm shows strong empirical performance.

Provided theoretical guarantees for the algorithm's convergence.

Abstract

This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge information, many real-world applications provide informative node features in addition to graph topology. To capture this setting, we introduce the featured correlated Gaussian Wigner model, where two graphs are coupled through an unknown vertex permutation, and the node features are correlated under the same permutation. We characterize the optimal information-theoretic thresholds for exact recovery and partial recovery of the latent mapping. On the algorithmic side, we propose QPAlign, an algorithm based on a quadratic programming relaxation, and demonstrate its strong empirical performance on both synthetic and real datasets. Moreover, we also derive theoretical guarantees for the proposed procedure, supporting its reliability and providing convergence guarantees.