Title: Sharp Statistical Limits and Algorithm for Attributed Graph Alignment
Primary area: learning on graphs and other geometries & topologies
Keywords: Graph alignment; Gaussian Wigner model; information-theoretic threshold; algorithm; quadratic programming

Abstract: This paper investigates the problem of recovering hidden vertex mappings between two correlated weighted graphs with both edge structure and node features. While most existing studies on graph alignment focus solely on edge information, many practical scenarios also provide node features in addition to graph topology. To address this setting, we introduce the featured correlated Gaussian Wigner model, in which the graphs are correlated through a latent vertex permutation, and the associated features are also correlated under the same permutation. We establish the optimal information-theoretic thresholds for recovering the latent vertex mappings. Furthermore, we propose QPAlign, a fast algorithm leveraging quadratic programming relaxation to the Birkhoff polytope, and validate its effectiveness on both synthetic and real datasets.

TL;DR: We introduce the featured correlated Gaussian Wigner model and establish sharp information-theoretic thresholds together with a fast algorithm for graph alignment.