Degree Matrix Comparison for Graph Alignment

TL;DR

This paper introduces Degree Matrix Comparison (DMC), a simple yet effective degree-based method for unsupervised graph alignment, achieving high accuracy on various network types and offering scalable variants.

Contribution

The paper proposes DMC, a novel degree-based graph alignment method, along with reduced and weighted variants, demonstrating its effectiveness through extensive experiments and mathematical proofs.

Findings

Achieves up to 99% correct alignment on 90%-overlap networks

Attains 100% accuracy on isomorphic graphs

Weighted DMC shows promise for weighted graph alignment

Abstract

The graph alignment problem, which considers the optimal node correspondence across networks, has recently gained significant attention due to its wide applications. There are graph alignment methods suited for various network types, but we focus on the unsupervised geometric alignment algorithms. We propose Degree Matrix Comparison (DMC), a very simple degree-based method that has shown to be effective for heterogeneous networks. Through extensive experiments and mathematical proofs, we demonstrate the potential of this method. Remarkably, DMC achieves up to 99% correct node alignment for 90%-overlap networks and 100% accuracy for isomorphic graphs. Additionally, we propose a reduced Greedy DMC with lower time complexity and Weighted DMC that has demonstrated potential for aligning weighted graphs. Positive results from applying Greedy DMC and the Weighted DMC furthermore speaks to the validity and potential of the DMC. The sequence of DMC methods could significantly impact graph alignment, offering reliable solutions for the task.