SeedGNN: Graph Neural Networks for Supervised Seeded Graph Matching

TL;DR

SeedGNN introduces a supervised graph neural network approach for seeded graph matching that learns transferable knowledge from training data, enabling effective matching of unseen graphs with minimal seed nodes.

Contribution

The paper presents a novel supervised GNN architecture for seeded graph matching that generalizes across different graph sizes and categories, unlike previous semi-supervised methods.

Findings

Significant performance improvements over existing algorithms.

Effective generalization to unseen graphs of different sizes.

Learned knowledge transfers well across various graph categories.

Abstract

There is a growing interest in designing Graph Neural Networks (GNNs) for seeded graph matching, which aims to match two unlabeled graphs using only topological information and a small set of seed nodes. However, most previous GNNs for this task use a semi-supervised approach, which requires a large number of seeds and cannot learn knowledge that is transferable to unseen graphs. In contrast, this paper proposes a new supervised approach that can learn from a training set how to match unseen graphs with only a few seeds. Our SeedGNN architecture incorporates several novel designs, inspired by theoretical studies of seeded graph matching: 1) it can learn to compute and use witness-like information from different hops, in a way that can be generalized to graphs of different sizes; 2) it can use easily-matched node-pairs as new seeds to improve the matching in subsequent layers. We evaluate SeedGNN on synthetic and real-world graphs and demonstrate significant performance improvements over both non-learning and learning algorithms in the existing literature. Furthermore, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs of different sizes and categories.