SeedGNN: Graph Neural Networks for Supervised Seeded Graph Matching

Recently, there have been significant interests 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 seeds. However, most previous GNN architectures for seeded graph matching employ a semi-supervised approach, which learns from only the seed set in a single pair of graphs, and therefore does not attempt to learn from many training examples/graphs to best match future unseen graphs. In contrast, this paper is the first to propose a supervised approach for seeded graph matching, which had so far only been used for seedless graph matching. Our proposed SeedGNN architecture employs a number of novel design choices that are inspired by theoretical studies of seeded graph matching. First, SeedGNN can easily learn the capability of counting and using witnesses of different hops, in a way that can be generalized to graphs with different sizes. Second, SeedGNN can use easily-matched pairs as new seeds to percolate and match other nodes. We evaluate SeedGNN on both synthetic and real graphs, and demonstrate significant performance improvement over both non-learning and learning algorithms in the existing literature. Further, our experiments confirm that the knowledge learned by SeedGNN from training graphs can be generalized to test graphs with different sizes and categories.