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In this paper, we study using graph neural networks (GNNs) for\textit{multi-node representation learning}, where a representation for a setof more than one node (such as a link) is to be learned. Existing GNNs aremainly designed to learn single-node representations. When used for multi-noderepresentation learning, a common practice is to directly aggregate thesingle-node representations obtained by a GNN. In this paper, we show afundamental limitation of such an approach, namely the inability to capture thedependence among multiple nodes in the node set. A straightforward solution isto distinguish target nodes from others. Formalizing this idea, we propose\text{labeling trick}, which first labels nodes in the graph according to theirrelationships with the target node set before applying a GNN and thenaggregates node representations obtained in the labeled graph for multi-noderepresentations. Besides node sets in graphs, we also extend labeling tricks toposets, subsets and hypergraphs. Experiments verify that the labeling tricktechnique can boost GNNs on various tasks, including undirected linkprediction, directed link prediction, hyperedge prediction, and subgraphprediction. Our work explains the superior performance of previousnode-labeling-based methods and establishes a theoretical foundation for usingGNNs for multi-node representation learning.

Improving Graph Neural Networks on Multi-node Tasks with the Labeling Trick