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Graph Neural Networks (GNNs) are an effective framework for representationlearning of graphs. GNNs follow a neighborhood aggregation scheme, where therepresentation vector of a node is computed by recursively aggregating andtransforming representation vectors of its neighboring nodes. Many GNN variantshave been proposed and have achieved state-of-the-art results on both node andgraph classification tasks. However, despite GNNs revolutionizing graphrepresentation learning, there is limited understanding of theirrepresentational properties and limitations. Here, we present a theoreticalframework for analyzing the expressive power of GNNs to capture different graphstructures. Our results characterize the discriminative power of popular GNNvariants, such as Graph Convolutional Networks and GraphSAGE, and show thatthey cannot learn to distinguish certain simple graph structures. We thendevelop a simple architecture that is provably the most expressive among theclass of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphismtest. We empirically validate our theoretical findings on a number of graphclassification benchmarks, and demonstrate that our model achievesstate-of-the-art performance.

How Powerful are Graph Neural Networks?