How Powerful are Graph Neural Networks?

TLDR

Graph Neural Networks (GNNs) are a powerful framework for graph representation learning, achieving state‑of‑the‑art results on node and graph classification, yet their expressive limits remain poorly understood. The authors aim to develop a theoretical framework and a maximally expressive GNN architecture to analyze and surpass existing GNNs in distinguishing graph structures. They analyze GNNs using a neighborhood‑aggregation framework, construct a theoretical model, and design a new architecture that matches the Weisfeiler–Lehman graph isomorphism test. The study shows that popular GNN variants lack the ability to distinguish some simple graph structures, while the proposed architecture achieves theoretical optimality and outperforms existing methods on benchmark graph classification tasks.

Abstract

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.