Extending Graph Neural Networks with Global Features

Abstract

A common approach to boost the predictive performance of message passing graph neural networks (MPNNs) is to attach additional features to nodes. In contrast, we propose to use expressive global graph features. This is motivated by the limited expressivity of MPNNs resulting in an inability to compute certain global graph properties, like the Wiener index and Hosoya index. Such global graph features are well known in fields like chemoinformatics but seem to be overlooked by the GNN community. We propose an architecture which extends graph embeddings learned by MPNNs with global graph features, for example, topological indices describing the entire graph. Analyzing different global graph features, we show that certain global features like the Wiener index increase the expressivity of MPNNs, while others like the Zagreb indices do not. Our first experiments indicate that adding global graph features improves the performance of MPNNs on molecular benchmark datasets.