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Subgraph GNNs are a recent class of expressive Graph Neural Networks (GNNs)which model graphs as collections of subgraphs. So far, the design space ofpossible Subgraph GNN architectures as well as their basic theoreticalproperties are still largely unexplored. In this paper, we study the mostprominent form of subgraph methods, which employs node-based subgraph selectionpolicies such as ego-networks or node marking and deletion. We address twocentral questions: (1) What is the upper-bound of the expressive power of thesemethods? and (2) What is the family of equivariant message passing layers onthese sets of subgraphs?. Our first step in answering these questions is anovel symmetry analysis which shows that modelling the symmetries of node-basedsubgraph collections requires a significantly smaller symmetry group than theone adopted in previous works. This analysis is then used to establish a linkbetween Subgraph GNNs and Invariant Graph Networks (IGNs). We answer thequestions above by first bounding the expressive power of subgraph methods by3-WL, and then proposing a general family of message-passing layers forsubgraph methods that generalises all previous node-based Subgraph GNNs.Finally, we design a novel Subgraph GNN dubbed SUN, which theoretically unifiesprevious architectures while providing better empirical performance on multiplebenchmarks.

Understanding and Extending Subgraph GNNs by Rethinking Their Symmetries