Determine the expressive power of NGNN relative to 3-WL

Determine whether Nested Graph Neural Networks (NGNNs), defined as applying a message passing graph neural network to each height-h rooted subgraph with subgraph pooling and an outer graph pooling layer, are more powerful than the 3-dimensional Weisfeiler–Lehman (3-WL) test in terms of discriminating non-isomorphic graphs, and establish the precise comparative relationship between NGNNs and 3-WL.

Background

The paper introduces Nested Graph Neural Networks (NGNNs), a two-level architecture that applies a base GNN to rooted subgraphs and then aggregates subgraph representations to form graph-level embeddings. The authors prove NGNNs are strictly more powerful than 1-WL and standard message-passing GNNs by showing NGNNs can distinguish almost all r-regular graphs, where 1-WL fails.

Beyond 1-WL/2-WL, the authors note that the relationship between NGNNs and the 3-dimensional Weisfeiler–Lehman (3-WL) test is unresolved. Preliminary analysis indicates both NGNNs and 3-WL fail on strongly regular graphs with identical parameters, but the exact comparative expressive power between NGNNs and 3-WL remains to be determined.