Under a k-separability condition for k greater than 1, k-hop subgraph GNNs are universal approximators on connected graphs with no cycle longer than 2k+1; k-hop GNNs without subgraph structure get a similar 2k-1 bound.
An optimal lower bound on the number of variables for graph identification
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On the Expressive Power of Subgraph Graph Neural Networks for Graphs with Bounded Cycles
Under a k-separability condition for k greater than 1, k-hop subgraph GNNs are universal approximators on connected graphs with no cycle longer than 2k+1; k-hop GNNs without subgraph structure get a similar 2k-1 bound.