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The message-passing scheme is the core of graph representation learning.While most existing message-passing graph neural networks (MPNNs) arepermutation-invariant in graph-level representation learning andpermutation-equivariant in node- and edge-level representation learning, theirexpressive power is commonly limited by the 1-Weisfeiler-Lehman (1-WL) graphisomorphism test. Recently proposed expressive graph neural networks (GNNs)with specially designed complex message-passing mechanisms are not practical.To bridge the gap, we propose a plug-in Equivariant Distance ENcoding (EDEN)for MPNNs. EDEN is derived from a series of interpretable transformations onthe graph's distance matrix. We theoretically prove that EDEN ispermutation-equivariant for all level graph representation learning, and weempirically illustrate that EDEN's expressive power can reach up to the 3-WLtest. Extensive experiments on real-world datasets show that combining EDENwith conventional GNNs surpasses recent advanced GNNs.

EDEN: A Plug-in Equivariant Distance Encoding to Beyond the 1-WL Test