“How Powerful are Graph Neural Networks?”, submitted to arXiv on October 1, 2018 by Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka, gave the field a rigorous theory of what message-passing graph networks can and cannot distinguish. It is the paper that introduced the Graph Isomorphism Network (GIN).
The authors connected graph neural networks to the Weisfeiler-Lehman graph isomorphism test, a classic procedure for checking whether two graphs have the same structure. They proved that no message-passing GNN can be more powerful at telling graphs apart than this test, and they showed that popular models like the GCN and mean or max pooling aggregators fall strictly short of that limit because their aggregation functions are not injective: different neighborhoods can collapse to the same representation.
GIN was their answer. By using a sum aggregator combined with a multilayer perceptron, GIN keeps neighborhood information injective and thus reaches the maximal expressiveness possible for this class of models, matching the Weisfeiler-Lehman test. The authors backed the theory with experiments on graph classification benchmarks where GIN performed at or near the top.
The paper matters because it shifted graph learning from heuristic design toward principled understanding. Knowing the expressive ceiling of message passing tells practitioners when a standard graph network will be enough and when a fundamentally different approach is needed.