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In recent years, graph neural networks (GNNs) have achieved great success inthe field of graph representation learning. Although prior work has shed lightinto the expressiveness of those models (\ie whether they can distinguish pairsof non-isomorphic graphs), it is still not clear what structural information isencoded into the node representations that are learned by those models. In thispaper, we investigate which properties of graphs are captured purely by thesemodels, when no node attributes are available. Specifically, we study fourpopular GNN models, and we show that two of them embed all nodes into the samefeature vector, while the other two models generate representations that arerelated to the number of walks over the input graph. Strikingly, structurallydissimilar nodes can have similar representations at some layer $k>1$, if theyhave the same number of walks of length $k$. We empirically verify ourtheoretical findings on real datasets.

What Do GNNs Actually Learn? Towards Understanding their Representations