Fig. 3

GNN accuracy for non-homophilic datasets. This figure presents the accuracy of GNN models on the non-homophilic datasets (original and manipulated). GNNs cannot outperform the feature-only baseline on the original graphs, and achieve a similar accuracy to the \(Hom^-\) graphs, where the structure is destroyed. This suggests that the graph structure is irrelevant to GNN accuracy. When we enforce homophily with \(Hom^+\) graphs, GNNs outperform the baseline on all datasets. In other words, homophily makes the graph structure useful for classification with GNNs. Destroying any aspect of the network does not improve the GNN performance over the baseline. Comparing these results to those in Fig. 2, we see that these aspects (degree distribution, community structures and sub-communities within labels) do not concern GNNs when homophily does not exist