  Many tasks that rely on representations of nodes in graphs would benefit if
those representations were faithful to distances between nodes in the graph.
Geometric techniques to extract such representations have poor scaling over
large graph size, and recent advances in Graph Neural Network (GNN) algorithms
have limited ability to reflect graph distance information beyond the first
degree neighborhood. To enable this highly desired capability, we propose a
technique to learn Isometric Graph Neural Networks (IGNN), which requires
changing the input representation space and loss function to enable any GNN
algorithm to generate representations that reflect distances between nodes. We
experiment with the isometric technique on several GNN architectures for
modeling multiple prediction tasks on multiple datasets. In addition to an
improvement in AUC-ROC as high as $43\%$ in these experiments, we observe a
consistent and substantial improvement as high as 400% in Kendall's Tau (KT), a
measure that directly reflects distance information, demonstrating that the
learned embeddings do account for graph distances.
