  Majority of the existing graph neural networks (GNN) learn node embeddings
that encode their local neighborhoods but not their positions. Consequently,
two nodes that are vastly distant but located in similar local neighborhoods
map to similar embeddings in those networks. This limitation prevents accurate
performance in predictive tasks that rely on position information. In this
paper, we develop GraphReach, a position-aware inductive GNN that captures the
global positions of nodes through reachability estimations with respect to a
set of anchor nodes. The anchors are strategically selected so that
reachability estimations across all the nodes are maximized. We show that this
combinatorial anchor selection problem is NP-hard and, consequently, develop a
greedy (1-1/e) approximation heuristic. Empirical evaluation against
state-of-the-art GNN architectures reveal that GraphReach provides up to 40%
relative improvement in accuracy. In addition, it is more robust to adversarial
attacks.
