GraphReach: Position-Aware Graph Neural Network using Reachability Estimations

TL;DR

GraphReach is a novel position-aware graph neural network that uses reachability estimations to incorporate global positional information, significantly improving accuracy and robustness over existing methods.

Contribution

We introduce GraphReach, a GNN that captures node positions via reachability estimations with strategically selected anchors, addressing a key limitation of existing GNNs.

Findings

Up to 40% accuracy improvement over state-of-the-art GNNs

More robust to adversarial attacks

Effective in capturing global node positions

Abstract

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.