From Linking Homophily and Label Informativeness to Rewiring in GNNs

TMLR Paper8994 Authors

Abstract: Message-passing graph neural networks (GNNs) are widely used for node classification. These models learn node representations by aggregating information along the edges of a given graph. A central open question remains which graph properties make message passing effective. While homophily was long viewed as a key ingredient, recent work has increasingly questioned this view, arguing that message passing can remain effective under heterophily when the label distribution is informative, i.e., when a node's label is predictable from its neighbors' labels. In this work, we bridge these perspectives by formally connecting label distribution informativeness and homophily, showing they are not independent and, crucially, that strong neighbor-label predictability is unlikely when homophily is low under realistic multi-class label marginals. Building on this insight, we propose a rewiring framework that increases homophily using a reference edge set, providing guarantees on the homophily of the rewired graph and, in regimes we characterize, also provably strengthening neighbor-label predictability. Across diverse heterophilic benchmarks, our approach outperforms existing rewiring methods and specialized heterophily GNNs, yielding higher node-classification accuracy while remaining efficient and scalable to large graphs.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Vicenç_Gómez1

Submission Number: 8994