  Graph contrastive learning (CL) methods learn node representations in a
self-supervised manner by maximizing the similarity between the augmented node
representations obtained via a GNN-based encoder. However, CL methods perform
poorly on graphs with heterophily, where connected nodes tend to belong to
different classes. In this work, we address this problem by proposing an
effective graph CL method, namely HLCL, for learning graph representations
under heterophily. HLCL first identifies a homophilic and a heterophilic
subgraph based on the cosine similarity of node features. It then uses a
low-pass and a high-pass graph filter to aggregate representations of nodes
connected in the homophilic subgraph and differentiate representations of nodes
in the heterophilic subgraph. The final node representations are learned by
contrasting both the augmented high-pass filtered views and the augmented
low-pass filtered node views. Our extensive experiments show that HLCL
outperforms state-of-the-art graph CL methods on benchmark datasets with
heterophily, as well as large-scale real-world graphs, by up to 7%, and
outperforms graph supervised learning methods on datasets with heterophily by
up to 10%.
