Link Prediction under Heterophily: A Physics-Inspired Graph Neural
  Network Approach
Andrea Giuseppe Di Francesco Francesco Caso Maria Sofia Bucarelli Fabrizio Silvestri
In the past years, Graph Neural Networks (GNNs) have become the `de facto'
standard in various deep learning domains, thanks to their flexibility in
modeling real-world phenomena represented as graphs. However, the
message-passing mechanism of GNNs faces challenges in learnability and
expressivity, hindering high performance on heterophilic graphs, where adjacent
nodes frequently have different labels. Most existing solutions addressing
these challenges are primarily confined to specific benchmarks focused on node
classification tasks. This narrow focus restricts the potential impact that
link prediction under heterophily could offer in several applications,
including recommender systems. For example, in social networks, two users may
be connected for some latent reason, making it challenging to predict such
connections in advance. Physics-Inspired GNNs such as GRAFF provided a
significant contribution to enhance node classification performance under
heterophily, thanks to the adoption of physics biases in the message-passing.
Drawing inspiration from these findings, we advocate that the methodology
employed by GRAFF can improve link prediction performance as well. To further
explore this hypothesis, we introduce GRAFF-LP, an extension of GRAFF to link
prediction. We evaluate its efficacy within a recent collection of heterophilic
graphs, establishing a new benchmark for link prediction under heterophily. Our
approach surpasses previous methods, in most of the datasets, showcasing a
strong flexibility in different contexts, and achieving relative AUROC
improvements of up to 26.7%.