  Graph Neural Networks (GNNs) have been predominant for graph learning tasks;
however, recent studies showed that a well-known graph algorithm, Label
Propagation (LP), combined with a shallow neural network can achieve comparable
performance to GNNs in semi-supervised node classification on graphs with high
homophily. In this paper, we show that this approach falls short on graphs with
low homophily, where nodes often connect to the nodes of the opposite classes.
To overcome this, we carefully design a combination of a base predictor with LP
algorithm that enjoys a closed-form solution as well as convergence guarantees.
Our algorithm first learns the class compatibility matrix and then aggregates
label predictions using LP algorithm weighted by class compatibilities. On a
wide variety of benchmarks, we show that our approach achieves the leading
performance on graphs with various levels of homophily. Meanwhile, it has
orders of magnitude fewer parameters and requires less execution time.
Empirical evaluations demonstrate that simple adaptations of LP can be
competitive in semi-supervised node classification in both homophily and
heterophily regimes.
