  Graph Neural Networks (GNNs) are well-suited for learning on homophilous
graphs, i.e., graphs in which edges tend to connect nodes of the same type.
Yet, achievement of consistent GNN performance on heterophilous graphs remains
an open research problem. Recent works have proposed extensions to standard GNN
architectures to improve performance on heterophilous graphs, trading off model
simplicity for prediction accuracy. However, these models fail to capture basic
graph properties, such as neighborhood label distribution, which are
fundamental for learning. In this work, we propose GCN for Heterophily (GCNH),
a simple yet effective GNN architecture applicable to both heterophilous and
homophilous scenarios. GCNH learns and combines separate representations for a
node and its neighbors, using one learned importance coefficient per layer to
balance the contributions of center nodes and neighborhoods. We conduct
extensive experiments on eight real-world graphs and a set of synthetic graphs
with varying degrees of heterophily to demonstrate how the design choices for
GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH
outperforms state-of-the-art models of much higher complexity on four out of
eight benchmarks, while producing comparable results on the remaining datasets.
Finally, we discuss and analyze the lower complexity of GCNH, which results in
fewer trainable parameters and faster training times than other methods, and
show how GCNH mitigates the oversmoothing problem.
