  Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the
graph structures based on the relational inductive bias (homophily assumption).
Though GNNs are believed to outperform NNs in real-world tasks, performance
advantages of GNNs over graph-agnostic NNs seem not generally satisfactory.
Heterophily has been considered as a main cause and numerous works have been
put forward to address it. In this paper, we first show that not all cases of
heterophily are harmful for GNNs with aggregation operation. Then, we propose
new metrics based on a similarity matrix which considers the influence of both
graph structure and input features on GNNs. The metrics demonstrate advantages
over the commonly used homophily metrics by tests on synthetic graphs. From the
metrics and the observations, we find some cases of harmful heterophily can be
addressed by diversification operation. With this fact and knowledge of
filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to
adaptively exploit aggregation, diversification and identity channels in each
GNN layer to address harmful heterophily. We validate the ACM-augmented
baselines with 10 real-world node classification tasks. They consistently
achieve significant performance gain and exceed the state-of-the-art GNNs on
most of the tasks without incurring significant computational burden.
