  Graph Neural Networks (GNNs) are widely used on a variety of graph-based
machine learning tasks. For node-level tasks, GNNs have strong power to model
the homophily property of graphs (i.e., connected nodes are more similar) while
their ability to capture the heterophily property is often doubtful. This is
partially caused by the design of the feature transformation with the same
kernel for the nodes in the same hop and the followed aggregation operator. One
kernel cannot model the similarity and the dissimilarity (i.e., the positive
and negative correlation) between node features simultaneously even though we
use attention mechanisms like Graph Attention Network (GAT), since the weight
calculated by attention is always a positive value. In this paper, we propose a
novel GNN model based on a bi-kernel feature transformation and a selection
gate. Two kernels capture homophily and heterophily information respectively,
and the gate is introduced to select which kernel we should use for the given
node pairs. We conduct extensive experiments on various datasets with different
homophily-heterophily properties. The experimental results show consistent and
significant improvements against state-of-the-art GNN methods.
