  Under circumstances of heterophily, where nodes with different labels tend to
be connected based on semantic meanings, Graph Neural Networks (GNNs) often
exhibit suboptimal performance. Current studies on graph heterophily mainly
focus on aggregation calibration or neighbor extension and address the
heterophily issue by utilizing node features or structural information to
improve GNN representations. In this paper, we propose and demonstrate that the
valuable semantic information inherent in heterophily can be utilized
effectively in graph learning by investigating the distribution of neighbors
for each individual node within the graph. The theoretical analysis is carried
out to demonstrate the efficacy of the idea in enhancing graph learning. Based
on this analysis, we propose HiGNN, an innovative approach that constructs an
additional new graph structure, that integrates heterophilous information by
leveraging node distribution to enhance connectivity between nodes that share
similar semantic characteristics. We conduct empirical assessments on node
classification tasks using both homophilous and heterophilous benchmark
datasets and compare HiGNN to popular GNN baselines and SoTA methods,
confirming the effectiveness in improving graph representations. In addition,
by incorporating heterophilous information, we demonstrate a notable
enhancement in existing GNN-based approaches, and the homophily degree across
real-world datasets, thus affirming the efficacy of our approach.
