LG-GNN: Local-Global Adaptive Graph Neural Network for Modeling Both Homophily and Heterophily

Most Graph Neural Networks (GNNs) are based on the homophily assumption, where nodes with the same labels or similar features tend to be connected to each other. However, real-world graphs often do not adhere to this homophily assumption. Currently, most researches aggregate multi-hop neighbor information to discover more potentially relevant nodes. However, in the aggregation process of GNNs, the difference in modeling global and local information is not considered, inevitably leading to information loss. Motivated by this limitation, we propose LG-GNN, a local-global adaptive graph neural network for modeling both homophily and heterophily. Specifically, we model the long-range structural similarity and local feature similarity between nodes from global and local perspectives, in order to capture distant dependencies in highly heterophilic networks while reducing the mixing of locally dissimilar feature nodes, thereby increasing the effectiveness of information aggregation in highly heterophilic graphs. Extensive experiments on a wide range of real-world datasets demonstrate that our proposed approach performs well in both heterophilic and homophilic graphs.