Graph Neural Network with Virtual Edge Message Passing for Heterophilous Graphs.

Graph Neural Networks (GNNs) have achieved great success in graph representation learning. Modern GNNs are built upon the homophily assumption and iteratively aggregate messages from immediate neighbors through the message-passing mechanism, which limits the ability of GNNs to represent graphs with heterophily. Existing GNNs considering heterophily adapt to the heterophilous graphs through reconstructing neighborhood and message fusion. However, noise information is constantly superimposed during message passing, due to the mixed propagation of different-order messages. In this paper, we propose a special graph convolutional network with virtual edge message passing (VEGCN), which consists of three important components: virtual edge message passing, message attention, and residual connection. Different from the message-passing mechanism of existing GNNs, virtual edge message passing can directly transfer messages from the second-order neighbors to the target nodes. By bypassing the first-order neighbors, VEGCN can avoid interference from first-order neighbors. In addition, we design an attention mechanism to adaptively obtain messages from first-order and second-order neighbors. This attention mechanism can distinguish the different importance of the messages from first-order neighbors and second-order neighbors. Finally, we introduce a residual connection to enhance the features of the nodes themselves and alleviate over-smoothing. We validate the effectiveness of VEGCN on several benchmark datasets including graphs with homophily and heterophily. Experimental results show that VEGCN outperforms representative baselines. Furthermore, we also designed ablation experiments to verify the role of the core components.