Flow2GNN: Flexible two-way flow message passing for enhancing GNNs beyond homophily

Message passing (MP) is crucial for effective graph neural networks (GNNs). Most local message-passing schemes have been shown to underperform on heterophily graphs due to the perturbation of updated representations caused by local redundant heterophily information. However, our experiment findings indicate that the distribution of heterophily information during MP can be disrupted by disentangling local neighborhoods. This finding can be applied to other GNNs, improving their performance on heterophily graphs in a more flexible manner compared to most heterophily GNNs with complex designs. This article proposes a new type of simple message-passing neural network called Flow2GNN. It uses a two-way flow message-passing scheme to enhance the ability of GNNs by disentangling and redistributing heterophily information in the topology space and the attribute space. Our proposed message-passing scheme consists of two steps in topology space and attribute space. First, we introduce a new disentangled operator with b