Adaptive node-level weighted learning for directed graph neural network

Directed graph neural networks (DGNNs) have garnered increasing interest, yet few studies have focused on node-level representation in directed graphs. In this paper, we argue that different nodes rely on neighbor information from different directions. Furthermore, the commonly used mean aggregation for in-neighbor sets and out-neighbor sets may lose expressive power for certain nodes. To achieve this, first, we estimate the homophily of each node to neighbors in different directions by extending the Dirichlet energy. This approach allows us to assign larger weights to neighbors in directions exhibiting higher homophilic ratios for any node. Second, we introduce out-degree and in-degree information in the learning of weights to avoid the problem of weak expressive power ability of mean aggregation. Moreover, we theoretically demonstrate that our method enhances the expressive ability of directed graphs. Extensive experiments on seven real-world datasets demonstrate that our method outperforms state-of-the-art approaches in both node classification and link prediction tasks.