  Graph Attention Network (GAT) is one of the most popular Graph Neural Network
(GNN) architecture, which employs the attention mechanism to learn edge weights
and has demonstrated promising performance in various applications. However,
since it only incorporates information from immediate neighborhood, it lacks
the ability to capture long-range and global graph information, leading to
unsatisfactory performance on some datasets, particularly on heterophilic
graphs. To address this limitation, we propose the Directional Graph Attention
Network (DGAT) in this paper. DGAT is able to combine the feature-based
attention with the global directional information extracted from the graph
topology. To this end, a new class of Laplacian matrices is proposed which can
provably reduce the diffusion distance between nodes. Based on the new
Laplacian, topology-guided neighbour pruning and edge adding mechanisms are
proposed to remove the noisy and capture the helpful long-range neighborhood
information. Besides, a global directional attention is designed to enable a
topological-aware information propagation. The superiority of the proposed DGAT
over the baseline GAT has also been verified through experiments on real-world
benchmarks and synthetic data sets. It also outperforms the state-of-the-art
(SOTA) models on 6 out of 7 real-world benchmark datasets.
