<p>The recent advancements in graph Transformers have demonstrated remarkable performance in graph representation learning, surpassing traditional graph neural networks (GNNs). In this work, we view the self-attention mechanism, which serves as the core component of graph Transformers, as a two-step aggregation operation on a fully connected graph. The self-attention mechanism exhibits the characteristic of generating positive attention values, effectively performing a smoothing operation on all nodes and preserving low-frequency information. However, previous studies have revealed that solely capturing low-frequency information is inefficient for learning complex relations of nodes on diverse graphs, and high-frequency information is also crucial for learning distinguishable node representations. To this end, we propose a Signed Attention-based Graph Transformer (SignGT) to adaptively capture various frequency information from graphs. Specifically, SignGT develops a new signed self-attention mechanism (SignSA) that produces signed attention values according to the semantic relevance of the node pairs. Consequently, the diverse frequency information between different node pairs could be carefully preserved. Additionally, SignGT proposes a structure-aware feed-forward network (SFFN) that incorporates neighborhood bias to retain local topology information. In this way, SignGT could learn informative node representations by considering both long-range dependencies and local topology information. Extensive empirical results on both node-level and graph-level tasks demonstrate the superiority of SignGT against state-of-the-art graph Transformers and advanced GNNs.</p>