Graph transformers need strong inductive biases to derive meaningful attention scores. Yet, current proposals rarely address methods capturing longer ranges, hierarchical structures, or community structures, as they appear in various graphs such as molecules, social networks, and citation networks. In this paper, we propose a hierarchy-distance structural encoding (HDSE), which models a hierarchical distance between the nodes in a graph focusing on its multi-level, hierarchical nature. In particular, this yields a framework which can be flexibly integrated with existing graph transformers, allowing for simultaneous application with other positional representations. Through extensive experiments on 12 real-world datasets, we demonstrate that our HDSE method successfully enhances various types of baseline transformers, achieving state-of-the-art empirical performances on 10 benchmark datasets.

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