Title: Does Structural Information have been Fully Exploited in Graph Data?. Abstract: In real world, graph-structured data is pervasive, operating as an abstraction of data containing nodes and interactions between nodes. There are numerous ways dedicated to excavating structure information overtly or implicitly, but whether structural information has been adequately exploited remains an unanswered question. We offer Curvphormer, a curvature-based topology-aware Graphormer that integrates Discrete Ricci Curvature (DRC) into a powerful graph-based Transformer architecture to construct a more expressive graph-based model. This work employs DRC, a geometric descriptor, to reveal additional structural information. We intuitively characterize how our model can make better use of the topological information in graph data, and extract desired structural information, such as inherent community structure in graphs with homogeneous information. We conduct extensive experiments on different scaled datasets, such asg PCQM4M-LSC, ZINC and MolHIV, and achieve remarkable performance gain on various graph-level tasks and finetune tasks. Codes
 will be released upon acceptance.