Edge-Aware Curvature Modeling for Graph Understanding in Large Language Models
Existing graph-aware large language models often neglect edge structure during graph-text alignment, leading to limited cross-modal information propagation and over-compression issues. This work proposes CureLLM, a novel framework that theoretically demonstrates for the first time that ignoring edge information results in suboptimal alignment. CureLLM introduces an innovative, training-free edge-aware textual prompting mechanism coupled with curvature-aware graph representation learning. By leveraging positively curved edges to guide message passing, the method effectively injects structural information into a frozen large language model. Evaluated on 11 real-world datasets, CureLLM significantly outperforms 20 baseline methods and achieves state-of-the-art performance in graph–text joint understanding tasks.