Bridging Graph and Language Structures: Structure-Aware Fine-Tuning for Graph Reasoning with LLMs

Serializing graphs as text enables large language models (LLMs) to perform graph reasoning, but structural differences between graphs and sequences limit effective use of graph information. We propose a structure-aware fine-tuning framework for decoder LLMs that addresses three key issues: insufficient global readouts, mismatch between sequence positions and graph relations, and unequal information aggregation under causal attention. The framework introduces hierarchical graph serialization to organize local and global structural information, structural role rotary position encoding to reduce permutation-sensitive positional bias, and a structural visibility mask with learnable attention biases to control information flow across edge, node, and graph levels. A thresholded readout decorrelation loss further encourages complementary global representations while retaining necessary information sharing. The framework requires no additional graph encoder and supports parameter-efficient fine-tuning of pretrained LLMs. Under the specified evaluation protocol, it improves macro-average accuracy by 20.88 and 14.11 percentage points on GraphInstruct and MolecularNet, respectively, over a recent attention-sink-based method, while achieving competitive performance on node classification and link prediction. Ablation studies further confirm the contribution of each component. These results demonstrate that jointly adapting graph serialization, positional relations, and structural information flow can substantially improve graph reasoning with LLMs.