Slash the Sink: Sharpening Structural Attention Inside LLMs

Large Language Models (LLMs) show remarkable semantic understanding but often struggle with structural understanding when processing graph topologies in a serialized format. Existing solutions rely on training external graph-based adapters or fine-tuning, which incur high costs and lost generalizability. In this work, we investigate the internal mechanisms of LLMs and present a critical finding: LLMs spontaneously reconstruct the graph's topology internally, evidenced by a distinct "sawtooth" pattern in their attention maps that structurally aligns with the "token-level adjacency matrix". However, this intrinsic structural understanding is diluted by the attention sink. We theoretically formalize this dilution as a representation bottleneck, stemming from a fundamental conflict: the model's anisotropic bias, essential for language tasks, suppresses the isotropic information flow required by graph topology. To address this, we propose a training-free solution, named StructuraL Attention SHarpening (Slash), which amplifies this internal structural understanding via a plug-and-play attention redistribution. Experiments on pure graph tasks and molecular prediction validate Slash delivers significant and consistent performance gains across diverse LLMs.