Detecting Differences Is Not Understanding Structure: Large Language Models Fail at Graph Isomorphism

Graphs have been used to enhance large language models (LLMs) for structured reasoning, mostly as external knowledge sources are provided to models at test time. In this paper, we take a different view: the value of graphs for LLMs lie not only in supplying information, but also in organizing reasoning. Inspired by how humans use graph-structured mind maps to organize branching and converging thoughts, we ask whether graphs can serve as an internal form of reasoning assistance. We study this question on multi-hop question answering tasks, where teacher-provided reasoning traces are rewritten as graph mind maps and used to guide a student model. Our experiments reveal a clear modality gap. When graph structures are flattened into text, their benefits become limited once direct answer hints are removed. Under this abstract guidance setting, both reasoning efficiency and answer quality degrade substantially. In contrast, visual graph guidance remains effective without direct answer clues, and its advantage persists after supervised fine-tuning and KL-based distillation. The above findings support the claim that graphs should be studied not only as external knowledge structures for LLMs, but also as visual scaffolds for organizing reasoning.

Using Large Language Models (LLMs) to process graph-structured data is an active research area, yet current state-of-the-art approaches typically rely on multi-step pipelines with Graph Neural Network (GNN) encoders that compress rich textual attributes into solitary tokens, creating a significant semantic bottleneck. In this paper, we introduce the Graph Transformer Language Model (GTLM), a novel architecture that enables pretrained LLMs to natively process graph topologies while entirely eliminating this compressive bottleneck. GTLM is exceptionally parameter-efficient: by injecting graph-aware attention biases directly into the LLM's attention modules, it introduces only 0.015% additional parameters relative to the base model. We theoretically prove that our bidirectional attention prefix preserves node permutation equivariance while maintaining exact backward compatibility with the pretrained base model. Extensive evaluations demonstrate that a 1B-parameter GTLM matches or exceeds the performance of 7B-parameter state-of-the-art models on standard Text-Attributed Graph benchmarks, while significantly surpassing baselines on GraphQA. Finally, we demonstrate that GTLM attention heads implicitly learn to simulate message passing, explaining its superior performance on algorithmic tasks. This paradigm shift enables true algorithmic reasoning within LLMs and provides a scalable foundation for next-generation GraphRAG and relational deep learning.

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 topology-aware local aggregation required for graph reasoning. 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 that SLASH delivers significant and consistent performance gains across diverse LLMs.