Evaluating LLMs on Large-Scale Graph Property Estimation via Random Walks

Graph reasoning provides a promising testbed for evaluating the reasoning ability of large language models (LLMs), as graph instances can be programmatically generated, structurally controlled, and naturally scaled to long-input settings. However, existing graph reasoning benchmarks have limited coverage of data complexity, rely heavily on manual construction, and lack unified evaluation across text-based and code-based reasoning modes. To address these limitations, we propose {\dataset}, a five-stage \textit{semi-automatic} framework for constructing complex graph reasoning benchmarks. It expands benchmark coverage along five dimensions: \textit{Graph Size}, \textit{Task Complexity}, \textit{Task Description}, \textit{Graph Loading}, and \textit{Task Source}. The framework uses an LLM-based data generator to automatically produce task descriptions, graph data, reference solutions, graph-loading scripts, question forms, and evaluation scripts, while retaining human validation at key quality-control stages. Based on it, we construct a benchmark with $202$ tasks and evaluate LLMs under text-based, code-based, and augmented reasoning settings. Experiments show that the complexity dimensions reveal model limitations that are less visible in existing benchmarks; existing fine-tuned models struggle to generalize to GraphGym, whereas retrieval-augmented methods show scenario-dependent adaptability, improving textual reasoning but not consistently improving coding reasoning. These findings suggest that ours serves as a challenging and diagnostic benchmark for graph reasoning and provides empirical guidance for future enhancement methods. Code and dataset will be published soon.

With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced reasoning over knowledge graphs. In this paper, we ask a complementary question: How can graphs help LLMs? We address this question from three perspectives: 1) graphs provide an up-to-date knowledge source that helps reduce LLM hallucinations, 2) graph-based prompting techniques-such as Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT)-enhance LLM reasoning capabilities, and 3) integrating graphs into LLMs improves their understanding of structured data, expanding their applicability to domains such as e-commerce, code, and relational databases (RDBs). We further outlook some future directions including designing sparse LLM architectures based on graphs and brain-inspired memory systems.

Large Language Models (LLMs) are increasingly asked to reason over structured data such as graphs, yet how reliably they can carry out multi-step graph algorithms in language remains unclear. Existing evaluations tend to use simple tasks on small graphs, to score code generation rather than reasoning over the graph itself, or to fix a single input format. We introduce Graph Theory Bench (GT Bench), a benchmark covering 24 classical graph problems in 44 task-structure settings, with over 100,000 examples across four representations: natural language, structured language, adjacency list, and adjacency matrix. Evaluating eight LLMs on GT Bench shows that accuracy is strongly tied to the input representation, that the best representation shifts with graph density, size, and topology as well as with the model, and that this sensitivity persists, attenuated, in the strongest reasoning models. Building on these observations, we propose the Graph Theory Agent (GTA), which pairs a preference-trained representation selector with plan-and-decompose scaffolding around a frozen executor LLM. GTA lifts Phi-4 from 53.5% to 69.1% on the benchmark's easy split and from 33.0% to 41.5% on its hard split, outperforming eight prompting and agent baselines, and transfers without retraining to GraCoRe and NLGraph. Code for benchmark generation and evaluation: https://github.com/xzx34/GTA. The project homepage is available at https://xzx34.github.io/gta/.