# CodeGraph: Enhancing Graph Reasoning of LLMs with Code

arXiv: https://arxiv.org/abs/2408.13863 · HTML: https://mlsanity.com/paper/2408.13863/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 64 of its 100 references that are in the map.
- First posted on arXiv 25 Aug 2024.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 30 of 64)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [ToolAlpaca: Generalized Tool Learning for Language Models with 3000 Simulated Cases](https://mlsanity.com/paper/2306.05301/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [FreshLLMs: Refreshing Large Language Models with Search Engine Augmentation](https://mlsanity.com/paper/2310.03214/) (2023)
- [ChatGPT for Robotics: Design Principles and Model Abilities](https://mlsanity.com/paper/2306.17582/) (2023)
- [Exploring the Potential of Large Language Models (LLMs) in Learning on Graphs](https://mlsanity.com/paper/2307.03393/) (2023)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)

## Built on by (most cited first, 6 of 6)

- [RTL++: Graph-enhanced LLM for RTL Code Generation](https://mlsanity.com/paper/2505.13479/) (2025)
- [Graph Counselor: Adaptive Graph Exploration via Multi-Agent Synergy to Enhance LLM Reasoning](https://mlsanity.com/paper/2506.03939/) (2025)
- [Actions Speak Louder than Prompts: A Large-Scale Study of LLMs for Graph Inference](https://mlsanity.com/paper/2509.18487/) (2025)
- [GraphSkill: Documentation-Guided Hierarchical Retrieval-Augmented Coding for Complex Graph Reasoning](https://mlsanity.com/paper/2603.06620/) (2026)
- [Hypergraph as Language](https://mlsanity.com/paper/2605.21858/) (2026)
- [Unified Multi-Dimensional Benchmark for Complex Graph Reasoning in Large Language Models](https://mlsanity.com/paper/2608.12391/) (2026)

## Abstract (arXiv)

With the increasing popularity of large language models (LLMs), reasoning on basic graph algorithm problems is an essential intermediate step in assessing their abilities to process and infer complex graph reasoning tasks. Existing methods usually convert graph-structured data to textual descriptions and then use LLMs for reasoning and computation. However, LLMs often produce computation errors on arithmetic parts in basic graph algorithm problems, such as counting number of edges. In addition, they struggle to control or understand the output of the reasoning process, raising concerns about whether LLMs are simply guessing. In this paper, we introduce CodeGraph, a method that encodes graph problem solutions as code. The methods solve new graph problems by learning from exemplars, generating programs, and executing them via a program interpreter. Using the few-shot setting, we evaluate CodeGraph with the base LLM being GPT-3.5 Turbo, Llama3-70B Instruct, Mixtral-8x22B Instruct, and Mixtral-8x7B Instruct. Experimental results on six tasks with six graph encoding methods in the GraphQA dataset demonstrate that CodeGraph can boost performance on graph reasoning tasks inside LLMs by 1.3% to 58.6%, depending on the task. Compared to the existing methods, CodeGraph demonstrates strong performance on arithmetic problems in graph tasks and offers a more controllable and interpretable approach to the reasoning process.