# Code-on-Graph: Iterative Programmatic Reasoning via Large Language Models on Knowledge Graphs

arXiv: https://arxiv.org/abs/2606.03705 · HTML: https://mlsanity.com/paper/2606.03705/

## Key facts

- Cited by 3 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 33 of its 50 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## 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 33)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models](https://mlsanity.com/paper/2512.02556/) (2025)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [ViperGPT: Visual Inference via Python Execution for Reasoning](https://mlsanity.com/paper/2303.08128/) (2023)
- [The Web as a Knowledge-base for Answering Complex Questions](https://mlsanity.com/paper/1803.06643/) (2018)
- [Chameleon: Plug-and-Play Compositional Reasoning with Large Language Models](https://mlsanity.com/paper/2304.09842/) (2023)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning](https://mlsanity.com/paper/2310.01061/) (2023)
- [Think-on-Graph: Deep and Responsible Reasoning of Large Language Model on Knowledge Graph](https://mlsanity.com/paper/2307.07697/) (2023)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [G-Retriever: Retrieval-Augmented Generation for Textual Graph Understanding and Question Answering](https://mlsanity.com/paper/2402.07630/) (2024)
- [UniKGQA: Unified Retrieval and Reasoning for Solving Multi-hop Question Answering Over Knowledge Graph](https://mlsanity.com/paper/2212.00959/) (2022)
- [KG-Agent: An Efficient Autonomous Agent Framework for Complex Reasoning over Knowledge Graph](https://mlsanity.com/paper/2402.11163/) (2024)
- [DecAF: Joint Decoding of Answers and Logical Forms for Question Answering over Knowledge Bases](https://mlsanity.com/paper/2210.00063/) (2022)
- [Plan-on-Graph: Self-Correcting Adaptive Planning of Large Language Model on Knowledge Graphs](https://mlsanity.com/paper/2410.23875/) (2024)
- [Few-shot In-context Learning for Knowledge Base Question Answering](https://mlsanity.com/paper/2305.01750/) (2023)
- [T-SciQ: Teaching Multimodal Chain-of-Thought Reasoning via Mixed Large Language Model Signals for Science Question Answering](https://mlsanity.com/paper/2305.03453/) (2023)
- [Generate-on-Graph: Treat LLM as both Agent and KG in Incomplete Knowledge Graph Question Answering](https://mlsanity.com/paper/2404.14741/) (2024)
- [TIARA: Multi-grained Retrieval for Robust Question Answering over Large Knowledge Bases](https://mlsanity.com/paper/2210.12925/) (2022)
- [Don't Generate, Discriminate: A Proposal for Grounding Language Models to Real-World Environments](https://mlsanity.com/paper/2212.09736/) (2022)
- [FlexKBQA: A Flexible LLM-Powered Framework for Few-Shot Knowledge Base Question Answering](https://mlsanity.com/paper/2308.12060/) (2023)
- [Call Me When Necessary: LLMs can Efficiently and Faithfully Reason over Structured Environments](https://mlsanity.com/paper/2403.08593/) (2024)
- [Reasoning of Large Language Models over Knowledge Graphs with Super-Relations](https://mlsanity.com/paper/2503.22166/) (2025)
- [UniGen: A Unified Generative Framework for Retrieval and Question Answering with Large Language Models](https://mlsanity.com/paper/2312.11036/) (2023)
- [EffiQA: Efficient Question-Answering with Strategic Multi-Model Collaboration on Knowledge Graphs](https://mlsanity.com/paper/2406.01238/) (2024)

## Built on by (most cited first, 3 of 3)

- [Schema-Anchored Latent Reasoning for Semantic Parsing-Based Knowledge Base Question Answering](https://mlsanity.com/paper/2609.20398/) (2026)
- [GraphCert: Bootstrap Agentic Graph Reasoning with Certified Evidence Rubrics](https://mlsanity.com/paper/2609.38798/) (2026)
- [Knowledge Graphs as Files: An Agent Harness Where Tool Creation and Tool Use Co-Evolve](https://mlsanity.com/paper/2610.18616/) (2026)

## Abstract (arXiv)

Knowledge Graphs (KGs) are widely used to mitigate the limitations of Large Language Models (LLMs), such as outdated knowledge and hallucinations. Existing LLM-KG integration frameworks typically rely on predefined operators to retrieve factual knowledge from KGs and inject it into prompts for answer generation. This paradigm faces two critical bottlenecks: 1) Inflexibility: The predefined operators are limited in scope and thus lack sufficient compositional expressiveness to fully capture the complex semantics required by KG questions. 2) Unscalability: Direct injection of factual knowledge into prompts limits scalability in handling large-scale factual knowledge. To address these two bottlenecks, we propose Code-on-Graph (CoG), a programmatic reasoning framework for LLM-KG integration. Specifically, given the factual knowledge retrieved at each reasoning step, CoG first identifies the corresponding KG schemas and represents these schemas as Python classes, which serve as abstract interfaces to the retrieved facts. It then generates executable code grounded in these classes, with the retrieved facts instantiated as objects of the corresponding classes during execution. This design enables flexible code-based reasoning while avoiding the direct injection of large-scale factual knowledge into prompts. Experiments on WebQSP, CWQ, and GrailQA demonstrate that CoG outperforms prior state-of-the-art models by up to 10.5%.