# Clustering as Reasoning: A k-Means Interpretation of Chain-of-Thought Graph Learning

arXiv: https://arxiv.org/abs/2605.24867 · HTML: https://mlsanity.com/paper/2605.24867/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 8 of its 60 references that are in the map.
- First posted on arXiv 24 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 8 of 8)

- [GPT4Graph: Can Large Language Models Understand Graph Structured Data ? An Empirical Evaluation and Benchmarking](https://mlsanity.com/paper/2305.15066/) (2023)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Graph Chain-of-Thought: Augmenting Large Language Models by Reasoning on Graphs](https://mlsanity.com/paper/2404.07103/) (2024)
- [GraphInstruct: Empowering Large Language Models with Graph Understanding and Reasoning Capability](https://mlsanity.com/paper/2403.04483/) (2024)
- [Evaluating Large Language Models on Graphs: Performance Insights and Comparative Analysis](https://mlsanity.com/paper/2308.11224/) (2023)
- [Can LLMs Effectively Leverage Graph Structural Information through Prompts, and Why?](https://mlsanity.com/paper/2309.16595/) (2023)
- [GraphChain: Large Language Models for Large-scale Graph Analysis via Tool Chaining](https://mlsanity.com/paper/2511.00457/) (2025)
- [Summaries as Centroids for Interpretable and Scalable Text Clustering](https://mlsanity.com/paper/2502.09667/) (2025)

## Built on by (most cited first, 1 of 1)

- [Spectral Reversal: Counteracting Singular Value Bias for Graph Prompting](https://mlsanity.com/paper/2609.32143/) (2026)

## Abstract (arXiv)

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a k-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the k-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.