# Exposing Weaknesses of Large Reasoning Models through Graph Algorithm Problems

arXiv: https://arxiv.org/abs/2602.06319 · HTML: https://mlsanity.com/paper/2602.06319/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 44 of its 77 references that are in the map.
- First posted on arXiv 6 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 44)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs](https://mlsanity.com/paper/2412.21187/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [ReTool: Reinforcement Learning for Strategic Tool Use in LLMs](https://mlsanity.com/paper/2504.11536/) (2025)
- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [GPT4Graph: Can Large Language Models Understand Graph Structured Data ? An Empirical Evaluation and Benchmarking](https://mlsanity.com/paper/2305.15066/) (2023)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [Talk like a Graph: Encoding Graphs for Large Language Models](https://mlsanity.com/paper/2310.04560/) (2023)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Imitate, Explore, and Self-Improve: A Reproduction Report on Slow-thinking Reasoning Systems](https://mlsanity.com/paper/2412.09413/) (2024)
- [O1 Replication Journey: A Strategic Progress Report -- Part 1](https://mlsanity.com/paper/2410.18982/) (2024)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [KoLA: Carefully Benchmarking World Knowledge of Large Language Models](https://mlsanity.com/paper/2306.09296/) (2023)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Tool-Star: Empowering LLM-Brained Multi-Tool Reasoner via Reinforcement Learning](https://mlsanity.com/paper/2505.16410/) (2025)
- [Challenging the Boundaries of Reasoning: An Olympiad-Level Math Benchmark for Large Language Models](https://mlsanity.com/paper/2503.21380/) (2025)
- [GraphInstruct: Empowering Large Language Models with Graph Understanding and Reasoning Capability](https://mlsanity.com/paper/2403.04483/) (2024)
- [LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?](https://mlsanity.com/paper/2506.11928/) (2025)
- [START: Self-taught Reasoner with Tools](https://mlsanity.com/paper/2503.04625/) (2025)

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

- [GABench: A Comprehensive Benchmark for Evaluating LLM Agents on Graph Analysis Tasks](https://mlsanity.com/paper/2608.01684/) (2026)
- [Are Large Language Models Suitable for Graph Computation? Progress and Prospects](https://mlsanity.com/paper/2606.06865/) (2026)
- [GTA: Graph Theory Agent and Benchmark for Algorithmic Graph Reasoning with LLMs](https://mlsanity.com/paper/2609.12265/) (2026)

## Abstract (arXiv)

Large Reasoning Models (LRMs) have advanced rapidly; however, existing benchmarks in mathematics, code, and common-sense reasoning remain limited. They lack long-context evaluation, offer insufficient challenge, and provide answers that are difficult to verify programmatically. We introduce GrAlgoBench, a benchmark designed to evaluate LRMs through graph algorithm problems. Such problems are particularly well suited for probing reasoning abilities: they demand long-context reasoning, allow fine-grained control of difficulty levels, and enable standardized, programmatic evaluation. Across nine tasks, our systematic experiments reveal two major weaknesses of current LRMs. First, accuracy deteriorates sharply as context length increases, falling below 50% once graphs exceed 120 nodes. This degradation is driven by frequent execution errors, weak memory, and redundant reasoning. Second, LRMs suffer from an over-thinking phenomenon, primarily caused by extensive yet largely ineffective self-verification, which inflates reasoning traces without improving correctness. By exposing these limitations, GrAlgoBench establishes graph algorithm problems as a rigorous, multidimensional, and practically relevant testbed for advancing the study of reasoning in LRMs. Code is available at https://github.com/Bklight999/GrAlgoBench.