Evolve on Graph: Self-Evolving Knowledge Graph Reasoning without Question Annotations· 图谱上的自进化：无需问题标注的知识图谱推理

Knowledge graphs (KGs) provide reliable external knowledge for multi-hop factual reasoning with large language models (LLMs), yet most KGs in real-world domains such as finance and industry lack question--answer (QA) annotations. Without such annotations, existing methods struggle to improve LLM graph reasoning: training-free agents cannot improve their exploration through interaction; reinforcement learning (RL) agents depend on QA data annotated by humans or synthesized by closed-source models; and training data is typically built offline, so its topology mix is fixed and cannot follow the agent's ability. We propose Evolve on Graph (EoG), a framework that lets an LLM self-evolve its graph reasoning without any QA annotations. Through Graph Self-Play, a single LLM alternates between a Pr