Informative keyframe selection is critical for applying large vision-language models (LVLMs) to long-form video understanding under limited frame budgets. However, existing methods heavily rely on query-frame similarity, which can yield coarse boundaries and miss latent contextual events that are answer-relevant but not explicitly mentioned in the query. To address this issue, we propose AGE-Sampler, a training-free Adaptive-granularity Graph-enhanced Event sampling framework for long-video understanding. AGE-Sampler jointly exploits low-level visual transition cues and query-relevance signals to construct query-adaptive events, thus preserving fine-grained structures in relevant regions while merging low-relevance regions into compact intervals. To recover answer-bearing contextual evidence, we further develop a fine-grained event graph and propagate importance from high-confidence query-relevant anchors via Personalized PageRank, followed by event-level budget allocation and representative keyframe selection. Extensive experiments with different LVLM backbones show that our AGE-Sampler consistently improves long-video understanding performance, achieving average absolute gains of +6.2% on LongVideoBench, +8.8% on MLVU, and +3.8% on Video-MME, while remaining lightweight and plug-and-play.