Automated Writing Evaluation has shifted from score-centered assessment toward revision-oriented feedback. However, current Large Language Models (LLMs) often generate generic comments that overlook essays’ explicit structure and discourse-level flaws. We propose Graph-Reasoned Automated Feedback and Evaluation (GRAFE), which uses genre-specific structural graphs to guide score-feedback generation. GRAFE encodes discourse-level priors, including argumentation logic, evidence integration, and narrative progression, as continuous representations injected into the LLM. Furthermore, we introduce a training pipeline that combines two-stage Supervised Fine-Tuning for score-calibrated initialization with Group Relative Policy Optimization to align the model toward structural diagnostic accuracy, scoring consistency, and format compliance. We construct a graph-augmented ASAP++ feedback dataset with an expert-calibrated evaluation set. Experiments show that GRAFE outperforms text-only baselines on Structure-Aware Diagnosis and Structure-Grounded Actionability, demonstrating the value of explicit structural modeling.