Necrotizing Enterocolitis (NEC) is a devastating condition affecting prematurely born neonates. Reviewing Abdominal X-rays (AXRs) is a key step in NEC diagnosis, staging and treatment decision-making, but poses significant challenges due to the subtle, difficult-to-identify radiological signs of the disease. In this paper, we propose AIDNEC - AI Diagnosis of NECrotizing enterocolitis, a deep learning method to automatically detect and stratify the severity (surgical or medical) of NEC from no pathology in AXRs. The model is trainable end-to-end and integrates a Detection Transformer and Graph Convolution modules for localizing discriminative areas in AXRs, used to formulate subtle local embeddings. These are then combined with global image features to perform Fine-Grained Visual Classification (FGVC). We evaluate AIDNEC on our GOSH NEC dataset of 1153 images from 334 patients, achieving 79.7% accuracy in classifying NEC against No Pathology. AIDNEC outperforms the backbone by 2.6%, FGVC models by 2.5% and CheXNet by 4.2%, with statistically significant (two-tailed p 0.05) improvements, while providing meaningful discriminative regions to support the classification decision. Additional validation in the publicly available Chest X-ray14 dataset yields comparable performance to state-of-the-art methods, illustrating AIDNEC's robustness in a different X-ray classification task.