Large Language Models (LLMs) are optimized to produce distributionally plausible continuations rather than to explicitly verify whether generated propositions are entailed by source documents. This inductive bias enables generalization, but it does not encode whether responses are grounded with respect to a reference. These issues limit the use of LLMs in domains where strict factual correctness is crucial, such as clinical decision support. Existing hallucination detection approaches improve factuality through retrieval augmentation, self-consistency, or claim verification, but generally do not learn directly over alignment topology. To leverage alignment topology as an inductive bias, we construct aligned bipartite graphs between reference information and LLM outputs and train a graph neural network (GNN) to model alignment structure using message passing. The method achieves state-of-the-art results on four diverse hallucination and question-answering datasets, outperforming all compared methods, including foundational LLMs such as GPT-4o.