This research studies graph-based approaches for Answer Sentence Selection (AS2), an essential component for retrieval-based Question Answering (QA) systems. During offline learning, our model constructs a small-scale relevant training graph per question in an unsupervised manner, and integrates with Graph Neural Networks. Graph nodes are question sentence to answer sentence pairs. We train and integrate state-of-the-art (SOTA) models for computing scores between question-question, question-answer, and answer-answer pairs, and use thresholding on relevance scores for creating graph edges. Online inference is then performed to solve the AS2 task on unseen queries. Experiments on two well-known academic benchmarks and a real-world dataset show that our approach consistently outperforms SOTA QA baseline models.