We present a graph-based semi-supervised learning for the question-answering (QA) task for ranking candidate sentences. Using textual entailment analysis, we obtain entailment scores between a natural language question posed by the user and the candidate sentences returned from search engine. The textual entailment between two sentences is assessed via features representing high-level attributes of the entailment problem such as sentence structure matching, question-type named-entity matching based on a question-classifier, etc. We implement a semi-supervised learning (SSL) approach to demonstrate that utilization of more unlabeled data points can improve the answer-ranking task of QA. We create a graph for labeled and unlabeled data using match-scores of textual entailment features as similarity weights between data points. We apply a summarization method on the graph to make the computations feasible on large datasets. With a new representation of graph-based SSL on QA datasets usin...