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Learning the dependency relations among entities and the hierarchy formed by these relations by mapping entities into some order embedding space can effectively enable several important applications, including knowledge base completion and prerequisite relations prediction. Nevertheless, it is very challenging to learn a good order embedding due to the existence of partial ordering and missing relations in the observed data. Moreover, most application scenarios do not provide non-trivial negative dependency relation instances. We therefore propose a framework that performs dependency relation prediction by exploring both rich semantic and hierarchical structure information in the data. In particular, we propose several negative sampling strategies based on graph-specific centrality properties, which supplement the positive dependency relations with appropriate negative samples to effectively learn order embeddings. This research not only addresses the needs of automatically recovering missing dependency relations, but also unravels dependencies among entities using several real-world datasets, such as course dependency hierarchy involving course prerequisite relations, job hierarchy in organizations, and paper citation hierarchy. Extensive experiments are conducted on both synthetic and real-world datasets to demonstrate the prediction accuracy as well as to gain insights using the learned order embedding.