User-specified trust relations are often very sparse and dynamic, making them difficult to accurately predict from online social media. In addition, trust relations are usually unavailable for most social media platforms. These issues pose a great challenge for predicting trust relations and further building trust networks. In this study, we investigate whether we can predict trust relations via a sparse learning model, and propose to build a trust network without trust relations using only pervasively available interaction data and homophily effect in an online world. In particular, we analyze the reliability of predicting trust relations by interaction behaviors, and provide a principled way to mathematically incorporate interaction behaviors and homophily effect in a novel framework, bTrust. Results of experiments on real-world datasets from Epinions and Ciao demonstrated the effectiveness of the proposed framework. Further experiments were conducted to understand the importance of interaction behaviors and homophily effect in building trust networks.