Firms are increasingly becoming interested in harnessing the potential of online social networks for marketing purposes. Marketers are therefore interested in understanding the antecedents and consequences of relationship formation within such social networks and in predicting the interactivity among users. In this paper we develop an integrated statistical framework for simultaneously modeling the connectivity structure of multiple relationships of different types on the same set of individuals. Our modeling approach accommodates both the directionality and intensity of network connections and in particular, we show how sparse network connections can be modeled when dealing with weighted relationships. We develop hierarchical Bayesian methods for inference for the resulting model, and then apply our model to data from an online social network of music artists. In our application we model friendship, communication and music download relationships among these artists. We find that these relationships are impacted by common antecedents and users exhibit similar roles across the three relationships. We also find that it is crucial to model the sparsity of connections so as to recover and predict the macrostructure of the network connections.