Social networking websites have facilitated a new style of communication through blogs, instant messaging, and various other techniques. Through collaboration, millions of users participate in millions of discussions every day. However, it is still difficult to determine the extent to which such discussions affect the emotions of the participants. We surmise that emotionally-oriented discussions may affect a given user's general emotional bent and be reflected in other discussions he or she may initiate or participate in. It is in this way that emotion (or sentiment) may propagate through a network. In this paper, we analyze sentiment propagation in social networks, review the importance and challenges of such a study, and provide methodologies for measuring this kind of propagation. A case study has been conducted on a large dataset gathered from the LiveJournal social network. Experimental results are promising in revealing some aspects of the sentiment propagation taking place in social networks.