By far, the most prevalent data available in social media is tagging information. For example, in del.icio.us a user may tag a URL or in Flickr she may tag an image. One of the questions that comes up is how to then cluster social data that is rich in tags. Some techniques available ignore the user information and use only a bipartite graph consisting of tags and URLs. Another method is to represent two pieces of evidence (user-tag;tag-blog) in a tripartite graph (where nodes are of three different types: users, tags and urls). However, even this type of structure actually misses the higher order relation between the three nodes. Note that the information available is really in triples of the type <user, tag, url>. This information is not captured by the tripartite graph model. In particular, two users may be connected via a common tag even if the actual URL they bookmarked is vastly different.
There are some techniques using Tensor Matrix Factorization that can handle such data. However, the question of how to deal with triple (or higher) information from social data is quite interesting. Moreover, being able to do so efficiently and in an online fashion would also be important. I believe that this topic may be of significant interest in the upcoming social media and data mining conferences. The implications of these techniques would be in building better recommendation systems and personalization algorithms.
[Thanks Vlad Korolev for some of the discussions related to this post]