The authors consider an application of PageRank to recommendation in the case where explicit ratings are available. The vertices of the graph represent items to be recommended, and the weight of the edge between any two vertices is proportional to the number of users that have interacted with both the corresponding items (thus the explicit ratings are not incorporated into the graph itself). To obtain recommendations for a particular user, the “reset-” (or “teleport-“) vector of is set to be the explicit ratings given by the user (0 is used for the absence of a rating), PageRank is run and then resulting importances are used to rank the items.
It seems to me that this set-up would be more sensible in contexts where the behavioural data was implicit (e.g. user looked at particular item) rather that explicit (user gave a particular rating to a particular item) – in the explicit context the use of the value 0 for the absence of rating can not be motivated.
The authors test their approach on the MovieLens dataset.
As the authors themselves note, PageRank had been used for personalised (more generally, deliberately biased) recommendation before their work (e.g. Haveliwala “Topic sensitive Pagerank”, 2002). The novelty here lies in the construction of the graph from the user-item interaction matrix.