  We consider the problem of recovering a binary rating matrix as well as
clusters of users and items based on a partially observed matrix together with
side-information in the form of social and item similarity graphs. These two
graphs are both generated according to the celebrated stochastic block model
(SBM). We develop lower and upper bounds on sample complexity that match for
various scenarios. Our information-theoretic results quantify the benefits of
the availability of the social and item similarity graphs. Further analysis
reveals that under certain scenarios, the social and item similarity graphs
produce an interesting synergistic effect. This means that observing two graphs
is strictly better than observing just one in terms of reducing the sample
complexity.
