What can connectivity characteristics of networks tell us about the quality of link predictions?

Link prediction in networks works better when those networks are connected and not sparse. But can we use common connec-tivity characteristics to decide once a network is well enough connected to allow a random walk process to predict links best? Recent results in our work on link prediction lead us to ask this question and we attempt to shed some light on it. We do this by combining networks stemming from different data sources into networks combining different numbers of layers, and connecting their connectivity characteristics to the AUC that can be achieved by a random walk algorithm for link prediction. What we find is that it seems to be very important to reduce the radius and diameter of the network as much as possible, and get close to having a single connected component in the network. We also argue that the five benchmark data sets that have been used in the literature on drug-target activity prediction might be too easy to allow meaningful evaluations.