  Network inference is the process of learning the properties of complex
networks from data. Besides using information about known links in the network,
node attributes and other forms of network metadata can help to solve network
inference problems. Indeed, several approaches have been proposed to introduce
metadata into probabilistic network models and to use them to make better
inferences. However, we know little about the effect of such metadata in the
inference process. Here, we investigate this issue. We find that, rather than
affecting inference gradually, adding metadata causes abrupt transitions in the
inference process and in our ability to make accurate predictions, from a
situation in which metadata does not play any role to a situation in which
metadata completely dominates the inference process. When network data and
metadata are partly correlated, metadata optimally contributes to the inference
process at the transition between data-dominated and metadata-dominated
regimes.
