  Community detection in networks is commonly performed using information about
interactions between nodes. Recent advances have been made to incorporate
multiple types of interactions, thus generalizing standard methods to
multilayer networks. Often though, one can access additional information
regarding individual nodes, attributes or covariates. A relevant question is
thus how to properly incorporate this extra information in such frameworks.
Here we develop a method that incorporates both the topology of interactions
and node attributes to extract communities in multilayer networks. We propose a
principled probabilistic method that does not assume any a priori correlation
structure between attributes and communities but rather infers this from data.
This leads to an efficient algorithmic implementation that exploits the
sparsity of the dataset and can be used to perform several inference tasks; we
provide an open-source implementation of the code online. We demonstrate our
method on both synthetic and real-world data and compare performance with
methods that do not use any attribute information. We find that including node
information helps in predicting missing links or attributes. It also leads to
more interpretable community structures and allows the quantification of the
impact of the node attributes given in input.
