  Modularity based community detection encompasses a number of widely used,
efficient heuristics for identification of structure in networks. Recently, a
belief propagation approach to modularity optimization provided a useful guide
for identifying non-trivial structure in single-layer networks in a way that
other optimization heuristics have not. In this paper, we extend modularity
belief propagation to multilayer networks. As part of this development, we also
directly incorporate a resolution parameter. We show that adjusting the
resolution parameter affects the convergence properties of the algorithm and
yields different community structures than the baseline. We compare our
approach with a widely used community detection tool, GenLouvain, across a
range of synthetic, multilayer benchmark networks, demonstrating that our
method performs comparably to the state of the art. Finally, we demonstrate the
practical advantages of the additional information provided by our tool by way
of two real-world network examples. We show how the convergence properties of
the algorithm can be used in selecting the appropriate resolution and coupling
parameters and how the node-level marginals provide an interpretation for the
strength of attachment to the identified communities. We have released our tool
as a Python package for convenient use.
