  The generalized version of modularity for multilayer networks, a.k.a.
multislice modularity, is characterized by two model parameters, namely
resolution factor and inter-layer coupling factor. The former corresponds to a
notion of layer-specific relevance, whereas the inter-layer coupling factor
represents the strength of node connections across the network layers. Despite
the potential of this approach, the setting of both parameters can be
arbitrarily selected, without considering specific characteristics from the
topology of the multilayer network as well as from an available community
structure. Also, the multislice modularity is not designed to explicitly model
order relations over the layers, which is of prior importance for dynamic
networks.
  This paper aims to overcome the main limitations of the multislice modularity
by introducing a new formulation of modularity for multilayer networks. We
revise the role and semantics of both the resolution and inter-layer coupling
factors based on information available from the within-layer and inter-layer
structures of the multilayer communities. Also, our proposed multilayer
modularity is general enough to consider orderings of network layers and their
constraints on layer coupling. Experiments were carried out on synthetic and
real-world multilayer networks using state-of-the-art approaches for multilayer
community detection. The obtained results have shown the meaningfulness of the
proposed modularity, revealing the effects of different combinations of the
resolution and inter-layer coupling functions. This work also represents a
starting point for the development of new optimization methods for community
detection in multilayer networks.
