  Complex systems are usually illustrated by networks which captures the
topology of the interactions between the entities. To better understand the
roles played by the entities in the system one needs to uncover the underlying
community structure of the system. In recent years, systems with interactions
that have various types or can change over time between the entities have
attracted an increasing research attention. However, algorithms aiming to solve
the key problem - community detection - in multilayer networks are still
limited. In this work, we first introduce the multilayer network model
representation with multiple aspects, which is flexible to a variety of
networks. Then based on this model, we naturally derive the multilayer
modularity - a widely adopted objective function of community detection in
networks - from a static perspective as an evaluation metric to evaluate the
quality of the communities detected in multilayer networks. It enables us to
better understand the essence of the modularity by pointing out the specific
kind of communities that will lead to a high modularity score. We also propose
a spectral method called mSpec for the optimization of the proposed modularity
function based on the supra-adjacency representation of the multilayer
networks. Experiments on the electroencephalograph network and the comparison
results on several empirical multilayer networks demonstrate the feasibility
and reliable performance of the proposed method.
