  A wide range of complex systems can be modeled as networks with corresponding
constraints on the edges and nodes, which have been extensively studied in
recent years. Nowadays, with the progress of information technology, systems
that contain the information collected from multiple perspectives have been
generated. The conventional models designed for single perspective networks
fail to depict the diverse topological properties of such systems, so
multilayer network models aiming at describing the structure of these networks
emerge. As a major concern in network science, decomposing the networks into
communities, which usually refers to closely interconnected node groups,
extracts valuable information about the structure and interactions of the
network. Unlike the contention of dozens of models and methods in conventional
single-layer networks, methods aiming at discovering the communities in the
multilayer networks are still limited. In order to help explore the community
structure in multilayer networks, we propose the multilayer edge mixture model,
which explores a relatively general form of a community structure evaluator
from an edge combination view. As an example, we demonstrate that the
multilayer modularity and stochastic blockmodels can be derived from the
proposed model. We also explore the decomposition of community structure
evaluators with specific forms to the multilayer edge mixture model
representation, which turns out to reveal some new interpretation of the
evaluators. The flexibility and performance on different networks of the
proposed model are illustrated with applications on a series of benchmark
networks.
