  Multilayer networks or MLNs (also called multiplexes or network of networks)
are being used extensively for modeling and analysis of data sets with multiple
entity and feature types as well as their relationships. As the concept of
communities and hubs are used for these analysis, a structure-preserving
definition for them on MLNs (that retains the original MLN structure and
node/edge labels and types) and its efficient detection are critical. There is
no structure-preserving definition of a community for a MLN as most of the
current analyses aggregate a MLN to a single graph. Although there is consensus
on community definition for single graphs (and detection packages) and to a
lesser extent for homogeneous MLNs, it is lacking for heterogeneous MLNs. In
this paper, we not only provide a structure-preserving definition for the first
time, but also its efficient computation using a decoupling approach, and
discuss its characteristics & significance for analysis. The proposed
decoupling approach for efficiency combines communities from individual layers
to form a serial k-community for connected k layers in a MLN. We propose
several weight metrics for composing layer-wise communities using the bipartite
graph match approach based on the analysis semantics. Our proposed approach has
a number of advantages. It: i) leverages extant single graph community
detection algorithms, ii) is based on the widely-used maximal flow bipartite
graph matching for composing k layers, iii) introduces several weight metrics
that are customized for the community concept, and iv) experimentally validates
the definition, mapping, and efficiency from a flexible analysis perspective on
widely-used IMDb data set.
  Keywords: Heterogeneous Multilayer Networks; Bipartite Graphs; Community
Definition and Detection; Decoupling-Based Composition
