  The analysis of temporal networks has a wide area of applications in a world
of technological advances. An important aspect of temporal network analysis is
the discovery of community structures. Real data networks are often very large
and the communities are observed to have a hierarchical structure referred to
as multi-scale communities. Changes in the community structure over time might
take place either at one scale or across all scales of the community structure.
The multilayer formulation of the modularity maximization (MM) method
introduced captures the changing multi-scale community structure of temporal
networks. This method introduces a coupling between communities in neighboring
time layers by allowing inter-layer connections, while different values of the
resolution parameter enable the detection of multi-scale communities. However,
the range of this parameter's values must be manually selected. When dealing
with real life data, communities at one or more scales can go undiscovered if
appropriate parameter ranges are not selected. A novel Temporal Multi-scale
Community Detection (TMSCD) method overcomes the obstacles mentioned above.
This is achieved by using the spectral properties of the temporal network
represented as a multilayer network. In this framework we select automatically
the range of relevant scales within which multi-scale community partitions are
sought.
