  Many systems exhibit complex temporal dynamics due to the presence of
different processes taking place simultaneously. An important task in such
systems is to extract a simplified view of their time-dependent network of
interactions. Community detection in temporal networks usually relies on
aggregation over time windows or consider sequences of different stationary
epochs. For dynamics-based methods, attempts to generalize static-network
methodologies also face the fundamental difficulty that a stationary state of
the dynamics does not always exist. Here, we derive a method based on a
dynamical process evolving on the temporal network. Our method allows dynamics
that do not reach a steady state and uncovers two sets of communities for a
given time interval that accounts for the ordering of edges in forward and
backward time. We show that our method provides a natural way to disentangle
the different dynamical scales present in a system with synthetic and
real-world examples.
