Abstract
The architecture of many complex systems is well described by multiplex
interaction networks, and their dynamics is often the result of several
intertwined processes taking place at different levels. However only in a few
cases can such multi-layered architecture be empirically observed, as one
usually only has experimental access to such structure from an aggregated
projection. A fundamental question is thus to determine whether the hidden
underlying architecture of complex systems is better modelled as a single
interaction layer or results from the aggregation and interplay of multiple
layers. Here we show that, by only using local information provided by a random
walker navigating the aggregated network, it is possible to decide in a robust
way if the underlying structure is a multiplex and, in the latter case, to
determine the most probable number of layers. The proposed methodology detects
and estimates the optimal architecture capable of reproducing observable non-
Markovian dynamics taking place on networks, with applications ranging from
human or animal mobility to electronic transport or molecular motors.
Furthermore, the mathematical theory extends above and beyond detection of
physical layers in networked complex systems, as it provides a general solution
for the optimal decomposition of complex dynamics in a Markov switching
combination of simple (diffusive) dynamics.
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