Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system is a qualitatively better model than the classical single-layer aggreagated network approach. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to an equivalent single-layer graph. We show how our measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful super-families, and to detect tipping points in different time-varying multilayer graphs. These results suggest that information-theoretic approaches can be effectively employed in the study of multi-dimensional complex systems, and pave the way to a more systematic analysis of static and time-varying multidimensional complex systems.
Algorithmic complexity of multiplex networks
A. Santoro, V. Nicosia