PhD ThesesThe multiplex network paradigm has proven very helpful in the study of many real-world
complex systems, by allowing to retain full information about all the different possible kinds of
relationships among the elements of a system. As a result, new non-trivial structural patterns
have been found in diverse multi-dimensional networked systems, from transportation networks to
the human brain. However, the analysis of multiplex structural and dynamical properties often
requires more sophisticated algorithms and takes longer time to run compared to traditional
single network methods. As a consequence, relying on a multiplex formulation should be the
outcome of a trade-off between the level of information and the resources required to store it.
In the first part of the thesis, we address the problem of quantifying and comparing the
amount of information contained in multiplex networks. We propose an algorithmic informationtheoretic
approach to evaluate the complexity of multiplex networks, by assessing to which extent
a given multiplex representation of a system is more informative than a single-layer graph. Then,
we demonstrate that the same measure is able to detect redundancy in a multiplex network and
to obtain meaningful lower-dimensional representations of a system. We finally show that such
method allows us to retain most of the structural complexity of the original system as well as
the salient characteristics determining the behaviour of dynamical processes happening on it.
In the second part of the thesis, we shift the focus to the modelling and analysis of some structural
features of real-world multiplex systems throughout optimisation principles. We demonstrate
that Pareto optimal principles provide remarkable tools not only to model real-world
multiplex transportation systems but also to characterise the robustness of multiplex systems
against targeted attacks in the context of optimal percolation
