Percolation in multiplex networks with overlap

From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different networks (layers). Multiplexes may display an increased fragility with respect to the single layers that constitute them. However, so far the overlap of the links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. Here we show that the overlap among layers can improve the robustness of interdependent multiplex systems and change the critical behavior of the percolation phase transition in a complex way.