Many complex systems, both natural, and man-made, can be represented as multiplex or interdependent networks. Multiple dependencies make a system more fragile: damage to one element can lead to avalanches of failures throughout the system. In this talk I will present recent developments about the structural properties of multiplex networks. The transition founded is asymmetric. It is hybrid in nature, having a discontinuity like a first-order transition, but exhibiting critical behavior, only above the transition, like a second-order transition.
I will also present a theory that enables us to find the giant mutually connected component in a two-layer multiplex network with arbitrary correlations between connections of different types. I will also show results for the case of “weak” percolation.