Percolation in real interdependent networks*

The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network layers is generally framed and characterized in terms of percolation models. In this talk, I will consider three different variants of percolation models that provide different insights on the robustness of real-world interdependent networks. I will first consider the ordinary percolation model and illustrate a theoretical approach consisting in a system of heuristic equations able to approximate the phase diagram for arbitrary networks. Second, I will introduce and characterize the redundant percolation model, a genuine model for interdependent networks where the addition of new layers boosts system robustness by creating redundant interdependencies among network layers. Third, I will generalize the problem of optimal percolation
from single-layer to multi-layer networks, and present several algorithms for finding approximate solutions to the problem.