Controlling the uncertain response of real multiplex networks to random damage

We reveal large fluctuations in the response of real multiplex networks to random damage of nodes. These results indicate that the average response to random damage, traditionally considered in mean-field approaches to percolation, is a poor metric of system robustness. We show instead that a large-deviation approach to percolation provides a more accurate characterization of system robustness. We identify an effective percolation threshold at which we observe a clear abrupt transition separating two distinct regimes in which the most likely response to damage is either a functional or a dismantled multiplex network. We leverage our findings to propose a metric, named safeguard centrality, able to single out the nodes that control the response of the entire multiplex network to random damage. We show that safeguarding the function of top-scoring nodes is sufficient to prevent system collapse.