Controlling the uncertain response of real multiplex networks to random damage

Abstract

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 new 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.

Influencer identification in dynamical complex systems

“…In statistical physics and network science, a number of works have explored the large deviations of percolation., i.e. the deviations from the mean-field theory of percolation [60,61,62,63,64]. At q rand , there exist a number of possible configurations n such that G ∞ (n) = 0.…”

Spreading of localized attacks on spatial multiplex networks with a community structure

“…Therefore, many studies have been carried out to analyze cascading failures in interdependent networks [1][2][3][4][5][6][7][8][9][10][11]. Many of these studies have focused on the multiplex network model, which is an important example of an interdependent network where the same nodes are linked by different layers [12][13][14][15]. Further, in many real systems such as power grids and transportation systems, the links are of typical relatively short length due to the embedding in space [16].…”

Large deviations of random walks on random graphs

“…A different approach is to look at rare events arising from atypical initial conditions such as a low number of "infected" or "damaged" nodes evolving by contact or percolation dynamics to a large connected component [7][8][9][10][11]. Similarly, one can study how an initially large population spread on a network becomes extinct in time [12][13][14][15][16] or how a process transitions, more generally, between macroscopically distinct states [17].…”