Scaling of percolation transitions on Erdös-Rényi networks under centrality-based attacks

Abstract

The study of network robustness focuses on the way the overall functionality of a network is affected as some of its constituent parts fail. Failures can occur at random or be part of an intentional attack and, in general, networks behave differently against different removal strategies. Although much effort has been put on this topic, there is no unified framework to study the problem. Whilst random failures have been mostly studied under percolation theory, targeted attacks have been recently restated in terms of network dismantling. In this work, we link these two approaches by performing a finite-size scaling analysis to four dismantling strategies over Erdös-Rényi networks: initial and recalculated high degree removal (ID and RD) and initial and recalculated high betweenness removal (IB and RB). We find that both degree-based attacks lie into the same universality class, but the betweenness-based attacks differ significantly. In particular, RB produces a very abrupt transition with a hump in the cluster size distribution near the critical point, resembling some explosive percolation processes. *

Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks

“…The extension of our analysis to updated attacks and its comparison with the present results would be an interesting research direction. In this line, we recall that in Erdös-Rényi networks, updating betweenness changes the universality class of the attack [28] and presents a percolation threshold close to the optimal value [20]. Also, in DT networks, Norrenbrock, et al [8] showed that this attack has a percolation threshold f c = 0, but the thermodynamic properties of the transition remain unknown.…”

“…They conclude that the RD attack belongs to the standard two-dimensional percolation transition universality class. For RB, the percolation threshold is located at f c = 1 − p c = 0, and even when the nature of the transition was not explored by these authors it seems to be abrupt as in the case of Erdös Renyi networks [28].…”

“…In particular, in the case of betweenness attacks, few works address this point. Previous works in planar graphs [8] and random Erdös Renyi networks [28] seem to indicate that recalculated attacks based on betweenness could induce discontinuous transitions. In particular, Norrenbrock, et al [8] study the percolation transition for both recalculated degree-based (RD) and betweenness-based (RB) attacks on four different models of spatial networks, including DT.…”

“…In most cases, BC attacks overtake the rest of the strategies considered. In a recent work [28], it was also reported that even networks with homogeneous betweenness distribution can be efficiently dismantled using betweenness-based attacks.…”

Percolation on feature-enriched interconnected systems

“…Degree is the most basic centrality measure in complex networks. However, there exist a plethora of alternatives to asses the importance of a node within a graph [22][23][24] , and accordingly, we can test the importance of these variables on the network robustness by performing attacks based on them [25][26][27] and evaluate how far is each attack strategy from being optimal 28 . Moreover, nodes could be characterized by non-topological properties as well, such as age 29 , biomass 30 or bank credibility 31 .…”