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

Abstract

In the present paper, we study the robustness of two-dimensional random lattices (Delaunay triangulations) under attacks based on betweenness centrality. Together with the standard definition of this centrality measure, we employ a range-limited approximation known as ℓ-betweenness, where paths having more than ℓ steps are ignored. For finite ℓ, the attacks produce continuous percolation transitions that belong to the universality class of random percolation. On the other hand, the attack under the full range betweenness induces a discontinuous transition that, in the thermodynamic limit, occurs after removing a sub-extensive amount of nodes. This behavior is recovered for ℓ-betweenness if the cutoff is allowed to scale with the linear length of the network faster than ℓ∼L0.91. Our results suggest that betweenness centrality encodes information on network robustness at all scales, and thus cannot be approximated using finite-ranged calculations without losing attack efficiency.