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

TL;DR

This study investigates how two-dimensional random lattices respond to betweenness centrality-based attacks, revealing that full-range attacks cause abrupt network failures, while limited-range attacks lead to gradual percolation transitions.

Contribution

The paper demonstrates that betweenness centrality captures network robustness across scales and shows that finite-range approximations can miss critical attack effects.

Findings

Full-range betweenness attacks cause discontinuous percolation transitions.

Finite-range approximations require the cutoff to scale faster than L^{0.91} to replicate full-range behavior.

Betweenness centrality encodes multi-scale information about network robustness.

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 $\ell$-betweenness, where paths having more than $\ell$ steps are ignored. For finite $\ell$, 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 $\ell$-betweenness if the cutoff is allowed to scale with the linear length of the network faster than $\ell\sim L^{0.91}$. 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.