Simultaneous Degradation of Percolation and Cascade Robustness Under Targeted Hub Removal

TL;DR

This paper demonstrates that targeted removal of hubs in Barabási–Albert networks simultaneously degrades network connectivity and increases vulnerability to cascades, revealing a counterintuitive regime of network fragility.

Contribution

It uncovers a regime where hub removal worsens both percolation robustness and cascade resilience, supported by theoretical analysis and empirical experiments.

Findings

Hub removal raises percolation threshold significantly.

Removing hubs increases cascade sizes dramatically.

The effect is specific to BA networks and not observed in ER or WS models.

Abstract

Targeted hub removal is known to weaken connectivity in heterogeneous networks. We show that in Barab\'asi--Albert networks the same intervention can also shift Watts threshold dynamics across the cascade critical point. For BA networks with $N=2{,}000$ and $m=2$, removing the top 10\% of nodes by degree raises the bond-percolation threshold from $p_c=0.174$ to $0.776$ and, at $\varphi=0.22$, increases mean cascade size from $0.86\%$ (95\% CI 0.43--1.30) to $23.1\%$ (21.3--24.9). A controlled hub-vulnerability experiment on fixed topology shows that most of this cascade effect is dynamical: lowering hub activation thresholds produces much larger cascades even without deleting nodes, while deletion partly offsets the increase by removing edges. Using a configuration-model approximation, we derive the post-removal branching factor $z_1$ and identify a window in which the original network is subcritical but the hub-removed network is supercritical. The effect persists across system sizes and is not seen in matched ER or WS controls. These results identify a regime in which hub removal simultaneously worsens connectivity and cascade exposure in BA networks.