Simultaneous Degradation of Percolation and Cascade Robustness Under Targeted Hub Removal

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.