arXiv:2603.04838v1 Announce Type: new
Abstract: Hub removal in scale-free networks is known to degrade percolation robustness by raising the bond percolation threshold. We show that this same intervention simultaneously triggers a cascade phase transition under the Watts threshold model. In Barab’asi–Albert networks, removing the top 10% of nodes by degree raises $p_c$ from 0.34 to 0.90, reducing robustness to random edge failure. Simultaneously, at cascade threshold $varphi=0.22$, mean cascade size increases from $0.29%$ to $20.6%$, crossing from the subcritical to supercritical regime — compounding, rather than trading off, the percolation degradation.
Using a controlled experiment that independently varies hub presence and hub activation threshold, we demonstrate that hub-mediated cascade suppression is primarily dynamical: making hubs vulnerable without removing them produces 95% cascades versus 19% with removal.
We operationalize Watts’ (2002) stable-node mechanism as a quantitative condition $k > 1/varphi$ and derive, under the configuration-model approximation, a closed-form expression for the post-removal cascade branching factor $z_1(varphi, alpha, m)$. This predicts a newly opened interval where the pre-removal network is subcritical but the post-removal network is supercritical. We define $varphi^*$ as the upper supercritical boundary, $varphi^* = sup{varphi : z_1(varphi) geq 1}$. The $z_1$ derivation confirms that at $varphi=0.22$, the pre-removal network is subcritical ($z_1=0.850$) while the post-removal network is supercritical ($z_1=1.195$). Our results establish that hub manipulation creates compounding vulnerability: both percolation and cascade metrics worsen simultaneously on static, unweighted networks. The effect vanishes in homogeneous networks (ER, WS).