Locally Optimal Percolation for Network Resilience Dismantling via Fiedler Vector Gradient Iterative Attack

Abstract: Network resilience, dynamically quantified by the Fiedler value ((\lambda_2),the second smallest eigenvalue of the Laplacian matrix) ensures functional stability and efficient energy transmission, yet also introduces vulnerabilities that dismantling the resilience of the network can cause a functional breakdown of the network. However, traditional percolation strategies focused on structural attacks often fail to effectively affect resilience and lack universal applicability. Here, we employ a Laplacian spectral perturbation approach to systematically identify and remove edges critical to resilience. We derive the sensitivity of (\lambda_2) to topological changes and employ the gradient of Fiedler vector to measure each edge's contribution of resilience, revealing an intrinsic relationship to community partition. Accordingly, we propose the Fiedler Gradient Iterative Attack (FGIA) algorithm, which constructs locally optimal edge removal sequences to maximize (\lambda_2) degradation with significantly lower computational cost than brute-force methods. Our results offer a rigorous approach for inducing controlled resilience collapse, with potential applications in neuroscience and critical infrastructure protection.