Spectral-gradient iterative edge attack for synchronization suppression in complex networks

The synchronization of complex networks, governed by the generalized Fiedler value (γ) of the Laplacian matrix, is critical for functional stability and energy efficiency. However, this property also renders networks vulnerable to targeted disruptions. Traditional percolation-based attack strategies, which focus on structural integrity, often fail to effectively suppress synchronization. This study introduces a Laplacian spectral perturbation approach to systematically identify and remove edges critical to synchronization. By deriving the sensitivity of γ to topological changes and leveraging the gradient of the Fiedler vector, we quantify each edge's contribution to synchronization, revealing its connection to community structure. We propose the Fiedler Gradient Iterative Attack (FGIA) algorithm for static networks, which constructs locally optimal edge-removal sequences to maximize γ degradation while preserving global connectivity. FGIA achieves computational efficiency, outperforming brute-force methods and conventional centrality-based attacks. Extensive simulations on synthetic and real-world networks demonstrate FGIA's superior performance in synchronization suppression, offering practical applications in neuroscience and critical infrastructure protection.