Bound and exact methods for assessing link vulnerability in complex networks

Assessing network systems for failures is critical to mitigate the risk and develop proactive responses. In this paper, we investigate devastating consequences of link failures in networks. We propose an exact algorithm and a spectral lowerbound on the minimum number of removed links to incur a significant level of disruption. Our exact solution can identify optimal solutions in both uniform and weighted networks through solving a well-constructed mixed integer program. Also, our spectral lower-bound derives from the Laplacian eigenvalues an estimation on the vulnerability of large networks that are intractable for exact methods. Through experiments on both synthetic and real-world networks, we demonstrate the efficiency of the proposed methods.