Vulnerability of complex networks under path-based attacks

• We study the longest-path attacks on complex networks.
• We propose two approximating algorithms for finding the approximately longest path.
• Homogeneous networks are fragile to longest-path attacks.

We investigate vulnerability of complex networks including model networks and real-world networks subject to path-based attacks. Specifically, we remove approximately the longest simple path from a network iteratively until there are no paths left in the network. We propose two algorithms, the random augmenting approach (RPA) and the Hamilton-path based approach (HPA), for finding the approximately longest simple path in a network. Results demonstrate that steps of longest-path attacks increase with network density linearly for random networks, while exponentially increasing for scale-free networks. The more homogeneous the degree distribution is, the more fragile the network, which is different from the previous results of node or edge attacks. HPA is generally more efficient than RPA in the longest-path attacks of complex networks. These findings further help us understand the vulnerability of complex systems, better protect complex systems, and design more tolerant complex systems.