Robustness of random networks with selective reinforcement against attacks

We investigate the robustness of random networks reinforced by adding hidden edges against targeted attacks. This study focuses on two types of reinforcement: uniform reinforcement, where edges are randomly added to all nodes, and selective reinforcement, where edges are randomly added only to the minimum degree nodes of the given network. We use generating functions to derive the giant component size and the critical threshold for the targeted attacks on reinforced networks. Applying our analysis and Monte Carlo simulations to the targeted attacks on scale-free networks, it becomes clear that selective reinforcement significantly improves the robustness of networks against the targeted attacks.