Percolation behaviors of a network of networks under intentional attack with limited information

As an important class of real coupled networks, a network of networks portrays the interdependence and coexistence between complex systems. Especially for large networks, one may not know the information of all nodes in the network, only limited information can be known. Motivated by this, we here propose a new attack strategy, the intentional attack with limited information, where the limited information represents that the information of only n nodes is known. Further, we investigate the percolation behavior of large-scale network systems, a network of networks with different dependency patterns, under intentional attack with limited information. We show analytically and numerically how the coupling strength q and n affect the percolation, critical threshold, and the critical coupling strength. Furthermore, as n increases, the results suggest that the system becomes more vulnerable and different to protect. But when n reaches a critical value, the critical threshold pc tends to a steady-state and doesn't change appreciably with n. In particular, we find a new general scaling relationship between 1/pc and 1/n for different network configuration. Our model sheds light on the resilience of large-scale interdependent networks under limited information attacks, and provides helpful insights into designing robust real-world systems.