An approach for modeling vulnerability of the network of networks

In this paper, a framework is given to model the network of networks and to investigate the vulnerability of the network of networks subjected to failures. Because there are several redundant systems in infrastructure systems, the dependent intensity between two networks is introduced and adopted to discuss the vulnerability of the interdependent infrastructure networks subjected to failures. Shanghai electrified rail transit network is used to illustrate the feasibility and effectiveness of the proposed framework. Because the rail network is dependent on the power grid and communication network, the corresponding power grid and communication network are also included in this system. Meanwhile the failures to the power grid and communication network are utilized to investigate the vulnerability of the rail network. The results show that the rail network strongly depends on the power grid and weakly depends on the communication network, and the transport functionality loss of the rail network increases with the increase of dependent intensity. Meanwhile the highest betweenness node-based attack to the power grid and the largest degree node-based attack to the communication network can result in the most functionality losses to the rail network. Moreover, the functionality loss of the rail network has the smallest value when the tolerance parameter of the power grid equals 0.75 and the critical nodes of the power grid and communication network can be obtained by simulations.