Robust allocation of weighted dependency links in cyber–physical networks

Interdependent network models are often used to show how one network has an effect on another network through dependencies. In this paper, we propose a novel interdependent network model which consists of two individual networks with unequal numbers of nodes and one-to-multiple weighted dependency links between the two networks. Based on realistic assumptions, this model differs from previous works that considered equal numbers of nodes in the two networks and identical dependency links. We formulate an optimization problem to allocate dependency links using least resources. This novel model enhances the practicability of traditional cyber–physical system structures, but it makes the dependency link deployment problem more complex and the optimization problem cannot be solved in large networks. To overcome this problem, we propose a new algorithm based on a revised network flow method. Extensive simulations on random networks and real networks show that our deployment method produces topologies that are more robust than the ones obtained by other deployment techniques. Results indicate that our algorithm is efficient and cost-effective in designing robust interdependent networks, and our deployment method is suitable for networks of any size.