Robustness of networks with dependency topology

The robustness of complex networks with dependency links has been studied in recent years. However, previous studies focused mostly on the robustness of networks with dependency relations having local and simple structures, not considering the general cases where global network topology is formed by dependency links. Here, we analyze the percolation properties of network models composed of both connectivity and dependency links, where in addition to the usual connectivity links, dependency links also follow a certain network topology. We perform theoretical analysis and numerical simulations to understand the critical effects of dependency topology on the network robustness. Our results suggest that for a given network topology of connectivity, dependency topology can influence the network robustness, leading to different percolation types. Furthermore, we also give the theoretical analysis and simulation results on different combinations of connectivity topology and dependency topology. Our results may help to design and optimize the network robustness considering the underlying complicated dependency relationships.