Robustness analysis of partially interdependent networks with different coupling preferences and multicluster functional nodes in VCMS

Networks shaped by different cells of a Virtual Cellular Manufacturing System (VCMS) are partially interdependent, and some nodes not belonging to the Global Giant Component (GGC) can still remain functional. In this case, a model of a VCMS network is partly different from or beyond the consideration of those in past studies. In this paper, the robustness of the interdependent network is explored, which is more similar to that of a VCMS. A demonstrative process is provided, and the cascading process of a network under random attacks is analyzed. Numerical simulations for three types of coupled networks [BA (Barabási and Albert)–BA, BA–WS (Watts and Strogatz), and WS–WS] are performed to study the relationship of the robustness with the coupling strength and the GGC coefficient. Some findings are summarized as follows: (i) increasing the coupling strength between subnetworks may decrease the robustness of the interdependent network and lead to a transition from a second-order phase to a first-order phase; (ii) a small GGC coefficient can enhance the robustness of the interdependent network, and gradually increasing the GGC coefficient can result in a second-order phase transition, hybrid phase transition, and first-order phase transition; and (iii) the WS–BA coupled network is more vulnerable than the BA–BA network, but is more robust than the WS–WS network.