Breakup of Directed Multipartite Networks

A complex network in reality often consists of profuse components, which might suffer from unpredictable perturbations. Because the components of a network could be interdependent, therefore the failures of a few components may trigger catastrophes to the entire network. It is thus pivotal to exploit the robustness of complex networks. Existing studies on network robustness mainly deal with interdependent or multilayer networks; little work is done to investigate the robustness of multipartite networks, which are an indispensable part of complex networks. Here, we plumb the robustness of directed multipartite networks. To be specific, we exploit the robustness of bi-directed and unidirectional multipartite networks in face of random node failures. We, respectively, establish cascading and non-cascading models based on the largest connected component concept for depicting the dynamical processes on bi-directed and unidirectional multipartite networks subject to perturbations. Based on our developed models, we, respectively, derive the corresponding percolation theories for mathematically computing the robustness of directed multipartite networks subject to random node failures. We unravel the first-order and second-order phase transition phenomena on the robustness of directed multipartite networks. The correctness of our developed theories has been verified through experiments on computer-generated as well as real-world multipartite networks.