Node Attacks on Two-Mode Networks

Complex networks in real world inevitably suffer from diverse kinds of attacks. Due to the external attacks, some components of a network will be destroyed and therefore will lose their functions. In reality, the components of a network normally interact with one another. As a consequence, the dysfunction of some components is likely to cause the dysfunction of components that rely on the failed components. As the newly failed components may continue to cause the dysfunction of other network components, a system-level cascading dysfunction eventually could happen which can lead to the breakdown of the original network. It is therefore of great significance to assess the robustness of complex networks under attacks. In the literature, many network models and theories have been developed to study the robustness of complex networks. However, the majority of existing studies only investigate multilayer networks, while very little attention is paid to two-mode networks. Two-mode networks are an import ingredient of network sciences. Nevertheless, the structures of two-mode networks are different from that of multilayer networks. As a consequence, theories developed for multilayer networks cannot be applied to two-mode networks. With regard to this, in this paper we put forward a theoretical method to assess the robustness of two-mode networks under node attacks. By taking into account the special structures of two-mode networks as well as making use of probability theory, we therefore put forward the corresponding theory for calculating the robustness of two-mode networks to node failures. In order to verify the correctness of the proposed theory, we carry out simulations on computer-generated two-mode networks with compound Poisson degree distributions. The simulation results are in accordance with what are obtained from our developed theory. The simulation results have validated the correctness of our proposed method for robustness assessment of two-mode networks.