Structural Cores and Problems of Vulnerability of Partially Overlapped Multilayer Networks

The concept of aggregate-network of multilayer network (MLN), which in many cases significantly simplifies the study of intersystem interactions is introduced, and the properties of its k-cores are investigated. The notion of p-cores is determined, with help of which the components of MLN that are directly involved in the implementation of intersystem interactions are distinguished. Methods of reducing the complexity of multilayer network models are investigated, which allow us to significantly decrease their dimensionality and better understand the processes that take place in intersystem interactions of different types. Effective scenarios of simultaneous group and system-wide targeted attacks on partially overlapped multilayer networks have been proposed, the main attention of which is focused on the transition points of MLN through which the intersystem interactions are actually implemented. It is shown that these scenarios can also be used to solve the inverse problem, namely, which elements of MLN should be blocked in the first place to prevent the acceleration of spread of dangerous infectious epidemics diseases, etc.