Flow cores and the problem of vulnerability of complex network systems

This article investigates vulnerability of complex network systems (NS) to simultaneous group negative impacts. Types of those impacts are analyzed, including, primarily targeted attacks and non-targeted system disruptions. The structural model of NS is considered and a modified pruning process algorithm is proposed with an aim to identify the network’s k-core. The scenario of simultaneous group attack on k-core as the primary assault target is developed. A flow model of network system is examined and a method is proposed to detect its flow core as the most functionally important system component. The flow core is used as a target for developed scenario of simultaneous group attack on the NS operation process. Implementations of scenarios of attacks on structural and flow cores of real-world network systems were compared. Also the usage of those scenarios in preventing spread of non-targeted disruptions was studied. The structural and flow-based approaches have been used to assess the consequences of simultaneous group negative impacts. This paper proposes methods for determining structural and flow aggregate-networks and its cores for multilayer network systems, that describe processes of intersystem interactions, and suggests how those methods can help developing strategies for protecting above mentioned cores before simultaneous group impacts.