Annotation: The concept of cyber resilience of complex systems is largely determined by the ability of their network structures to be rebuilt in such a way as to neutralize the impact of an attack already implemented on the system or to make its successful implementation impossible when detected at an early stage. It is proposed to solve the problem of synthesis to ensure cyber resilience of network structures both at the stage of system design (synthesis "from scratch") and at the stage of their operation (synthesis-restructuring). The paper presents modeling of the impact of massive and targeted attacks on the system, considers the constraints on synthesis, and formulates synthesis criteria in terms of graph theory. The obtained theoretical results are the basis for practical construction of cyber-resistant network structures and their rebuilding under attack

Keywords: cyber resilience, target function, synthesis, graph stability, graph integrity