Methods for assessing the connectivity of an undirected bipolar labeled graph taking into account the destructive impact of external threats on its vertices

Abstract

Objective. The main arguments that position the problem of assessing the connectivity of the bipolar graph in relation to the conditions of destructive impact of external threats (threats) as relevant for assessing the vitality of information systems (IS) are discussed operating under conditions of information security threats.Method. The following are presented: formulation of the problem of assessing connectivity for conditions of exposure to threats; a brief overview of existing methods for structural modeling of bipolar structures; results of the analysis of the applicability of existing methods for assessing the stability of functioning (stability) of bipolar structures in relation to conditions of exposure to threats. The initial conditions are accepted: the stability of the information system as a whole depends deterministically on the stability of its structural elements and the network structure itself; the problem of assessing the connectivity of a two-pole structure is basic for assessing the connectivity of the corresponding multi-pole structures; the stability analysis of the impacted object is carried out using minimax criteria, and the result is presented in the form of the minimum value of the stability function and the moment in time of the occurrence of this event.Result. Limiting factors that prevent the use of existing methods to solve the problem have been identified. The main limiting factor is that existing methods are based on probabilistic stationary models that require representative statistics. The second, no less important limiting factor is that the situation characterizing the impact of threats is very dynamic (not stationary), the events themselves are very rare, and the assessment period is comparable to the period of response to threats, which does not allow obtaining effective assessments of sustainability. It is proposed to: generalize existing methods for conditions of non-stationary functioning process, for which, when assessing, take into account changes in the probabilistic characteristics of nodal elements over time; as an indicator characterizing connectivity, use the minimum value of the stability function determined during the period of exposure to threats. The price to pay for ensuring the sustainability of the functioning of the affected object under the influence of threats is the need to ensure structural redundancy.Conclusion. The results of the study can be used by persons who simulate both the object of impact and the processes of its functioning, to make a decision on ensuring the continuity of production processes under the conditions of the impact of threats.