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An analysis is made of the dependence of the probability of network failure, presented in the form of reliability graphs, on the topological indicators of its elements, in particular, the variety of centrality proposed in the article in mediation. In connection with the study of the reliability of large networks (networks containing millions of elements), it became necessary to find critical groups of elements that have the greatest impact on the reliability of the system. The article solves the problem of quickly finding such elements without laborious analytical calculation. Monte Carlo analytical and statistical methods are used as methods in the article. As a result of the study, a method is obtained that allows one to find such groups of elements with a certain accuracy. As a confirmation of the great influence on the reliability of the system of the found group of elements, a repeated calculation of reliability was made with an increased probability of failure of the most influential nodes. The results obtained can effectively distribute resources to the most significant system nodes, and, accordingly, increase the reliability of these systems. The absence of a laborious calculation in the method makes it effective when working with large networks.

Dependence of the reliable graph failure probability on the topological indicators of its elements