Abstract
At present, there are no quantitative studies of the dependence of the index of protection of personal data of actors in social medias on the parameters of its centrality, so this article presents the results of such researches in this area. Since the system of information protection of a social media network is nonlinear and depends on the parameters of a specific indicator of its centrality, mathematical equations have been developed to study the quantitative indicators of such a system, and the stability of the system has been investigated, which is graphically illustrated. The results obtained allow network administrators to analyze the behavior of the security system stability and take technical actions (operating system, firewall, network filter, etc.) that will keep the security indicator within the specified limits.
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