Method of calculating of the information in social networks protection depending on the number of communities

Abstract

A mathematical model (linear system of differential equations) was developed and a research of the model of personal data protection against the number of communities and the intensity of data transfer in social networks was conducted. The linear system of information protection in social networks in the mathematical sense of this term is considered. When described by linear models, the object should be linear, at least approximately. This approach makes it quite simple to consider mathematical models. If such a thing is not noticed, it is necessary to examine the security system for linearity. Such dependecies has been studied: the dependence of the amount of information flow in the social network on the components of information protection, the amount of personal data, and the speed of the data flow; the security of the system on the size of the system (as well as on the amount of personal data); information security threats on the number of communities, and also calculated: – coefficient representing the impact of information protection measures; – coefficient representing the impact of data leakage rate; – the coefficient representing the influence of the amount of data on its leakage; – the coefficient representing the influence of the system size on system security; – coefficient representing the impact of system security on data leakage; – the number of connections in the social networks; – number of vertices in the social networks; – the parameter can be used to configure the network partitioning algorithm. The solution has been obtained - the harmonic oscillator equation, which breaks down into three cases: pre-resonance zone, resonance zone and post-resonance zone. So, the impact of the parameters of the number of communities on the parameters of the social network security system was investigated. Such a study is useful and important from the point of view of information protection in the network, since the parameters of the number of communities has significant influence, up to 100%, per protection indicator. As the result of research, it was established that social network security systems are non-linear.