Abstract
Based on the empirical analysis of contacts in the social network VKontakte, quantitative patterns are established that describe the distribution of users of social networks by the number of contacts (the number of friends). The parameter entering into the differential equation, whose solution is the proposed distribution, makes sense, similar to the Dunbar number and approximately coincides with it in magnitude. The fact that parameters characterizing a given distribution, depending on the size of the communication space in different cities, has been shown. However, the basic parameter that characterizes the fractal dimension of the communication space remains constant for all cities studied.