Social network growth model with local rules

I propose a description of a social network with indirect binding. This allows you to exclude completely the preferred choice of nodes from the rules. A model built on this basis generates a sparse network with a power-law distribution of nodes degree.
The formulas for the distribution index obtained from the mean-field quasi-linear approximation satisfied with good accuracy. Their empirical characteristics are determined from the simulation results. However, this approximation doesn’t agree with the value of the distribution shift. That limits the applicability of the proposed approach.