The model of social network growth

We propose a new model of social network growth. This model bases on the following assumptions: the random attachment of new vertices, the preferential choice of vertices for creating links with existing vertices and the restriction of the second ends of these links by the neighbors of the neighbors.
The model generates the graph with power-law distributed vertices degree. The exponent of the distribution varies in a wide range.
We give a mean-field quasi-linear description for the model. This description allows to claim essential customization of high-order vertices and to propose a number of approximations for the results of simulations.