On the Number of Subgraphs of a Random Graph in the Barabasi-Albert Model

The number of subgraphs of a random graph in the Barabasi-Albert model are studied. The number of models appearing as a result of removing the inaccuracy of the graph is very large, and the properties of the models are very diverse. For any integer function there exists a Barabasi-Albert type model in which a random graph contains precisely triangles with probability tending to 1. A random graph on t vertices with some edges is constructed and a sequence of vertices is taken. One more Barabasi-Albert-type model is considered, two very general assertions are valid. Under homogenization, any random variable from a very large class of quantities defined on the space transforms into a constant multiplied by a random variable on the space.