Distribution of small subgraphs in Buckley–Osthus random graphs

We study a random graph model similar to the Buckley–Osthus preferential attachment model and develop a technique for estimating the expectation of a wide class of random variables in this model. By means of this technique, we prove a theorem on the asymptotic behaviour of the expectation of the number of subgraphs isomorphic to a fixed graph in the random graphs of the model.