Iowa State University
Department of Statistics and Statistical Laboratory
Ames IA 50011-1210
United States of America
Abstract: We will start with the classical Albert - Barabasi model of preferential attachment random graphs. We shall prove rigorously using an embedding in Markov branching processes the power law growth of degrees and the power law decay of the limiting empirical distribution of the degree. Next we will consider the case of general weight function and show the different behaviours for the superlinear, linear and sublinear cases.