Levels of a scale-free tree
Consider the random graph model of Barabdsi and Albert, where we add a new vertex in every step and connect it to some old vertices with probabilities proportional to their degrees. If we connect it to only one of the old vertices the graph will be a tree. These graphs have been shown to have power law degree distributions, the same as observed in some large real-world networks. We show that the degree distribution is the same on every sufficiently high level of the tree. (c) 2005 Wiley Periodicals, Inc.
random graphs scale-free disribution width of trees