Angelica Pachon

On preferential attachment models and continuous time Markov processes

One of the most popular models for network growth is the preferential attachment model proposed by Barabási and Albert. In this model, a newly created vertex is connected to one of those already present in the graph with a probability proportional to their degrees. In this talk we present a new technique to analyse the degree of a vertex which has appeared at a large enough time in the Barabási–Albert model, as well as the distribution of a vertex selected uniformly at random in this random graph model. The main idea is to couple the degree growth process of a vertex to a set of Markov processes, and introduce an auxiliary branching structure superimposed to the random graph.

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