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Contents of PMS, Vol. 36, Fasc. 1,
pages 59 - 74
 

EXISTENCE OF A PERSISTENT HUB IN THE CONVEX PREFERENTIAL ATTACHMENT MODEL

Pavel Galashin

Abstract: A vertex of a randomly growing graph is called a persistent hub if at all but finitely many moments of time it has the maximal degree in the graph. We establish the existence of a persistent hub in the Barabási–Albert random graph model with probability one. We also extend this result to the class of convex preferential attachment graphs, where a vertex of degree k gets a new edge with probability proportional to some convex function of k .

2000 AMS Mathematics Subject Classification: Primary: 05C80; Secondary: 60B20.

Keywords and phrases: Preferential attachment, persistent hub, Barabá si–Albert model.

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