EXISTENCE OF A PERSISTENT HUB IN THE CONVEX PREFERENTIAL
ATTACHMENT MODEL
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 gets a new edge with probability proportional to some convex function of .
2000 AMS Mathematics Subject Classification: Primary: 05C80; Secondary:
60B20.
Keywords and phrases: Preferential attachment, persistent hub, Barabá si–Albert
model.