Statistics of leaders and lead changes in growing networks

Details Statistics of leaders and lead changes in growing networks Statistics of leaders and lead changes in growing networks

2009-11-16

arxiv.org/abs/0911.3057v1

J. Stat. Mech. (2010) P02001

Physics

Physics and Society

28 pages, 14 figures, 1 table

Scientific paper

10.1088/1742-5468/2010/02/P02001

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there are co-leaders). This comprehensive study includes the full distribution of the degree of the leader, its identity, the number of co-leaders, as well as several observables characterizing the whole history of lead changes: number of lead changes, number of distinct leaders, lead persistence probability. We successively consider the following network models: uniform attachment, linear attachment (the Barabasi-Albert model), and generalized preferential attachment with initial attractiveness.

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