Statistics of leaders and lead changes in growing networks

Abstract

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.

28 pages, 14 figures, 1 table

References in corpus (4)

• Aging, rejuvenation and memory : the example of spin glasses
• A record-driven growth process
• Dynamics of condensation in growing complex networks
• Finite-time fluctuations in the degree statistics of growing networks

Cited by in corpus (6)

• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Impact of leader on cluster synchronization
• Existence of a persistent hub in the convex preferential attachment model
• Persistence of Random Walk Records
• On leaders and condensates in a growing network
• How the fittest compete for leadership: A tale of tails