On leaders and condensates in a growing network

Abstract

The Bianconi-Barabasi model of a growing network is revisited. This model, defined by a preferential attachment rule involving both the degrees of the nodes and their intrinsic fitnesses, has the fundamental property to undergo a phase transition to a condensed phase below some finite critical temperature, for an appropriate choice of the distribution of fitnesses. At high temperature it exhibits a crossover to the Barabasi-Albert model, and at low temperature, where the fitness landscape becomes very rugged, a crossover to the recently introduced record-driven growth process. We first present an analysis of the history of leaders, the leader being defined as the node with largest degree at a given time. In the generic finite-temperature regime, new leaders appear endlessly, albeit on a doubly logarithmic time scale, i.e., extremely slowly. We then give a novel picture for the dynamics in the condensed phase. The latter is characterized by an infinite hierarchy of condensates, whose sizes are non-self-averaging and keep fluctuating forever.

29 pages, 13 figures, 3 tables. A few minor changes

References in corpus (6)

• Dynamics of the condensate in zero-range processes
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• A record-driven growth process
• Dynamics of condensation in growing complex networks
• Statistics of leaders and lead changes in growing networks
• Finite-time fluctuations in the degree statistics of growing networks

Cited by in corpus (4)

• Condensation in stochastic particle systems with stationary product measures
• Structural preferential attachment: Stochastic process for the growth of scale-free, modular and self-similar systems
• A k-deformed Model of Growing Complex Networks with Fitness
• How the fittest compete for leadership: A tale of tails