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Abstract: This paper presents a comprehensive analysis of the degree statistics inmodels for growing networks where new nodes enter one at a time and attach toone earlier node according to a stochastic rule. The models with uniformattachment, linear attachment the Barab\-asi-Albert model, and generalizedpreferential attachment with initial attractiveness are successivelyconsidered. The main emphasis is on finite-size i.e., finite-time effects,which are shown to exhibit different behaviors in three regimes of thesize-degree plane: stationary, finite-size scaling, large deviations.



Author: C. Godreche, H. Grandclaude, J.M. Luck

Source: https://arxiv.org/



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