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Finite-Time Fluctuations in the Degree Statistics of Growing Networks

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Abstract

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barabási-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.

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Authors and Affiliations

  1. Institut de Physique Théorique, IPhT, CEA Saclay, and URA 2306, CNRS, 91191, Gif-sur-Yvette cedex, France

    C. Godrèche, H. Grandclaude & J. M. Luck

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  1. C. Godrèche
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  2. H. Grandclaude
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  3. J. M. Luck
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Correspondence to J. M. Luck.

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Godrèche, C., Grandclaude, H. & Luck, J.M. Finite-Time Fluctuations in the Degree Statistics of Growing Networks. J Stat Phys 137, 1117–1146 (2009). https://doi.org/10.1007/s10955-009-9847-5

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  • DOI: https://doi.org/10.1007/s10955-009-9847-5

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