Preferential attachment in growing spatial networks

Luca Ferretti, Michele Cortelezzi

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    31 Citations (Scopus)

    Abstract

    We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models is similar to that of the fitness model of Bianconi and Barabási, with a fitness distribution dependent on the metric and the density of nodes. We show that curvature singularities in these spaces can give rise to asymptotic Bose-Einstein condensation, but transient condensation can be observed also in smooth hyperbolic spaces with strong curvature. We provide numerical results for spaces of constant curvature (sphere, flat, and hyperbolic space) and we discuss the conditions for the breakdown of this approach and the critical points of the transition to distance-dominated attachment. Finally, we discuss the distribution of link lengths. © 2011 American Physical Society.
    Original languageEnglish
    Article number016103
    JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
    Volume84
    Issue number1
    DOIs
    Publication statusPublished - 8 Jul 2011

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