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Multigraph limit of the dense configuration model and the preferential attachment graph

Ráth, Balázs ; Szakács, László

In: Acta Mathematica Hungarica, 2012, vol. 136, no. 3, p. 196-221

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    Titre
    • Multigraph limit of the dense configuration model and the preferential attachment graph
    Auteur
    • Ráth, Balázs. Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
    • Szakács, László. Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Acta Mathematica Hungarica, 2012, vol. 136, no. 3, p. 196-221. Springer Netherlands
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:312593
    Summary
    The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of configuration models. We apply these results to calculate the limit object corresponding to the dense preferential attachment graph and the edge reconnecting model. Our main tools in doing so are (1) the relation between the theory of graph limits and that of partially exchangeable random arrays (2) an explicit construction of our random graphs that uses urn models