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

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

2011-06-10

arxiv.org/abs/1106.2058v2

Mathematics

Probability

Some of the results of this submission already appeared in an older version of arXiv:0912.3904v3, "Time evolution of dense mul

Scientific paper

10.1007/s10474-012-0217-4

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.

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