University of Cambridge > > Combinatorics Seminar > Graphons and Graphexes as Limits of Sparse Graphs: Part II

Graphons and Graphexes as Limits of Sparse Graphs: Part II

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  • UserChristian Borgs (Microsoft Research New England)
  • ClockThursday 05 April 2018, 15:30-16:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

Graphons and graphexes are limits of graphs which allow us to model and estimate properties of large-scale networks. In this pair of talks, we review the theory of dense graph limits, and give two alternative theories for limits of sparse graphs: one leading to unbounded graphons over probability spaces, and the other leading to bounded graphons (and graphexes) over sigma-finite measure spaces.

Talk II, to be given by Christian Borgs, will recast limits of dense graphs in terms of exchangeability and the Aldous Hoover Theorem, and generalize this to obtain sparse graphons and graphexes as limits of subgraph samples from sparse graph sequences. This will provide a dual view of sparse graph limits as processes and random measures, an approach which allows a generalization of many of the well-known results and techniques for dense graph sequences.

This talk is part of the Combinatorics Seminar series.

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