The paper establishes sampling convergence of the configuration model, preferential attachment model, generalized random graph, and bipartite configuration model to graphexes, giving necessary and sufficient conditions for convergence.
Graph limits and exchangeable random graphs
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abstract
We develop a clear connection between deFinetti's theorem for exchangeable arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph limits (work of Lovasz and many coauthors). Along the way, we translate the graph theory into more classical probability.
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math.PR 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Limits of Sparse Configuration Models and Beyond: Graphexes and Multi-Graphexes
The paper establishes sampling convergence of the configuration model, preferential attachment model, generalized random graph, and bipartite configuration model to graphexes, giving necessary and sufficient conditions for convergence.