Graphons, mergeons, and so on!
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Abstract
In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary setting for recent progress in the statistical theory of graph clustering. We de?ne what it means for an algorithm to produce the “correct" clustering, give su?cient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.
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