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In this work we develop a theory of hierarchical clustering for graphs. Ourmodeling assumption is that graphs are sampled from a graphon, which is apowerful 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 graphclustering. We define what it means for an algorithm to produce the "correct"clustering, give sufficient conditions in which a method is statisticallyconsistent, and provide an explicit algorithm satisfying these properties.

Graphons, mergeons, and so on!