Graphons, mergeons, and so on!
This addresses the problem of clustering graphs in a more general model than stochastic blockmodels, which is incremental over prior work.
The authors developed a hierarchical clustering theory for graphs sampled from graphons, establishing conditions for statistical consistency and providing an explicit algorithm that achieves this.
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 define what it means for an algorithm to produce the "correct" clustering, give sufficient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.