Graphons, mergeons, and so on!

TL;DR

This paper develops a theoretical framework for hierarchical clustering of graphs based on graphons, providing conditions for statistical consistency and an explicit algorithm, advancing understanding beyond stochastic blockmodels.

Contribution

It introduces a new theory for graph clustering using graphons, including definitions, conditions for correctness, and an explicit consistent algorithm.

Findings

Defined what correct clustering means for graphons

Provided sufficient conditions for statistical consistency

Presented an explicit clustering algorithm

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 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.