Graphons, mergeons, and so on!
Justin Eldridge, Mikhail Belkin, Yusu Wang

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.
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Taxonomy
TopicsAdvanced Clustering Algorithms Research · Complex Network Analysis Techniques · Data Management and Algorithms
