# Graphons, mergeons, and so on!

arXiv: https://arxiv.org/abs/1607.01718 · HTML: https://mlsanity.com/paper/1607.01718/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2016.

## Built on by (most cited first, 10 of 10)

- [SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators](https://mlsanity.com/paper/2204.01613/) (2022)
- [Diffusion Models for Graphs Benefit From Discrete State Spaces](https://mlsanity.com/paper/2210.01549/) (2022)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [Convergence of Invariant Graph Networks](https://mlsanity.com/paper/2201.10129/) (2022)
- [Nonparametric Modeling of Higher-Order Interactions via Hypergraphons](https://mlsanity.com/paper/2105.08678/) (2021)
- [Discovering Graph Generation Algorithms](https://mlsanity.com/paper/2304.12895/) (2023)
- [A Poincar'e Inequality and Consistency Results for Signal Sampling on Large Graphs](https://mlsanity.com/paper/2311.10610/) (2023)
- [A Generative Model for Controllable Feature Heterophily in Graphs](https://mlsanity.com/paper/2509.23230/) (2025)
- [Low-Complexity and Consistent Graphon Estimation from Multiple Networks](https://mlsanity.com/paper/2603.15578/) (2026)

## Abstract (arXiv)

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.