Scalable Implicit Graphon Learning

TL;DR

This paper introduces SIGL, a scalable method combining implicit neural representations and graph neural networks to estimate continuous graphons from observed graphs, overcoming previous limitations in resolution and scalability.

Contribution

The paper presents a novel scalable approach for graphon estimation that integrates INRs and GNNs, enabling continuous modeling at arbitrary resolutions and improved graph alignment.

Findings

SIGL outperforms existing methods in synthetic and real-world graph experiments.

SIGL scales effectively to larger graphs, suitable for data augmentation.

Theoretical analysis confirms the asymptotic consistency of the estimator.

Abstract

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.