Low-Complexity and Consistent Graphon Estimation from Multiple Networks

TL;DR

This paper introduces a low-complexity, consistent histogram-based estimator for graphon functions that effectively aligns multiple networks of varying sizes, outperforming existing methods in accuracy and speed.

Contribution

The paper proposes a novel histogram-based graphon estimator that jointly aligns nodes across multiple networks, achieving high accuracy with low computational complexity and enabling better data augmentation.

Findings

Outperforms existing methods in accuracy on small, variable-size networks

Significantly reduces computation time compared to prior approaches

Enhances graph neural network classification performance through improved data augmentation

Abstract

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is the estimation of the graphon function that parametrizes the nonparametric exchangeable random graph model. Existing methods typically suffer from either limited accuracy or high computational complexity. We introduce a new histogram-based estimator with low algorithmic complexity that achieves high accuracy by jointly aligning the nodes of all graphs, in contrast to most conventional methods that order nodes graph by graph. Consistency results of the proposed graphon estimator are established. A numerical study shows that the proposed estimator outperforms existing methods in terms of accuracy, especially when the dataset comprises only small and variable-size networks. Moreover, the computing time of the new method is considerably shorter than that of other consistent methodologies. Additionally, when applied to a graph neural network classification task, the proposed estimator enables more effective data augmentation, yielding improved performance across diverse real-world datasets.