Low-Complexity and Consistent Graphon Estimation from Multiple Networks

2026-03-16

AI Summary

This work addresses graphon estimation in multi-network settings where node sets are non-overlapping and vary in size. The authors propose a low-complexity method that introduces a joint node alignment strategy, replacing conventional per-graph sorting to significantly reduce computational overhead while preserving estimation consistency. Built upon histogram-based estimation and nonparametric exchangeable random graph models, the proposed approach achieves higher accuracy than existing techniques and substantially outperforms other consistent estimators in computational speed. Furthermore, it effectively enhances the classification performance of graph neural networks when applied to data augmentation scenarios.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• graphon estimation
• multiple networks
• nonparametric random graph model
• variable-size networks
• node alignment

Innovation

• graphon estimation
• low-complexity
• joint node alignment
• consistent estimator
• multiple networks