Real-world graph datasets often arise from mixtures of populations, where graphs are generated by multiple distinct underlying distributions. In this work, we propose a unified framework that explicitly models graph data as a mixture of probabilistic graph generative models represented by graphons. To characterize and estimate these graphons, we leverage graph moments (motif densities) to cluster graphs generated from the same underlying model. We establish a novel theoretical guarantee, deriving a tighter bound showing that graphs sampled from structurally similar graphons exhibit similar motif densities with high probability. This result enables principled estimation of graphon mixture components. We show how incorporating estimated graphon mixture components enhances two widely used downstream paradigms: graph data augmentation via mixup and graph contrastive learning. By conditioning these methods on the underlying generative models, we develop graphon-mixture-aware mixup (GMAM) and model-aware graph contrastive learning (MGCL). Extensive experiments on both simulated and real-world datasets demonstrate strong empirical performance. In supervised learning, GMAM outperforms existing augmentation strategies, achieving new state-of-the-art accuracy on 6 out of 7 datasets. In unsupervised learning, MGCL performs competitively across seven benchmark datasets and achieves the lowest average rank overall.

翻译：现实中的图数据集往往源于群体混合，其中图由多个不同的潜在分布生成。本文提出一个统一框架，将图数据显式建模为由图模型（graphon）表示的概率图生成模型的混合。为刻画并估计这些图模型，我们利用图矩（motif密度）将来自相同潜在模型的图进行聚类。我们建立了新颖的理论保证，推导出更紧的界：从结构相似的图模型中采样的图，其motif密度以高概率呈现相似性。这一结果使得图模型混合成分的估计具有原理性。我们展示如何将估计的图模型混合成分融入两种广泛使用的下游范式：基于混合的图数据增强和图对比学习。通过使这些方法条件于潜在生成模型，我们开发了图模型感知混合（GMAM）和模型感知图对比学习（MGCL）。在模拟与真实数据集上的大量实验展现了强大的实证性能。在监督学习中，GMAM超越现有增强策略，在7个数据集中的6个上达到新的最高准确率。在无监督学习中，MGCL在七个基准数据集上表现优异，并取得整体最低平均排名。