  Graphs are ubiquitous in various fields, and deep learning methods have been
successful applied in graph classification tasks. However, building large and
diverse graph datasets for training can be expensive. While augmentation
techniques exist for structured data like images or numerical data, the
augmentation of graph data remains challenging. This is primarily due to the
complex and non-Euclidean nature of graph data. In this paper, it has been
proposed a novel augmentation strategy for graphs that operates in a
non-Euclidean space. This approach leverages graphon estimation, which models
the generative mechanism of networks sequences. Computational results
demonstrate the effectiveness of the proposed augmentation framework in
improving the performance of graph classification models. Additionally, using a
non-Euclidean distance, specifically the Gromow-Wasserstein distance, results
in better approximations of the graphon. This framework also provides a means
to validate different graphon estimation approaches, particularly in real-world
scenarios where the true graphon is unknown.
