Scalable Implicit Graphon Learning
This work addresses scalability and resolution limitations in graphon learning for tasks like graph data augmentation, representing an incremental improvement over prior methods.
The authors tackled the problem of learning continuous graphon models from observed graphs, which existing methods struggled with due to fixed resolution and scalability issues, and proposed SIGL, a scalable method that outperforms existing approaches and scales effectively to larger graphs.
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.