Efficient and Scalable Graph Generation through Iterative Local Expansion

Andreas Bergmeister, Karolis Martinkus, Nathanaël Perraudin, Roger Wattenhofer

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Keywords: Graph Generation, Denoising Diffusion, Spectral Graph Theory

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TL;DR: We introduce a novel method to build a graph by progressively expanding a single node to a target graph, adding nodes and edges in a localized manner through denoising diffusion, building first the global structure and then refining.

Abstract:

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously.
To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation.
Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

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Primary Area: generative models

Submission Number: 3733