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We approach the graph generation problem from a spectral perspective by firstgenerating the dominant parts of the graph Laplacian spectrum and then buildinga graph matching these eigenvalues and eigenvectors. Spectral conditioningallows for direct modeling of the global and local graph structure and helps toovercome the expressivity and mode collapse issues of one-shot graphgenerators. Our novel GAN, called SPECTRE, enables the one-shot generation ofmuch larger graphs than previously possible with one-shot models. SPECTREoutperforms state-of-the-art deep autoregressive generators in terms ofmodeling fidelity, while also avoiding expensive sequential generation anddependence on node ordering. A case in point, in sizable synthetic andreal-world graphs SPECTRE achieves a 4-to-170 fold improvement over the bestcompetitor that does not overfit and is 23-to-30 times faster thanautoregressive generators.

SPECTRE: Spectral Conditioning Helps to Overcome the Expressivity Limits of One-shot Graph Generators