GG-GAN: A Geometric Graph Generative Adversarial Network

Abstract

We study the fundamental problem of graph generation. Specifically, we treat graph generation from a geometric perspective by associating each node with a position in space and then connecting the edges based on a similarity function. We then provide new solutions to the key challenges that prevent the widespread application of this classical geometric interpretation: (1) modeling complex relations, (2) modeling isomorphic graphs consistently, and (3) fully exploiting the latent distribution. Our main contribution is dubbed as the geometric graph (GG) generative adversarial network (GAN), which is a Wasserstein GAN that addresses the above challenges. GG-GAN is permutation equivariant and easily scales to generate graphs of tens of thousands of nodes. GG-GAN also strikes a good trade-off between novelty and modeling the distribution statistics, being competitive or surpassing the state-of-the-art methods that are either slower or that are non-equivariant, or that exploit problem-specific knowledge.