Adversarially Generating Rank-Constrained Graphs

Graph generation is a task that has been explored with a wide variety of methods. Recently, several papers have applied Generative Adversarial Networks (GANs) to this task, but most of these methods result in graphs of full or unknown rank. Many real-world graphs have low rank, which roughly translates to the number of communities in that graph. Furthermore, it has been shown that taking the low rank approximation of a graph can defend against adversarial attacks. This suggests that testing models against graphs of different rank may be useful. However, current methods provide no way to control the rank of generated graphs. In this paper, we propose two variants of BRGAN: GAN architectures that generates synthetic graphs, which in addition to having realistic graph features, also have bounded rank. Our first variant, BRGAN-A, generates synthetic graphs competitive with state-of-the-art models, with rank equal to or lower than the desired rank. Our second variant, BRGAN-B, generates graphs of almost exactly the desired rank, but results in less realistic results. We also propose a novel rank penalty term on the generator, which allows us to control this realism-rank tradeoff.