Learning graph generative models is a challenging task for deep learning and has wide applicability to a range of domains like chemistry, biology and social science. However current deep neural methods suffer from limited scalability: for a graph with $n$ nodes and $m$ edges, existing deep neural methods require $\Omega(n^2)$ complexity by building up the adjacency matrix. On the other hand, many real world graphs are actually sparse in the sense that $m\ll n^2$. Based on this, we develop a novel autoregressive model, named BiGG, that utilizes this sparsity to avoid generating the full adjacency matrix, and importantly reduces the graph generation time complexity to $O((n + m)\log n)$. Furthermore, during training this autoregressive model can be parallelized with $O(\log n)$ synchronization stages, which makes it much more efficient than other autoregressive models that require $\Omega(n)$. Experiments on several benchmarks show that the proposed approach not only scales to orders of magnitude larger graphs than previously possible with deep autoregressive graph generative models, but also yields better graph generation quality.

本研究提出了一种基于自回归模型的图生成方法(BiGG)，其利用稀疏性避免生成完整的邻接矩阵，并将图生成时间复杂度降至O((n + m)logn)。实验表明，该方法不仅比之前的自回归图生成模型能够处理更大的图像，而且生成质量更高。

基于深度生成模型的稀疏图可扩展建模