  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.
