  Deep learning-based graph generation approaches have remarkable capacities
for graph data modeling, allowing them to solve a wide range of real-world
problems. Making these methods able to consider different conditions during the
generation procedure even increases their effectiveness by empowering them to
generate new graph samples that meet the desired criteria. This paper presents
a conditional deep graph generation method called SCGG that considers a
particular type of structural conditions. Specifically, our proposed SCGG model
takes an initial subgraph and autoregressively generates new nodes and their
corresponding edges on top of the given conditioning substructure. The
architecture of SCGG consists of a graph representation learning network and an
autoregressive generative model, which is trained end-to-end. Using this model,
we can address graph completion, a rampant and inherently difficult problem of
recovering missing nodes and their associated edges of partially observed
graphs. Experimental results on both synthetic and real-world datasets
demonstrate the superiority of our method compared with state-of-the-art
baselines.
