SCGG: A deep structure-conditioned graph generative model.

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. More precisely, the graph representation learning network is designed to compute continuous representations for each node in a graph, which are not only affected by the features of adjacent nodes, but also by the ones of farther nodes. This network is primarily responsible for providing the generation procedure with the structural condition, while the autoregressive generative model mainly maintains the generation history. 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. The computational complexity of the SCGG method is shown to be linear in the number of graph nodes. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method compared with state-of-the-art baselines.