Hierarchical Graph Generation with $K^{2}$-trees

Generating graphs from a target distribution is a significant challenge across many domains, including drug discovery and social network analysis. In this work, we introduce a novel graph generation method leveraging $K^{2}$-tree representation which was originally designed for lossless graph compression. Our motivation stems from the ability of the $K^{2}$-trees to enable compact generation while concurrently capturing the inherent hierarchical structure of a graph. In addition, we make further contributions by (1) presenting a sequential $K^{2}$-tree representation that incorporates pruning, flattening, and tokenization processes and (2) introducing a Transformer-based architecture designed to generate the sequence by incorporating a specialized tree positional encoding scheme. Finally, we extensively evaluate our algorithm on four general and two molecular graph datasets to confirm its superiority for graph generation.