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.

翻译：从目标分布中生成图是多个领域（包括药物发现和社会网络分析）中的重大挑战。在本工作中，我们提出了一种新颖的图生成方法，该方法利用原本为无损图压缩设计的$K^2$-树表示。我们的动机源于$K^2$-树能够实现紧凑生成，同时捕捉图固有的层级结构。此外，我们进一步做出以下贡献：(1) 提出了一种结合剪枝、扁平化和分词化过程的序列化$K^2$-树表示；(2) 引入了一种基于Transformer的架构，通过结合专门的树位置编码方案来生成序列。最后，我们在四个通用图数据集和两个分子图数据集上广泛评估了我们的算法，以证实其在图生成中的优越性。