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, originally designed for lossless graph compression. The $K^2$-tree representation {encompasses inherent hierarchy while enabling compact graph generation}. In addition, we make contributions by (1) presenting a sequential $K^2$-treerepresentation 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：从目标分布生成图是包括药物发现和社交网络分析在内的众多领域中的一项重大挑战。本文提出了一种新颖的图生成方法，利用了最初为无损图压缩而设计的$K^2$-树表示。$K^2$-树表示既包含了固有的层次结构，又实现了紧凑的图生成。此外，我们的贡献还包括：(1) 提出了一种包含剪枝、展平和标记化过程的序列化$K^2$-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该序列。最后，我们在四个通用图数据集和两个分子图数据集上对我们的算法进行了广泛评估，证实了其在图生成方面的优越性。