Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and synthetic datasets among others. While GNN (Graph Neural Network) models have been applied in these domains their high in-memory costs restrict them to small graphs. Conversely less costly rule-based methods struggle to reproduce complex structures. We propose HIGGS (Hierarchical Generation of Graphs) as a model-agnostic framework of producing large graphs with realistic local structures. HIGGS uses GNN models with conditional generation capabilities to sample graphs in hierarchies of resolution. As a result HIGGS has the capacity to extend the scale of generated graphs from a given GNN model by quadratic order. As a demonstration we implement HIGGS using DiGress, a recent graph-diffusion model, including a novel edge-predictive-diffusion variant edge-DiGress. We use this implementation to generate categorically attributed graphs with tens of thousands of nodes. These HIGGS generated graphs are far larger than any previously produced using GNNs. Despite this jump in scale we demonstrate that the graphs produced by HIGGS are, on the local scale, more realistic than those from the rule-based model BTER.

翻译：大规模图存在于众多领域，包括社交网络、民用基础设施和物理科学等。图生成同样应用广泛，涵盖药物发现、网络分析和合成数据集等多个方面。尽管图神经网络（GNN）模型已被应用于这些领域，但其高内存成本限制了模型仅能处理小规模图。相比之下，成本较低的基于规则的方法难以复现复杂结构。我们提出HIGGS（分层图生成）作为模型无关框架，用于生成具有真实局部结构的大规模图。HIGGS利用具有条件生成能力的GNN模型，以分辨率层次对图进行采样。因此，HIGGS能够将给定GNN模型生成的图规模按二次方数量级扩展。为演示效果，我们使用近期提出的图扩散模型DiGress实现HIGGS，并包含一种新颖的边缘预测扩散变体edge-DiGress。利用该实现生成了包含数万个节点的分类属性图。这些由HIGGS生成的图规模远超以往任何基于GNN生成的图。尽管规模大幅提升，我们仍证明HIGGS生成的图在局部尺度上比基于规则的BTER模型生成的图更加真实。