In this work, we introduce a novel evaluation framework for generative models of graphs, emphasizing the importance of model-generated graph overlap (Chanpuriya et al., 2021) to ensure both accuracy and edge-diversity. We delineate a hierarchy of graph generative models categorized into three levels of complexity: edge independent, node independent, and fully dependent models. This hierarchy encapsulates a wide range of prevalent methods. We derive theoretical bounds on the number of triangles and other short-length cycles producible by each level of the hierarchy, contingent on the model overlap. We provide instances demonstrating the asymptotic optimality of our bounds. Furthermore, we introduce new generative models for each of the three hierarchical levels, leveraging dense subgraph discovery (Gionis & Tsourakakis, 2015). Our evaluation, conducted on real-world datasets, focuses on assessing the output quality and overlap of our proposed models in comparison to other popular models. Our results indicate that our simple, interpretable models provide competitive baselines to popular generative models. Through this investigation, we aim to propel the advancement of graph generative models by offering a structured framework and robust evaluation metrics, thereby facilitating the development of models capable of generating accurate and edge-diverse graphs.

翻译：本文介绍了一种针对图生成模型的新型评估框架，强调模型生成图重叠（Chanpuriya等人，2021）对于确保准确性和边多样性的重要性。我们划分了图生成模型的层级结构，将其分为三个复杂度级别：边独立模型、节点独立模型和完全依赖模型。该层级结构涵盖了一系列主流方法。我们推导出每个层级基于模型重叠可生成的三角形及其他短周期环数量的理论界限，并提供了证明这些界限渐近最优性的实例。此外，我们引入三种分别对应上述层级的生成模型，利用稠密子图发现技术（Gionis & Tsourakakis，2015）。我们在真实数据集上的评估聚焦于所提模型与其他流行模型的输出质量和重叠度比较。结果表明，我们简单且可解释的模型为流行生成模型提供了具有竞争力的基线。通过本研究，我们旨在通过提供结构化框架和稳健的评估指标来推动图生成模型的发展，从而促进能够生成准确且边多样性丰富图的模型开发。