For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives insights about the sensitivity of the graph distance underlying the diversity measure.

翻译：对于许多与图相关的问题，拥有一个结构多样化的图集至关重要。例如，此类图可用于测试图算法或其神经近似模型。然而，据我们所知，生成结构多样性图的问题在现有文献中尚未得到充分探讨。本文旨在填补这一空白。首先，我们讨论了如何定义图集的多样性、为何该任务具有非平凡性，以及如何选择合适的多样性度量指标。随后，针对给定的多样性度量指标，我们提出并比较了多种优化算法：基于标准随机图模型、局部图优化、遗传算法和神经生成模型的方法。研究表明，相较于基础随机图生成器，我们能够显著提升图集的多样性。此外，通过对生成图的分析，我们能够更深入地理解图距离的特性：根据优化所使用的多样性度量指标，所得图可能具有截然不同的结构特性，这揭示了支撑多样性度量的图距离的敏感性。