Graph representations that preserve relevant topological information allow the use of a rich machine learning toolset for data-driven network analytics. Some notable graph representations in the literature are fruitful in their respective applications but they either lack interpretability or are unable to effectively encode a graph’s structure at both local and global scale. In this work, we propose the Higher-Order Structure Descriptor (HOSD): an interpretable graph descriptor that captures information about the patterns in a graph at multiple scales. Scaling is achieved using a novel graph compression technique that reveals successive higher-order structures. The proposed descriptor is invariant to node permutations due to its graph-theoretic nature. We analyze the HOSD algorithm for time complexity and also prove the NP-completeness of three interesting graph compression problems. A faster version, HOSD-Lite, is also presented to approximate HOSD on dense graphs. We showcase the interpretability of our model by discussing structural patterns found within real-world datasets using HOSD. HOSD and HOSD-Lite are evaluated on benchmark datasets for applicability to classification problems; results demonstrate that a simple random forest setup based on our representations competes well with the current state-of-the-art graph embeddings.

保留相关拓扑信息的图形表示允许将丰富的机器学习工具集用于数据驱动的网络分析。文献中一些著名的图形表示在它们各自的应用中都取得了丰硕的成果，但是它们要么缺乏解释性，要么无法在本地和全局范围内有效地编码图形结构。在这项工作中，我们提出了高阶结构描述符（HOSD）：一种可解释的图形描述符，它以多种比例捕获图形中有关模式的信息。使用新颖的图形压缩技术可实现缩放，该技术可显示连续的高阶结构。所提出的描述符由于其图论性质而对于节点置换是不变的。我们分析了HOSD算法的时间复杂度，并证明了三个有趣的图压缩问题的NP完备性。还提出了一种更快的版本HOSD-Lite，用于在密集图上近似HOSD。通过讨论使用HOSD在现实数据集中发现的结构模式，我们展示了模型的可解释性。在基准数据集上评估了HOSD和HOSD-Lite是否适用于分类问题；结果表明，基于我们的表示的简单随机森林设置可以与当前最新的图形嵌入竞争。在基准数据集上评估了HOSD和HOSD-Lite是否适用于分类问题；结果表明，基于我们的表示的简单随机森林设置与当前最新的图形嵌入竞争良好。在基准数据集上评估了HOSD和HOSD-Lite是否适用于分类问题；结果表明，基于我们的表示的简单随机森林设置可以与当前最新的图形嵌入竞争。