Counting the number of small patterns is a central task in network analysis. While this problem is well studied for graphs, many real-world datasets are naturally modeled as hypergraphs, motivating the need for efficient hypergraph motif counting algorithms. In particular, we study the problem of counting hypertriangles - collections of three pairwise-intersecting hyperedges. These hypergraph patterns have a rich structure with multiple distinct intersection patterns unlike graph triangles. Inspired by classical graph algorithms based on orientations and degeneracy, we develop a theoretical framework that generalizes these concepts to hypergraphs and yields provable algorithms for hypertriangle counting. We implement these ideas in DITCH (Degeneracy Inspired Triangle Counter for Hypergraphs) and show experimentally that it is 10-100x faster and more memory efficient than existing state-of-the-art methods.

翻译：在复杂网络分析中，统计小规模模式的数量是一项核心任务。尽管该问题在图结构上已有深入研究，但许多现实世界数据集天然适合用超图建模，这推动了对高效超图模体计数算法的需求。本文重点研究超三角形的计数问题——即三个两两相交的超边构成的集合。与图三角形不同，这类超图模式具有丰富的结构特征，存在多种不同的相交模式。受基于定向和退化度的经典图算法启发，我们构建了一个理论框架，将这些概念推广至超图，并提出了具有可证明性能的超三角形计数算法。我们在DITCH（基于退化度的超图三角形计数器）中实现了这些思想，实验表明其计算速度比现有最先进方法快10-100倍，且内存效率更高。