Local graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most (local) graph clustering algorithms is to find a vertex set of low conductance, there has been a sequence of recent studies that highlight the importance of the inter-connection between clusters when analysing real-world datasets. Following this line of research, in this work we study local algorithms for finding a pair of vertex sets defined with respect to their inter-connection and their relationship with the rest of the graph. The key to our analysis is a new reduction technique that relates the structure of multiple sets to a single vertex set in the reduced graph. Among many potential applications, we show that our algorithms successfully recover densely connected clusters in the Interstate Disputes Dataset and the US Migration Dataset.

中文翻译：

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用于查找密集连接集群的本地算法

局部图聚类是分析海量图的重要算法技术，已广泛应用于数据科学的许多研究领域。虽然大多数（本地）图聚类算法的目标是找到一个低电导的顶点集，但最近有一系列研究强调了在分析现实世界数据集时集群之间相互连接的重要性。遵循这一研究路线，在这项工作中，我们研究了局部算法，用于查找根据它们的相互连接以及它们与图其余部分的关系定义的一对顶点集。我们分析的关键是一种新的缩减技术，它将多个集合的结构与缩减图中的单个顶点集合相关联。在众多潜在应用中，