We provide a rearrangement based algorithm for fast detection of subgraphs of $k$ vertices with long escape times for directed or undirected networks. Complementing other notions of densest subgraphs and graph cuts, our method is based on the mean hitting time required for a random walker to leave a designated set and hit the complement. We provide a new relaxation of this notion of hitting time on a given subgraph and use that relaxation to construct a fast subgraph detection algorithm and a generalization to $K$-partitioning schemes. Using a modification of the subgraph detector on each component, we propose a graph partitioner that identifies regions where random walks live for comparably large times. Importantly, our method implicitly respects the directed nature of the data for directed graphs while also being applicable to undirected graphs. We apply the partitioning method for community detection to a large class of model and real-world data sets.

翻译：我们提供了一种基于重新排列的算法,用于快速探测有定向或无定向网络长期逃逸时间的以K为单位的脊椎的子图。我们用一个图表分割器来补充其他最密集的子图和图形切割的概念,我们的方法是以随机行走者离开指定数据集并击中补充物所需的平均打击时间为基础。我们用这个算法来放松这种在特定子图上点击时间的概念,并用这种放松来构建一个快速子图检测算法和对美元分割方案的概括化。我们使用对每个组成部分的子图探测器的修改,我们建议了一个图形分割器,以辨别随机行走可比较大时间的区域。重要的是,我们的方法暗含尊重定向图的数据的定向性质,同时也适用于非定向图。我们将社区探测的分割法应用于大量的模型和真实世界数据集。