Modeling and exploring high-order connectivity patterns, also called network motifs, are essential for understanding the fundamental structures that control and mediate the behavior of many complex systems. For example, in social networks, triangles have been proven to play the fundamental role in understanding social network communities; in online transaction networks, detecting directed looped transactions helps identify money laundering activities; in personally identifiable information networks, the star-shaped structures may correspond to a set of synthetic identities. Despite the ubiquity of such high-order structures, many existing graph clustering methods are either not designed for the high-order connectivity patterns, or suffer from the prohibitive computational cost when modeling high-order structures in the large-scale networks. This article generalizes the challenges in multiple dimensions. First ( Model ), we introduce the notion of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by the user-specified high-order network structure. Second ( Algorithm ), we propose a novel high-order structure-preserving graph clustering framework named HOSGRAP , which partitions the graph into structure-rich clusters in polylogarithmic time with respect to the number of edges in the graph. Third ( Generalization ), we generalize our proposed algorithm to solve the real-world problems on various types of graphs, such as signed graphs, bipartite graphs, and multi-partite graphs. Experimental results on both synthetic and real graphs demonstrate the effectiveness and efficiency of the proposed algorithms.

中文翻译：

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海量图的高阶结构探索

建模和探索高阶连接模式（也称为网络基序）对于理解控制和调节许多复杂系统行为的基本结构至关重要。例如，在社交网络中，三角形已被证明在理解社交网络社区方面发挥着基础性作用；在在线交易网络中，检测定向循环交易有助于识别洗钱活动；在个人身份信息网络中，星形结构可能对应于一组合成身份。尽管这种高阶结构无处不在，但许多现有的图聚类方法要么不是为高阶连接模式设计的，要么在对大规模网络中的高阶结构进行建模时受到过高的计算成本。本文概括了多个维度的挑战。第一的 （模型），我们引入了高阶电导的概念，并定义了高阶扩散核心，它基于由用户指定的高阶网络结构。第二 （算法)，我们提出了一种新颖的高阶结构保持图聚类框架命名户型图, 将图划分为结构丰富关于图中边数的多对数时间聚类。第三 （概括)，我们推广我们提出的算法来解决各种类型图的实际问题，例如有符号图、二分图和多分图。合成图和真实图的实验结果证明了所提出算法的有效性和效率。