It is a challenging problem to assign communities in a complex network so that nodes in a community are tightly connected on the basis of higher-order connectivity patterns such as motifs. In this paper, we develop an efficient algorithm that detects communities based on higher-order structures. Our algorithm can also detect communities based on a signed motif, a colored motif, a weighted motif, as well as multiple motifs. We also introduce stochastic block models on the basis of higher-order structures. Then, we test our community detection algorithm on real-world networks and computer generated graphs drawn from the stochastic block models. The results of the tests indicate that our community detection algorithm is effective to identify communities on the basis of higher-order connectivity patterns.

中文翻译：

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复杂网络中基于高阶结构的高效社区检测算法。

在复杂的网络中分配社区是一个具有挑战性的问题，以使社区中的节点根据诸如主题的高阶连接模式紧密连接。在本文中，我们开发了一种基于高阶结构检测社区的有效算法。我们的算法还可以基于签名的主题，彩色的主题，加权的主题以及多个主题来检测社区。我们还介绍了基于高阶结构的随机块模型。然后，我们在现实世界的网络上测试我们的社区检测算法，并从随机块模型中提取计算机生成的图形。测试结果表明，我们的社区检测算法可有效地根据高阶连接模式识别社区。