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.
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