Network community detection using higher-order structures
提出一种利用三角形等高阶子图结构进行网络社区检测的新方法，在考虑边依赖的模型下给出首个有限样本误差界和一致性结果，能发现传统方法忽略的社区。
Summary In many real-world networks, it is often observed that subgraphs or higher-order structures of certain configurations, e.g., triangles and by-fans, are overly abundant compared to standard randomly generated networks (Milo et al., 2002). However, statistical models accounting for this phenomenon are limited, especially when community structure is of interest. This limitation is coupled with a lack of community detection methods that leverage subgraphs or higher-order structures. In this paper, we propose a new community detection method that effectively uses higher-order structures in a network. Furthermore, for the community detection accuracy, under an edge-dependent network model that consists of both community and triangle structures, we develop a finite-sample error bound characterized by the expected triangle degree, which leads to the consistency of the proposed method. To the best of our knowledge, this is the first statistical error bound and consistency result for community detection of a single network considering a network model with dependent edges. We also show, in both simulation studies and a real-world data example, that our method unveils network communities that are otherwise invisible to methods that ignore higher-order structures.