Graph clustering using triangle-aware measures in large networks

Graph clustering (also referred to as community detection) is an important topic in network analysis. Although a large amount of literature has been published on the problem, most of them are designed at the level of lower-order structure of networks, e.g., individual vertices and edges, and fail to capture higher-order information of networks. Recently, higher-order units (under the name of motifs) are introduced to graph clustering. These methods typically focus on constructing a motif-based hypergraph where higher-order information is preserved, and communities abstracted from the hypergraph usually achieve better accuracy. However, the hypergraph is often fragmented for a sparse network and contains a large number of isolated vertices that will be outliers of the identified community cover. To address the fragmentation problem, we propose an asymmetric triangle enhancement approach for graph clustering, in which a mixture of edges and asymmetric triangles is taken into consideration for cluster measures. We also design an approximation model to speed up the algorithm by estimating the measures. Extensive experiments on real and synthetic networks demonstrate the accuracy and efficiency of the proposed method.