New Methods for Testing Community Structures in General Networks

Network data, characterized by interconnected nodes and edges, is pervasivein various domains and has gained significant popularity in recent years. In network data analysis, testing the presence of community structure in a network is one of the most important research tasks. Existing tests are mainly developed for unweighted networks. In practice, many real networks are weighted and our simulation study shows that the existing methods designed for unweighted networks may not be powerful for testing weighted networks. In this paper, we study the problem of testing the existence of a community structure in general networks that are either unweighted or weighted, and either dense or sparse. We propose two new tests, namely, the weighted signed-triangle test and the empirical likelihood test. We find that both methods outperform the existing tests when the network size is small; the empirical likelihood test may further outperform the weighted signed-triangle test in small networks. MSC2020 subject classifications: 60K35; 05C80.