Consistent community detection approach in the nonparametric weighted stochastic blockmodel with unspecified number of communities

The stochastic blockmodel (SBM) is a widely used model for representing graphs. Numerous approaches have been applied to the SBM to detect latent community structures in graphs, typically using two types of consistency (strong and weak) to evaluate their performance. Most of these methods have been studied and shown to be consistent under the SBM framework. However, the consistency of the weighted SBM, an important extension of the SBM, has been largely overlooked. Moreover, few approaches are capable of detecting communities when the number of communities is unknown. In this paper, we propose a nonparametric method for effective community detection under the assortative, nonparametric weighted SBM with an unknown number of communities, and we establish the consistency of our approach. We introduce a novel concept, “consistency in relationship”, as a more practical criterion to assess the performance of community detection algorithms. Since solving the optimization problem in our approach becomes intractable for large sample sizes, we propose an efficient algorithm to approximate it. Simulations demonstrate that our community detection method is both efficient and robust, particularly for unbalanced networks. We illustrate the effectiveness of our approach on three real-world networks.