Modeling sparsity in count-weighted networks with stochastic block models

Abstract Community detection methods have been extensively studied to recover community structures in network data. While many existing approaches focus on binary networks, real-world networks often exhibit weighted connections, which provide additional information about the strength of interactions. However, most methods do not simultaneously account for both network sparsity and heterogeneous node degrees, which are crucial for accurately modeling real-world networks. To address this, we propose a probabilistic model for generating weighted networks that explicitly incorporates sparsity control and degree corrections. We develop a community detection method based on the likelihood using a Variational Expectation-Maximization algorithm, allowing efficient estimation of both community memberships and model parameters. Through simulations, we show that our approach accurately recovers community structures. We further analyze the Brazilian airport network to compare the community structures before and during the COVID-19 pandemic.