Degree-corrected distribution-free model for community detection in weighted networks

A degree-corrected distribution-free model is proposed for weighted social networks with latent structural information. The model extends the previous distribution-free models by considering variation in node degree to fit real-world weighted networks, and it also extends the classical degree-corrected stochastic block model from un-weighted network to weighted network. We design an algorithm based on the idea of spectral clustering to fit the model. Theoretical framework on consistent estimation for the algorithm is developed under the model. Theoretical results when edge weights are generated from different distributions are analyzed. We also propose a general modularity as an extension of Newman's modularity from un-weighted network to weighted network. Using experiments with simulated and real-world networks, we show that our method significantly outperforms the uncorrected one, and the general modularity is effective.