  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.
