Determining the Number of Communities in Degree-corrected Stochastic Block Models

Understand

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio statistic.

• To this end, we introduce a method that combines spectral clustering with binary segmentation.
• This approach guarantees an upper bound for the pseudo likelihood ratio statistic when the model is over-fitted.
• We also derive its limiting distribution when the model is under-fitted.