Social and Behavioral Sciences Commons^™

Determining The Number Of Communities In Degree-Corrected Stochastic Block Models, Shujie Ma, Liangjun Su, Yichong Zhang

Research Collection School Of Economics

We propose to estimate the number of communities in degree-corrected stochastic block models based on a pseudo likelihood ratio. For estimation, we consider a spectral clustering together with binary segmentation method. 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. Based on these properties, we establish the consistency of our estimator for the true number of communities. Developing these theoretical properties require a mild condition on the average degree: growing at a rate faster than log(n), where n is the number …