A Note on the Identifiability of the Degree-Corrected Stochastic Block Model

Abstract

In this short note, we address the identifiability issues inherent in the Degree-Corrected Stochastic Block Model (DCSBM). We provide a rigorous proof demonstrating that the parameters of the DCSBM are identifiable up to a scaling factor and a permutation of the community labels, under a mild condition.

arXiv commentAdded example in section 3.2; added section 3.4 Updated notation in example 3