Two-Sample Test for Stochastic Block Models via the Largest Singular Value

Understand

The stochastic block model is widely used for detecting community structures in network data.

• However, the research interest of much literature focuses on the study of one sample of stochastic block models.
• How to detect the difference of the community structures is a less studied issue for stochastic block models.
• In this article, we propose a novel test statistic based on the largest singular value of a residual matrix obtained by subtracting the geometric mean of two estimated block mean effects from the sum of two observed adjacency matrices.