# A likelihood-ratio type test for stochastic block models with bounded degrees

arXiv: https://arxiv.org/abs/1807.04426 · HTML: https://mlsanity.com/paper/1807.04426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2018.

## Built on by (most cited first, 1 of 1)

- [Fitting networks with a cancellation trick](https://mlsanity.com/paper/2502.16728/) (2025)

## Abstract (arXiv)

A fundamental problem in network data analysis is to test Erd"os-R'enyi model Gleft(n,fraca+b2nright) versus a bisection stochastic block model Gleft(n,fracan,fracbnright), where a,b>0 are constants that represent the expected degrees of the graphs and n denotes the number of nodes. This problem serves as the foundation of many other problems such as testing-based methods for determining the number of communities (citeBS16,L16) and community detection (citeMS16). Existing work has been focusing on growing-degree regime a,b→∞ (citeBS16,L16,MS16,BM17,B18,GL17a,GL17b) while leaving the bounded-degree regime untreated. In this paper, we propose a likelihood-ratio (LR) type procedure based on regularization to test stochastic block models with bounded degrees. We derive the limit distributions as power Poisson laws under both null and alternative hypotheses, based on which the limit power of the test is carefully analyzed. We also examine a Monte-Carlo method that partly resolves the computational cost issue. The proposed procedures are examined by both simulated and real-world data. The proof depends on a contiguity theory developed by Janson citeJ95.