# A spectral based goodness-of-fit test for stochastic block models

arXiv: https://arxiv.org/abs/2303.14508 · HTML: https://mlsanity.com/paper/2303.14508/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2023.

## Built on by (most cited first, 2 of 2)

- [Latent class analysis by regularized spectral clustering](https://mlsanity.com/paper/2310.18727/) (2023)
- [A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy](https://mlsanity.com/paper/2505.21580/) (2025)

## Abstract (arXiv)

Community detection is a fundamental problem in complex network data analysis. Though many methods have been proposed, most existing methods require the number of communities to be the known parameter, which is not in practice. In this paper, we propose a novel goodness-of-fit test for the stochastic block model. The test statistic is based on the linear spectral of the adjacency matrix. Under the null hypothesis, we prove that the linear spectral statistic converges in distribution to N(0,1). Some recent results in generalized Wigner matrices are used to prove the main theorems. Numerical experiments and real world data examples illustrate that our proposed linear spectral statistic has good performance.