mlsanityData to 7 Oct 2026

A goodness-of-fit test for stochastic block models

arXiv 1412.4857 ↗First posted 16 Dec 2014math.ST stat.ME stat.THcited by 20

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Abstract (arXiv)

The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models with finer structures. These results naturally lead to a consistent sequential testing estimate of the number of communities.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Dec 2014.

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Citing papers per year: 2021: 9; 2022: 2; 2023: 4; 2024: 2; 2025: 3.

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  1. 2021Estimating Graph Dimension with Cross-validated Eigenvaluescited by 6
  2. 2021Hypothesis Testing for Equality of Latent Positions in Random Graphscited by 5
  3. 2021Network Estimation by Mixing: Adaptivity and Morecited by 4
  4. 2021Training Graph Neural Networks by Graphon Estimationcited by 4
  5. 2021A useful criterion on studying consistent estimation in community detectioncited by 3
  6. 2022Lost in the Shuffle: Testing Power in the Presence of Errorful Network Vertex Labelscited by 3
  7. 2021Exact Recovery of Community Structures Using DeepWalk and Node2veccited by 2
  8. 2021Directed degree corrected mixed membership model and estimating community memberships in directed networkscited by 2
  9. 2023Graphon Estimation in bipartite graphs with observable edge labels and unobservable node labelscited by 2
  10. 2023Restricted Tweedie Stochastic Block Modelscited by 2
  11. 2023Detection problems in the spiked matrix modelscited by 1
  12. 2023Inferences on Mixing Probabilities and Ranking in Mixed-Membership Modelscited by 1
8 more
  1. 2024Estimating the number of clusters of a Block Markov Chaincited by 1
  2. 2025A statistically consistent measure of semantic uncertainty using Language Modelscited by 1
  3. 2021A Goodness-of-fit Test on the Number of Biclusters in a Relational Data Matrixcited by 0
  4. 2021Spectral goodness-of-fit tests for complete and partial network datacited by 0
  5. 2022Adversarial contamination of networks in the setting of vertex nomination: a new trimming methodcited by 0
  6. 2024Selecting the Number of Communities for Weighted Degree-Corrected Stochastic Block Modelscited by 0
  7. 2025A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancycited by 0
  8. 2025Simultaneous estimation of connectivity and dimensionality in samples of networkscited by 0