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

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  • Wu, Qianyong
  • Hu, Jiang

Abstract

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). The proof uses some recent results in generalized Wigner matrices to prove the main theorem. Numerical experiments and real world data examples illustrate that our proposed linear spectral statistic has good performance.

Suggested Citation

  • Wu, Qianyong & Hu, Jiang, 2024. "A spectral based goodness-of-fit test for stochastic block models," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000737
    DOI: 10.1016/j.spl.2024.110104
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    References listed on IDEAS

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    1. Peter J. Bickel & Purnamrita Sarkar, 2016. "Hypothesis testing for automated community detection in networks," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 253-273, January.
    2. Ma, Xiaoke & Wang, Bingbo & Yu, Liang, 2018. "Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 786-802.
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