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1 results

  • Phase transition for the generalized two-community stochastic block model

  • Part of
  • Sunmin Lee, Ji Oon Lee
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 2 / June 2024
    Published online by Cambridge University Press:
    31 July 2023, pp. 385-400
    Print publication:
    June 2024
    • Article
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  • We study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2-SBM). Based on analysis of the Stieljtes transform of the empirical spectral distribution, we prove a Baik–Ben Arous–Péché (BBP)-type transition for the largest eigenvalue of the G2-SBM. For specific models, such as a hidden community model and an unbalanced stochastic block model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.