English

Phase Transition in the Generalized Stochastic Block Model

Statistics Theory 2022-06-22 v1 Probability Statistics Theory

Abstract

We study the problem of detecting the community structure from the generalized stochastic block model (GSBM). Based on the analysis of the Stieljtes transform of the empirical spectral distribution, we prove a BBP-type transition for the largest eigenvalue of the GSBM. For specific models such as a hidden community model and an unbalanced stochastic model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.

Cite

@article{arxiv.2206.09566,
  title  = {Phase Transition in the Generalized Stochastic Block Model},
  author = {Sun Min Lee and Ji Oon Lee},
  journal= {arXiv preprint arXiv:2206.09566},
  year   = {2022}
}

Comments

18 pages, 4 figures

R2 v1 2026-06-24T11:56:51.648Z