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Phase transition for the generalized two-community stochastic block model
Published online by Cambridge University Press: 31 July 2023
Abstract
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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust