Stochastic Block Model — Planted Partition

p_in within blocks · p_out between · BBP detectability transition at (p_in−p_out)²N = 2(p_in+p_out)

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Modularity Q:
Detectable:
The SBM is the canonical generative model for community structure. The Baik-Ben Arous-Péché transition gives a sharp threshold below which community recovery is information-theoretically impossible. Spectral clustering uses the top-K eigenvectors of the normalized Laplacian followed by k-means assignment. Colors show community membership.