Stochastic Block Model — Communities

Nodes belong to latent blocks; edges form with probability p_in within blocks and p_out between them. The Kesten-Stigum threshold separates detectable from undetectable community structure.

Controls

Nodes N 80 Blocks K 3 p_in 0.35 p_out 0.05

Edges: —

KS detectable: —

Modularity Q: —

Colors = true blocks.
KS threshold:
(p_in-p_out)² > (K-1)·p̄
where p̄ = mean edge prob.