Stochastic Block Model: Community & Belief Propagation

The stochastic block model (SBM) generates random graphs where nodes belong to hidden communities, with within-community edge probability p_in > p_out (across communities). Belief propagation (BP) infers community membership from the graph structure alone. Near the Kesten-Stigum threshold (p_in - p_out)² > c·(p_in + p_out), detection becomes impossible without superhuman algorithms.

SBM Parameters

Nodes N60
Communities K3
p_in0.00
p_out0.00
KS detectable?
BP accuracy0.000