stochastic block model

an $n$-node stochastic block model (SBM) graph with $C$ communities is given by

where

• $Y\in \{0,1{\}}^{n\times c}$ is the community assignment matrix (if $y_{ic}=1$ then node $i$ belongs to community $c$)
• $B$ is the matrix of intra- and inter-community probabilities: $B_{c_1,c_2}$ is the edge probability for a node pair $(i,j)$ such that $Y_{i{c}_1}=1,Y_{j{c}_2}=1$
• $A$ is the adjacency matrix