stochastic block model

Data

subject:: Data Science Methods for Large Scale Graphs
parent:: Graph Signals and Graph Signal Processing
theme:: math notes

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

P = Y B Y^{T}, A \sim P

where

$Y \in {0, 1}^{n \times c}$ is the community assignment matrix (if $y_{i c} = 1$ 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

Note

While $B$ can take any value (as long as it is symmetric), often we have $$B = \begin{cases}p \text{ if }c_{1}=c_{2} \ q \text{ otherwise}\end{cases}$$
with $q = 1 - p$

References

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stochastic block model

References

See Also

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