# Stochastic block model

A class of generative models that assumes that the connectivity between nodes is determined by the block membership of them.

Assume a network with $N$ nodes. Each node $i$ has a block membership $z_i \in \{1, 2, \dots, k\}$. The block matrix $\mathbf{M} ~(k \times k)$ prescribes the connectivity between blocks either by setting the expected number of edges (canonical) or the exact number of edges (microcanonical).

## History

It has a long history in social science and computer science. Holland1983stochastic introduced the name and concept.

## Variations

### Mixed membership models

A “mixed-membership” model assumes that each node may have multiple hidden labels (see Overlapping community structure).