Stochastic block models

In the previous chapters, we have already discussed stochastic models using the Monte Carlo simulation. So far, we have been discussing graphs and networks, so purely from that context, a community structure can also be viewed as a graph. In such graphs, nodes often cluster together as densely connected subgraphs. In general, the probability of an edge between two such nodes is a function of the cluster to which the node belongs.

A popular choice for such a network partition is the stochastic block model. A simple definition of a stochastic block model is characterized by a scalar n. This represents the number of groups or the number of clusters and a matrix that shows the nodes and their connections. For a more rigorous ...

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