Figure 2. An example of the Metropolis-Hastings transition step.

The current network, , with node labeling is updated to a proposed network, , by adding/deleting a single edge to/from at random. This picture shows two possible ways for to be updated. In one instance, a new edge is added between and to obtain , while the other is obtained by deleting the the edge between and . As for the proposed node labeling, an integer , in this example , is selected randomly from . From there the node labels and are swapped to get .