  Due to Fortuin and Kastelyin the $q$ state Potts model has a representation
as a sum over random graphs, generalizing the Potts model to arbitrary $q$ is
based on this representation. A key element of the Random Cluster
representation is the combinatorial factor
$\Gamma_{\Graph{G}}(\Clusters,\Edges)$, which is the number of ways to form
$\Clusters$ distinct clusters, consisting of totally $\Edges$ edges. We have
devised a method to calculate $\Gamma_{\Graph{G}}(\Clusters,\Edges)$ from Monte
Carlo simulations.

Statistical Mechanics