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Due to Fortuin and Kastelyin the q state Potts model has a representation as asum over random graphs, generalizing the Potts model to arbitrary q is based onthis representation. A key element of the random cluster representation is thecombinatorial factor ΓG(C, E), which is the number of ways to form C distinctclusters, consisting of totally E edges. We have devised a method to calculateΓG(C, E) from Monte Carlo simulations

The number of link and cluster states: the core of the 2Dqstate Potts model