Figure 4.

Reduction of the Gibbs/Boltzmann distribution. While objects may appear maximally statistically random in all other properties but the ones constrained by a problem of interest for which Maxent is relevant, there may actually be of different nature and some may actually be algorithmically random while others recursively generated hence they should not be placed in the same distribution. The original graph G has a shortest description $minG$ and perturbations to either the original and compressed version can lead to randomised graphs for different purposes. Some of them will have maximum entropy denoted by $max{G}_n^{\prime }$ but among them only some will also be of $maxK\left(G\right)$.