Figure 3.

Algorithmic Maxent in the generation of graphs (without loss of generality, no other restrictions are imposed). The paths to statistical and algorithmic randomness are different, and they determine different principles for different purposes. Algorithmic Maxent tells apart recursive cases from non-recursive (thus algorithmic random) ones. Classical Maxent quantifies statistical randomness but its algorithmic refinement quantifies both statistical and algorithmic randomness. This opens up the range of possibilities for moving toward and reaching a random graph, by not only considering whether it is random-looking but also whether it is actually algorithmically random. Because the worse case for algorithmic Maxent is not to distinguish recursive cases (due to, e.g., semi-computability) its worse performance is to retrieve the same Gibbs measure and produce the same ensemble as classical Maxent would do.