Canonical and monophonic convexities in hypergraphs

Known properties of “canonical connections” from database theory and of “closed sets” from statistics implicitly define a hypergraph convexity, here called canonical convexity ( c -convexity), and provide an efficient algorithm to compute c -convex hulls. We characterize the class of hypergraphs in which c -convexity enjoys the Minkowski–Krein–Milman property. Moreover, we compare c -convexity with the natural extension to hypergraphs of monophonic convexity (or m -convexity), and prove that: (1) m -convexity is coarser than c -convexity, (2) m -convexity and c -convexity are equivalent in conformal hypergraphs, and (3) m -convex hulls can be computed in the same efficient way as c -convex hulls.