A transitive and incomplete binary relation is a "preorder".
A transitive and complete binary relation is a "weak order".
A transitive, antisymmetric, and complete binary relation is a "total order" or linear order.
What "order" is it if it is intransitive and complete?
(reflexivity is always assumed)
"Completeness" means "connexity" in Wikipedia. It seems like that Wikipedia was recently edited to remove the nomenclature of "completeness"
Ok solution found: it is called a "majority relation". With an additional axiom of "asymmetry", it becomes a strict majority relation or a tournament graph.