Hypergraphs induced by algebras of fixed type

A characterization of the weak subalgebra lattice of a partial algebra of a fixed type is a natural algebraic problem. In Pióro (2000, 2002) [13] and [15] we have shown that this algebraic problem is equivalent to the following hypergraph question, interesting in itself: When can edges of a hypergraph be directed to form a partial algebra of a fixed type (equivalently, to form a directed hypergraph of a fixed type)? This problem will be solved in the present paper.