Geodesic
Directed hypergraphs: a tool for researching digraphs and hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 313-335.

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In this paper we introduce the concept of directed hypergraph. It is a generalisation of the concept of digraph and is closely related with hypergraphs. The basic idea is to take a hypergraph, partition its edges non-trivially (when possible), and give a total order to such partitions. The elements of these partitions are called levels. In order to preserve the structure of the underlying hypergraph, we ask that only vertices which belong to exactly the same edges may be in the same level of any edge they belong to. Some little adjustments are needed to avoid directed walks within a single edge of the underlying hypergraph, and to deal with isolated vertices.
Keywords: hypergraph, strongly independent set, transversal set, kernel 
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Galeana-Sánchez, Hortensia; Manrique, Martín. Directed hypergraphs: a tool for researching digraphs and hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 2, pp. 313-335. http://geodesic.mathdoc.fr/item/DMGT_2009_29_2_a7/

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