Geodesic
Niche Hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 819-832

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If D = (V,A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set ℰ = ℯ ⊆ V | |e| ≥ 2 ∧ ∃ v ∈ V : e = ND-(v) ∨ ℯ = ND+(v). Niche hypergraphs generalize the well-known niche graphs (see [11]) and are closely related to competition hypergraphs (see [40]) as well as double competition hypergraphs (see [33]). We present several properties of niche hypergraphs of acyclic digraphs.
Keywords: niche hypergraph, niche number 
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Garske, Christian; Sonntag, Martin; Teichert, Hanns-Martin. Niche Hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 819-832. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a3/