Niche hypergraphs

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