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I have been struggling quite a while with a question, which I suspect might have a simple answer to:

I have a Graph G = (X,E,Ψ) with E (hyperedge) being a family of subsets of X and Ψ being a mapping between two hyperedges (E is a hyperedge and X = set of elements x1 ...xn).

I define subset X1 = X - X2.

What i want to achieve is G' = (X1,E1, Ψ). Basically, the hypergraph elements and the edges are all just a subset of the original graph G.

I want to give that function a name, since I need it to project a graph that has the same structure, in terms of mappings of hypergraphs, with each hypergraph having less elements. The hypergraph is [X,E].

Help is very much appreciated. I am quite at a loss. Thank you.

p.s. I am happy to provide additional information, since I don't have a strong math background, it is possible that I omitted some important information

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