  We partially characterize nuclearity for the recently introduced class of
hypergraph C*-algebras using a tailor-made hypergraph minor relation. The
latter is generated by certain operations on hypergraphs which resemble the
moves on directed graphs used by Eilers, Restorff, Ruiz and S{\o}rensen to
classify unital graph C*-algebras. In particular, we obtain a new proof of the
fact that every graph C*-algebra associated to a finite graph is nuclear.
