  We study entanglement properties of hypergraph states in arbitrary finite
dimension. We compute multipartite entanglement of elementary qudit hypergraph
states, namely those endowed with a single maximum-cardinality hyperedge. We
show that, analogously to the qubit case, also for arbitrary dimension there
exists a lower bound for multipartite entanglement of connected qudit
hypergraph states; this is given by the multipartite entanglement of an
equal-dimension elementary hypergraph state featuring the same number of qudits
as the largest-cardinality hyperedge. We highlight interesting differences
between prime and non-prime dimension in the entanglement features.
