  Multipartite entanglement, a higher-order interaction unique to quantum
information, offers various advantages over bipartite entanglement in quantum
network (QN) applications. Establishing multipartite entanglement across remote
parties in QN requires entanglement routing, which irreversibly transforms the
QN topology at the cost of existing entanglement links. Here, we address the
question of whether a QN can be topologically transformed into another via
entanglement routing. Our key result is an exact mapping from multipartite
entanglement routing to Nash-Williams's graph immersion problem, extended to
hypergraphs. This generalized hypergraph immersion problem introduces a partial
order between QN topologies, permitting certain topological transformations
while precluding others, offering discerning insights into the design and
manipulation of higher-order network topologies in QNs.
