  We introduce a class of multiqubit quantum states which generalizes graph
states. These states correspond to an underlying mathematical hypergraph, i.e.
a graph where edges connecting more than two vertices are considered. We derive
a generalised stabilizer formalism to describe this class of states. We
introduce the notion of k-uniformity and show that this gives rise to classes
of states which are inequivalent under the action of the local Pauli group.
Finally we disclose a one-to-one correspondence with states employed in quantum
algorithms, such as Deutsch-Jozsa's and Grover's.
