  In this work, we generalize the graph-theoretic techniques used for the
holographic entropy cone to study hypergraphs and their analogously-defined
entropy cone. This allows us to develop a framework to efficiently compute
entropies and prove inequalities satisfied by hypergraphs. In doing so, we
discover a class of quantum entropy vectors which reach beyond those of
holographic states and obey constraints intimately related to the ones obeyed
by stabilizer states and linear ranks. We show that, at least up to 4 parties,
the hypergraph cone is identical to the stabilizer entropy cone, thus
demonstrating that the hypergraph framework is broadly applicable to the study
of entanglement entropy. We conjecture that this equality continues to hold for
higher party numbers and report on partial progress on this direction. To
physically motivate this conjectured equivalence, we also propose a plausible
method inspired by tensor networks to construct a quantum state from a given
hypergraph such that their entropy vectors match.
