  Motivated by bit threads, we introduce a new prescription for computing
entropy vectors outside the holographic entropy cone. By utilizing cycle flows
on directed graphs, we show that the maximum cycle flow associated to any
subset of vertices, which corresponds to a subsystem, manifestly obeys
purification symmetry. Furthermore, by restricting ourselves to a subclass of
directed graphs, we prove that the maximum cycle flow obeys both subadditivity
and strong subadditivity, thereby establishing it as a viable candidate for the
entropy associated to the subsystem. Finally, we demonstrate how our model
generalizes the entropy vectors obtainable via conventional flows in undirected
graphs, as well as conjecture that our model similarly generalizes the entropy
vectors arising from hypergraphs.
