  Graph states are an important class of multipartite entangled quantum states.
We propose a new approach for distributing graph states across a quantum
network. We consider a quantum network consisting of nodes-quantum computers
within which local operations are free-and EPR pairs shared between nodes that
can continually be generated. We prove upper bounds for our approach on the
number of EPR pairs consumed, number of timesteps taken, and amount of
classical communication required, all of which are equal to or better than that
of prior work. We also reduce the problem of minimizing the number of timesteps
taken to distribute a graph state using our approach to a network flow problem
having polynomial time complexity.
