  Distributing entanglement among multiple users is a fundamental problem in
quantum networks, requiring an efficient solution. In this work, a protocol is
proposed for extracting maximally entangled (GHZn) states for any number of
parties in quantum networks of arbitrary topology. It is based on the graph
state formalism and requires minimal assumptions on the network state. The
protocol only requires local measurements at the network nodes and just a
single qubit memory per user. Existing protocols on bipartite entanglement
routing are also improved for specific nearest-neighbor network architectures.
To this end, the concept of majorization is utilized to establish a hierarchy
among different paths in a network based on their efficacy. This approach
utilizes the symmetry of the underlying graph state to obtain better-performing
algorithms.
