  Quantum networks are of high interest nowadays and a quantum internet has
been long envisioned. Network-entanglement adapts the notion of entanglement to
the network scenario and network-entangled states are considered to be a
resource to overcome the limitations of a given network structure. In this work
we introduce measures of quantum network-entanglement that are well-defined
within the general framework of quantum resource theories, which at the same
time have a clear operational interpretation characterizing the extra resources
necessary to prepare a targeted quantum state within a given network. In
particular, we define the network communication cost and the network round
complexity, which turn out to be intimately related to graph-theoretic
parameters. We also provide device-dependent and device-independent methods to
estimate these measures.
