  Quantum networks are promising tools for the implementation of long-range
quantum communication. The characterization of quantum correlations in networks
and their usefulness for information processing is therefore central for the
progress of the field, but so far only results for small basic network
structures or pure quantum states are known. Here we show that symmetries
provide a versatile tool for the analysis of correlations in quantum networks.
We provide an analytical approach to characterize correlations in large network
structures with arbitrary topologies. As examples, we show that entangled
quantum states with a bosonic or fermionic symmetry can not be generated in
networks; moreover, cluster and graph states are not accessible. Our methods
can be used to design certification methods for the functionality of specific
links in a network and have implications for the design of future network
structures.
