  Graph structures are ubiquitous throughout the natural sciences. Here we
consider graph-structured quantum data and describe how to carry out its
quantum machine learning via quantum neural networks. In particular, we
consider training data in the form of pairs of input and output quantum states
associated with the vertices of a graph, together with edges encoding
correlations between the vertices. We explain how to systematically exploit
this additional graph structure to improve quantum learning algorithms. These
algorithms are numerically simulated and exhibit excellent learning behavior.
Scalable quantum implementations of the learning procedures are likely feasible
on the next generation of quantum computing devices.
