  Prediction of node and graph labels are prominent network science tasks. Data
analyzed in these tasks are sometimes related: entities represented by nodes in
a higher-level (higher-scale) network can themselves be modeled as networks at
a lower level. We argue that systems involving such entities should be
integrated with a "network of networks" (NoN) representation. Then, we ask
whether entity label prediction using multi-level NoN data via our proposed
approaches is more accurate than using each of single-level node and graph data
alone, i.e., than traditional node label prediction on the higher-level network
and graph label prediction on the lower-level networks. To obtain data, we
develop the first synthetic NoN generator and construct a real biological NoN.
We evaluate accuracy of considered approaches when predicting artificial labels
from the synthetic NoNs and proteins' functions from the biological NoN. For
the synthetic NoNs, our NoN approaches outperform or are as good as node- and
network-level ones depending on the NoN properties. For the biological NoN, our
NoN approaches outperform the single-level approaches for just under half of
the protein functions, and for 30% of the functions, only our NoN approaches
make meaningful predictions, while node- and network-level ones achieve random
accuracy. So, NoN-based data integration is important.
