  Given a node-attributed graph, and a graph task (link prediction or node
classification), can we tell if a graph neural network (GNN) will perform well?
More specifically, do the graph structure and the node features carry enough
usable information for the task? Our goals are (1) to develop a fast tool to
measure how much information is in the graph structure and in the node
features, and (2) to exploit the information to solve the task, if there is
enough. We propose NetInfoF, a framework including NetInfoF_Probe and
NetInfoF_Act, for the measurement and the exploitation of network usable
information (NUI), respectively. Given a graph data, NetInfoF_Probe measures
NUI without any model training, and NetInfoF_Act solves link prediction and
node classification, while two modules share the same backbone. In summary,
NetInfoF has following notable advantages: (a) General, handling both link
prediction and node classification; (b) Principled, with theoretical guarantee
and closed-form solution; (c) Effective, thanks to the proposed adjustment to
node similarity; (d) Scalable, scaling linearly with the input size. In our
carefully designed synthetic datasets, NetInfoF correctly identifies the ground
truth of NUI and is the only method being robust to all graph scenarios.
Applied on real-world datasets, NetInfoF wins in 11 out of 12 times on link
prediction compared to general GNN baselines.
