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.

给定节点属性图和图任务（链接预测或节点分类），我们能否判断图神经网络（GNN）能否表现良好？我们提出 NetInfoF，一个包括 NetInfoF_Probe 和 NetInfoF_Act 的框架，用于测量和利用网络可用信息（NUI）。NetInfoF 具有广泛的适用性，基于理论保证和闭式解，通过对节点相似度的调整，可有效扩展到大规模输入。在合成数据集和真实世界数据集上的应用中，NetInfoF 在链接预测方面获得了显著优势。