  Graph neural networks (GNNs) have achieved superior performance in various
applications, but training dedicated GNNs can be costly for large-scale graphs.
Some recent work started to study the pre-training of GNNs. However, none of
them provide theoretical insights into the design of their frameworks, or clear
requirements and guarantees towards their transferability. In this work, we
establish a theoretically grounded and practically useful framework for the
transfer learning of GNNs. Firstly, we propose a novel view towards the
essential graph information and advocate the capturing of it as the goal of
transferable GNN training, which motivates the design of EGI (Ego-Graph
Information maximization) to analytically achieve this goal. Secondly, when
node features are structure-relevant, we conduct an analysis of EGI
transferability regarding the difference between the local graph Laplacians of
the source and target graphs. We conduct controlled synthetic experiments to
directly justify our theoretical conclusions. Comprehensive experiments on two
real-world network datasets show consistent results in the analyzed setting of
direct-transfering, while those on large-scale knowledge graphs show promising
results in the more practical setting of transfering with fine-tuning.
