  Prevailing methods for graphs require abundant label and edge information for
learning. When data for a new task are scarce, meta-learning can learn from
prior experiences and form much-needed inductive biases for fast adaption to
new tasks. Here, we introduce G-Meta, a novel meta-learning algorithm for
graphs. G-Meta uses local subgraphs to transfer subgraph-specific information
and learn transferable knowledge faster via meta gradients. G-Meta learns how
to quickly adapt to a new task using only a handful of nodes or edges in the
new task and does so by learning from data points in other graphs or related,
albeit disjoint label sets. G-Meta is theoretically justified as we show that
the evidence for a prediction can be found in the local subgraph surrounding
the target node or edge. Experiments on seven datasets and nine baseline
methods show that G-Meta outperforms existing methods by up to 16.3%. Unlike
previous methods, G-Meta successfully learns in challenging, few-shot learning
settings that require generalization to completely new graphs and
never-before-seen labels. Finally, G-Meta scales to large graphs, which we
demonstrate on a new Tree-of-Life dataset comprising of 1,840 graphs, a
two-orders of magnitude increase in the number of graphs used in prior work.
