  Graphs have a superior ability to represent relational data, like chemical
compounds, proteins, and social networks. Hence, graph-level learning, which
takes a set of graphs as input, has been applied to many tasks including
comparison, regression, classification, and more. Traditional approaches to
learning a set of graphs heavily rely on hand-crafted features, such as
substructures. But while these methods benefit from good interpretability, they
often suffer from computational bottlenecks as they cannot skirt the graph
isomorphism problem. Conversely, deep learning has helped graph-level learning
adapt to the growing scale of graphs by extracting features automatically and
encoding graphs into low-dimensional representations. As a result, these deep
graph learning methods have been responsible for many successes. Yet, there is
no comprehensive survey that reviews graph-level learning starting with
traditional learning and moving through to the deep learning approaches. This
article fills this gap and frames the representative algorithms into a
systematic taxonomy covering traditional learning, graph-level deep neural
networks, graph-level graph neural networks, and graph pooling. To ensure a
thoroughly comprehensive survey, the evolutions, interactions, and
communications between methods from four different branches of development are
also examined. This is followed by a brief review of the benchmark data sets,
evaluation metrics, and common downstream applications. The survey concludes
with a broad overview of 12 current and future directions in this booming
field.
