  Graphs are ubiquitous in nature and can therefore serve as models for many
practical but also theoretical problems. For this purpose, they can be defined
as many different types which suitably reflect the individual contexts of the
represented problem. To address cutting-edge problems based on graph data, the
research field of Graph Neural Networks (GNNs) has emerged. Despite the field's
youth and the speed at which new models are developed, many recent surveys have
been published to keep track of them. Nevertheless, it has not yet been
gathered which GNN can process what kind of graph types. In this survey, we
give a detailed overview of already existing GNNs and, unlike previous surveys,
categorize them according to their ability to handle different graph types and
properties. We consider GNNs operating on static and dynamic graphs of
different structural constitutions, with or without node or edge attributes.
Moreover, we distinguish between GNN models for discrete-time or
continuous-time dynamic graphs and group the models according to their
architecture. We find that there are still graph types that are not or only
rarely covered by existing GNN models. We point out where models are missing
and give potential reasons for their absence.
