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.
