Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. Based on this, the young research field of Graph Neural Networks (GNNs) has emerged. Despite the youth of the field and the speed in which new models are developed, many good surveys have been published in the last years. Nevertheless, an overview on which graph types can be modeled by GNNs is missing. 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 as well as on dynamic graphs of different structural constitutions, with or without node or edge attributes. Moreover in the dynamic case, we separate the models in discrete-time and continuous-time dynamic graphs based on their architecture. While ordering the existing GNN models, 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.
