Relational data is one of the most valuable types of data collected, appearing in various physical, social, and technological systems. The simplest form of relational data can be represented by graph structures, which encode pairwise relations between elements. Graph Neural Networks (GNNs) are Deep Learning models specifically designed for graph data. Our goal is to design distributed GNNs for use cases where the data is distributed across agents and should not be shared. Improvements may include, but are not limited to, communication and computational efficiency, privacy enhancement, more scalable or effective relational structures. Application areas include internet of things and digital twins as well as coordination and control of autonomous vehicles.