Given graphs as input, Graph Neural Networks (GNNs) support the inference of nodes, edges, attributes, or graph properties. Graph Rewriting investigates the rule-based manipulation of graphs to model complex graph transformations.

We propose that, therefore, (i) graph rewriting subsumes GNNs and could serve as an operational semantic model to study and compare them, and (ii) the representation of GNNs as graph rewrite systems can help to design and analyse GNNs, their architectures and algorithms. Hence we propose Graph Rewriting Neural Networks (GReNN) as both novel semantic foundation and engineering discipline for GNNs.

We develop a case study of a Message Passing Neural Network and its realisation in graph rewriting and explore its incremental operation in the face of dynamic updates.