An Algebraic Foundation for Graph-based Diagrams in Computing
We develop an algebraic foundation for some of the graph-based structures underlying a variety of popular diagrammatic notations for the specification, modelling and programming of computing systems. Using hypergraphs and higraphs as leading examples, a locally ordered category Graph(C) of graphs in a locally ordered category C is defined and endowed with symmetric monoidal closed structure. Two other operations on higraphs and variants, selected for relevance to computing applications, are generalised in this setting.