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.
Power, J., & Tourlas, K. (2001). An Algebraic Foundation for Graph-based Diagrams in Computing. Electronic Notes in Theoretical Computer Science, 45, 346-357. https://doi.org/10.1016/S1571-0661(04)80971-X