A Graph is a well-defined concept in mathematics, computer science and engineering disciplines that depend on them. However, oftentimes a practical implementation of a (directed) graph in a certain domain or application requires that edges don't merely connect vertices, but instead connect ports that exist on these vertices. In a directed graph, this would imply separation between input ports and output ports, wherein typically an edge starts at an output port and arrives at an input port.
Examples are easy to find: shader design tools, signal flow graphs in compiler theory, electronic schemas, high-level ETL scripting... all these tools require that vertices have named or distinct inputs and outputs.
Now for my Math question: is there any theory and nomenclature on these kinds of graphs, or is this considered to be an "implementation problem" of the engineering sciences? As you notice from my question, I can't quite pinpoint what this kind of thing is called ("A Graph With Node Ports"), and I'd love to see that answered.