Terminology for a graph with ports on its nodes
I was wondering the same thing. It seems that there are a number of publications revolving around this idea, most of them at the TERMGRAPH workshop. They are usually called “port graphs” there.

Tracing the related work of a random sample of papers yields that the following might be the prime paper that introduces this formalism:


  Andrei, O. and H. Kirchner, A Rewriting Calculus for Multigraphs with Ports., in: Proceedings of RULE’07, Electronic Notes in Theoretical Computer Science 219, 2008, pp. 67–82. 


One that I find particularly interesting is


  Sandra Alves, Maribel Fernández, and Ian Mackie. A new graphical calculus of proofs. In TERMGRAPH, volume 48 of EPTCS, pages 69–84, 2011