I have been looking for a desktop GUI app that allows the connection of defined nodes similar to Quartz Composer. The nodes themselves don't need any functionality, I just need it for visual representation.
Some examples:
http://bergie.iki.fi/blog/inspiration-for-fbp-ui/
And the node editor of this project: https://github.com/vurtun/nuklear
Is there a singular term to define this type of graph? I suspect node graph, but google searches for anything with node in it tend to also have .js
Your question seems unclear but I'll try to answer it.
There are some apps with NodeGraph (aka NodeTree/PatchTree) similar to QC: Vuo, Derivative TouchDesigner, VVVV, Troikatronix Isadora, Cycling'74 MaxMSP, etc.
There are also some digital compositing apps for building a script with nodes: The Foundry Nuke, Blackmagic Fusion, Apple Shake, etc. Compositing packages have a DAG (Directed Acyclic Graph) in their User Interface. DAG is like NodeTree/PatchTree.
For your tasks you could use The Foundry Nuke. It allows build trees with nodes' names whatever you want. Nuke's nodes are convenient for visual representation.