I\'m looking for a library in c or objective c that does node-data visualizations similar to http://arborjs.org/
Actually there seems to be an Objective-C port of arborjs, see https://github.com/epreston/PSArborTouch.
This is called graph visualization and the best toolkit that I know for it is called GraphViz. It has C libraries.
That sort of graph doesn't have a particular name; not without knowing more context. So without more information, it's a "graph".
As for a library, there's an open source project called GraphViz. You'll have to dig a bit to find the drawing code, but it's in there somewhere. :)