I have a hierarchy of categories, where a category can have a single parent (and you can have multiple levels of children.)
I\'m investigating ways to display this infor
Your question treats your design problem as if it is an abstract thing. Unfortunately, it's not that simple - if only there was one perfect solution!
UI Design is highly contextualised. You have to think about the user group (i.e. their needs, goals and expectations) and the type of activity you are trying to support (i.e. what exactly is the user doing when they browse this tree? What's their goal? Are they going to use your app daily or once a year? etc). What works in your context may not work well elsewhere.
People are always disappointed when told "go build a quick prototype and test it on a sample of your end users". It involves further work and it outside a typcial developer's comfort zone. However, it is the only way to be sure that your UI is right for your given context.