Can a scene graph be stored in the GPU? I am starting to learn WebGL. Can a scene graph be stored in the GPU? Or is that type of thing more for the main thread (or webworker)?

For example, I want to calculate some layout, and apply it as a transform matrix. Can I keep track of a scene graph node in the GPU over time, and modify it's properties over time?

I'm just wondering because I know the GPU architecture is different. Do people normally do scene graph stuff outside the GPU? Can it be done in the GPU?
Short answer: Yes, It can be done. But no one does so.

Long answer: 
Scene graphs can be stored and processed on a GPU using OpenCL/WebCL. But it is not practical to do so. Updating scene graphs (a tree not in flat memory) on a GPU is slow, and processing it on a GPU is also slow (again, the tree is not in flat memory), while computing transformation matrices is cheap on a CPU. Thus no one is doing this.