So how is JSON a graph? Or maybe the answer is just, No. Not generally. I'm confused by your question.
No. JSON is not a graph.
Any visualization of a graph from JSON would be a specific encoding of a graph (probably using IDs) which is not generally interpreted as a graph.
{ Left:{}, Right:{} }
Has a tree with 3 nodes
If you don't parse the JSON, you tend to traverse it as a graph