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Is there a way to display/list the folder hierarchy of an Alfresco document library as a diagram, tree graph, or image?
You could use the PathTree widget as provided by Aikau. However this would not expand all the nodes within the tree when first displayed (although I think it could be relatively extended to provide that capability). The issue really is that there is no single REST API that will provide the data for you.
You could provide an API to generate the data - but then you would need to create a custom way of displaying the visualization of the data.
The short answer is no, but it is possible to provide a custom solution to do this.