Ask HN: Quantitatively describing directory/folder + file structure

I'm looking for a way to quantitatively describe hierarchical directory/folder and file structures. Parameters that could be calculated and used to give a broad idea of the depth and breadth of the contents of the top-level directory in terms of nested subdirectories and files. Something like the Flesch-Kincaid readability test score or cyclomatic complexity values.

Searching hasn't yet turned up anything relevant, but I have a feeling that I'm just not plugging in the right terminology.