I've not found any sort of good examples of the however i am thinking about representing an entire directory structure with updates, etc while using hierarchyid datatype. This can be a common use situation reported for that hierarchyid however i aren't able to find any articles building this kind of example.

Among the finest to represent an entire directory structure for example:

/dir1
/file1
/dir2
/dir2/dir3
/dir2/dir3/file2

** I'm not attempting to synch this having a file system on disk. It's purely symbolized with the database. **

Here's a good example of representing personal files system through hierarchyid:

/*
Setup:
 - Create the table to hold the files
 - nodeDepth is identifier of the depth for readability
 - fullpath is the full path of the file or directory
 - nodePath is the HierarchyID
 - nodePath identifies the row within the tree
*/

DECLARE @t TABLE (
  nodeID INT NOT NULL IDENTITY(1,1) PRIMARY KEY,
  nodeDepth VARCHAR(10) NOT NULL,
  fullPath VARCHAR(20) NOT NULL,
  nodePath HIERARCHYID NOT NULL
) 

Load data:

/*
Load the nodePath value with the Parse command: 
 - The root node has a single /
 - Every nodePath must begin and end with /
 - /1/2/ the second item on level 2
*/

INSERT @t (fullPath, nodeDepth, nodePath) VALUES  
('/','1',HIERARCHYID::Parse('/')),
('/dir1','1.1',HIERARCHYID::Parse('/1/1/')),
('/file1','1.2',HIERARCHYID::Parse('/1/2/')),
('/dir2','1.3',HIERARCHYID::Parse('/1/3/')),
('/dir2/dir3','1.3.1',HIERARCHYID::Parse('/1/3/1/')),
('/dir2/dir3/file2','1.3.1.1',HIERARCHYID::Parse('/1/3/1/1/'))

Show the pathways:

SELECT *
FROM @t 

nodeID      nodeDepth  fullPath             nodePath
----------- ---------- -------------------- --------
1           1          /                    0x
2           1.1        /dir1                0x5AC0
3           1.2        /file1               0x5B40
4           1.3        /dir2                0x5BC0
5           1.3.1      /dir2/dir3           0x5BD6
6           1.3.1.1    /dir2/dir3/file2     0x5BD6B0

Get forefathers of file2 (up one level):

SELECT * 
FROM @t 
WHERE nodePath = 
  (SELECT nodePath.GetAncestor(1)
   FROM @t 
   WHERE fullPath = '/dir2/dir3/file2')

nodeID      nodeDepth  fullPath             nodePath
----------- ---------- -------------------- ---------
5           1.3.1      /dir2/dir3           0x5BD6

Get all descentants of dir2:

SELECT *
FROM @t 
WHERE nodePath.IsDescendantOf(
  (SELECT nodePath 
   FROM @t 
   WHERE fullPath = '/dir2')) = 1
AND fullPath <> '/dir2' /* Parent is considered its own descendant */

nodeID      nodeDepth  fullPath             nodePath
----------- ---------- -------------------- --------
5           1.3.1      /dir2/dir3           0x5BD6
6           1.3.1.1    /dir2/dir3/file2     0x5BD6B0

Obtain the root path:

SELECT * 
FROM @t 
WHERE nodePath = HIERARCHYID::GetRoot()

nodeID      nodeDepth  fullPath             nodePath
----------- ---------- -------------------- --------
1           1          /                    0x

Get the amount of file2:

SELECT nodePath.GetLevel() AS level
FROM @t 
WHERE fullPath = '/dir2/dir3/file2'

level
------
4

References: