You need to separate the identification of a node (a unique ID, which in this proposal would resemble an inode number) from its globally-visible name, which would just become a vertex attribute. That's how in Unix filesystems you can have hard-links, with multiple directory entries pointing at the same real disk-entity.

In concrete terms, stop naming the Graph vertices "/a/blah", and name them 1, 2, etc (with 0 as your FS root). Each directory-entry (which isn't quite the same as a file) would have a "local_name" attribute, and you'd find "/a/blah" by starting at the root, finding a child dir-node with the name "a", etc.