There are algorithmic ways of doing what you are asking for, but there are no existing out-of-the-box tools in Network Analyst to do this.
Could you provide some use cases for why you need this functionality? Perhaps providing some additional context for what you are trying to do will allow me to better help you arrive at a suitable solution.
As for the link you provided in your original post, this appears to be referring to something different than what your post suggests. The linked thread is referring to loop edges, which are just single edges which have the same starting and ending junction (i.e., the edge loops back to its origin). You seem to be asking to detect entire sections of your network which can only be entered or exited via one junction (at least, that is what your image suggests). Can you verify this or elaborate further?