I am looking to use this concept in one of my upcoming project.
More info: Managing Hierarchical Data in MySQL.
Please share your experiences good or bad with ex
Your requirement for multiple parents immediately violates the fundamental nature of nested sets, as pointed out in your referenced article, so I'd say you're headed for trouble to start with. Since you'll be using a relational database, which (using it's core capabilties) will handle everything you've described so far, I think just working in that conceptual framework and polishing your skills will provide everything you need, without adding additional abstractions that (at least in this case) don't add any value.
If you still want to go there, I'd call this a networked node structure. Here's a reference.