Sounds like a marked graph to me, and not directed at all, or did I
miss the arrows? That of course is a very general
thing, I therefore doubt that this statement is helpfull.
I do not understand with what you mean that a node can be connected to
a group of nodes?
Do you mean that if the nodes are e.g. lower case letters, there might
be an edge X in e(a,{b,c}) (X being the marking)
without implying that there is X in e(a,b) and X in e(a,c)?
If that is the case you still have just a general graph only that you
have to expand the nodeset to its powerset.

Cheers
Robert

-- 
Il computer non una macchina intelligente che aiuta le persone
stupide, anzi, una macchina stupida che funziona solo nelle mani
delle persone intelligenti.
Computers are not smart to help stupid people, rather they are stupid
and will work only if taken care of by smart people.

Umberto Eco