Pairings that are impossible are wrong.

Examples:

  A connects to B
  B connects to A
  C connects to D
  C connects to E

The first two connections are fine.
However, last two connections are impossible, C can connect to D or E but not both.

You can have as many classes as you like, just remember that the method public static string Interpret(string input) is the entry point to your solution and all logic has to begin there, so you need to instantiate your parser somewhere in this method. But it can be in separate class.