I am trying to make a slitherlink game, and am not too sure how to approach creating the game, more specifically the grid structure on which the puzzle will be played on.

This is what a empty and completed slitherlink grid would look like:

The numbers in the squares are sort of clues and the areas between the dots need to be clickable:

I would like to create the game in VB .NET. What data structures should I try to use, and would it be beneficial using any frameworks such as XNA?