Each "node" is basically one tile of your board, i.e. a potential mine. Each node has a list of neighbours - in a usual grid those would be 8 for most nodes (2 vertical, 2 horizontal, 4 diagonal), and those neighbours are the ones that are counted to get the amount of mines.
So usually your node graph would look somewhat like this:
O---O---O---O---O---O
|\ /|\ /|\ /|\ /|\ /|
| X | X | X | X | X |
|/ \|/ \|/ \|/ \|/ \|
O---O---O---O---O---O
|\ /|\ /|\ /|\ /|\ /|
| X | X | X | X | X |
|/ \|/ \|/ \|/ \|/ \|
O---O---O---O---O---O
|\ /|\ /|\ /|\ /|\ /|
| X | X | X | X | X |
|/ \|/ \|/ \|/ \|/ \|
O---O---O---O---O---O
|\ /|\ /|\ /|\ /|\ /|
| X | X | X | X | X |
|/ \|/ \|/ \|/ \|/ \|
O---O---O---O---O---O
A regular grid, each node ("O") having 8 neighbours (apart from the outer ones, that have either 5 neighbours or 3 (3 for the four nodes in the corners)).
However, I don't think there's a need to use such a
regular node graph. Instead of such a grid you could create more interesting, less homogeneous structures.
I think I'll just try to come up with a simple example of what I mean and post it here later.
Edit: Very small example attached. Of course the levels in the game would be much more complex than this.
In this case the round cells are nodes (that may or may not contain a mine), the black lines represent the "neighbour"-relationship, hence the numbers within some of the nodes tell you how many mines are distributed over their individual set of neighbours.
...Of course I have no idea whether this kind of minesweeper would be fun, or work well at all.
