On a larger scale, the complete board configuration (the locations of all the pieces for both players) can be a vertex, and a legal move (edge) will result in a different board configuration (vertex)....

On a larger scale, the complete board configuration (the locations of all the pieces for both players) can be a vertex, and a legal move (edge) will result in a different board configuration (vertex). A computer program can consider all valid moves from a particular board configuration many turns ahead to determine the best current move for a player.