The Maze
The program for creating the connection game is based on a maze algorithm. As it builds the maze, it adds nodes to the maze's path, basically layering the nodes on top of the maze's path. But while there should always be only one way through the underlying maze, there may be many ways across the connection grid, because the nodes are more interconnected than the path they are built on.
If a grid has just been built on the home page, the maze below will show the original path through the maze.