Hamilton Circuits & Paths
The first time you click on a vertex the vertex turns blue. The blue vertex indicates your "current" position. From your position on a blue vertex you can only move to an adjacent vertex by clicking on it. When you click on the "next" vertex, the edge connecting the two vertices disappears. Solid red vertices are vertices that have already been visited once - you don't want to go there again!
A Hamilton circuit (path) is realized when all the vertices are solid red (except for the last vertex which is blue). At that moment the Hamilton circuit (path) appears marked in magenta. The actual sequence of vertices that gives the Hamilton circuit (path) is shown at the bottom of the window.
You can always "undo" your last move by clicking on the "Back" button. Clicking on the "Restore" button will restore the original graph and allow you to start again.