Each player takes turns creating edges between nodes. Every edge you draw is worth a point — and if that edge completes a triangle, or a group of four all joined to each other, it is worth a great deal more. The line does not have to be straight; it can curve or wiggle. The one rule about where you may draw is that your line may not cross a line that is already there.
This game comes from Dan and Andrew's Game Place: https://danandandrewsgamingplace.wordpress.com/2017/11/22/cliquer-a-graph-theory-game/
How Cliquer is played
Notice what is not on the price list: a 5-clique. It is not an oversight. A drawing with no crossings is a planar drawing, and K₅ — five dots with all ten pairs joined — is the smallest graph that cannot be drawn flat without a crossing. Curving the lines does not help: a curve is still a drawing in the plane. So a 4-clique is the biggest prize there is, and the rule that keeps your pencil honest is the same rule that caps the payout.
The number of moves never changes: whatever either of you does, the finished picture is a triangulation, and every triangulation of the same dots has the same number of edges. Once lines may curve, the outside of the drawing is a face like any other — you can always loop round it — so the count is 3n − 6 and the shape of the board drops out of it entirely. A whole seven-dot game is far too big to solve here, but the last few moves are not, and the computer solves them exactly. One honest difference between this and paper: a pencil line can be as thin as you like, and a drawn one cannot. In a crowded finish the screen sometimes cannot fit a legal curve in the gap it belongs in — so it draws it a little wide, crossing something, and marks it faded and broken. The move is legal; the crossing is the size of the board. Blow the picture up big enough and that curve would clear.