Hexcellent Minesweeping
7 5 vertices, 14 10 edges



(Graph made with this online tool and paint.)

A-F are our six nodes, and J is a helper node. The three 1-nodes enforce that opposite nodes are different, while the 2-node makes sure that A, C and E can neither be all mines, nor all empty.

Edit: -2 vertices thanks to  CalculatorFeline and H.PWiz!