Contraction of Ω is relatively complicated. To contract one edge "e", the procedure depends on the kind of edge "e" is. If "e" is a link, contract it in "G". A circle "C" in the contraction "G"/"e" is balanced if either "C" or formula_1 is a balanced circle of "G". If "e" is a balanced loop or a loose edge, it is simply deleted. If it is an unbalanced loop or a half-edge, it and its vertex "v" are deleted; each other edge with "v" as an endpoint loses that endpoint, so a link with "v" as one endpoint becomes a half-edge at its other endpoint, while a loop or half-edge at "v" becomes a loose edge.