N' = newEdges L
N = newEdges S
N = newEdges G
The list of "new edge" graphs are formed as follows: Let $ab$ and $cd$ be disjoint edges of $G$. Then the associated "new edge" graph $H$ is $G$ with the edges $ab$ and $cd$ removed, the vertices $e$ and $f$ added, and the new edges $ae, be, cf, df,$ and $ef$ added.

If the List input format is used, then one should use care as the list may contain isomorphic pairs.
The object newEdges is a method function.