nauty-newedgeg - Man Page
create new edges from pairs of non-adjacent edges in each possible way
newedgeg [-lq] [infile [outfile]]
For each pair of non-adjacent edges, output the graph obtained
by subdividing the edges and joining the new vertices.
The output file has a header if and only if the input file does.
Canonically label outputs
Suppress auxiliary information
January 2023 nauty 2.8.6 Nauty Manual