nautyaddedgeg(1)
add an edge in each possible way
SYNOPSIS
addedgeg
[,lq/] [,D#/] [,btfF/] [,z#/] [,infile /[,outfile/]]
DESCRIPTION

For each edge nonedge e, output G+e if it satisfies certain conditions

The output file has a header if and only if the input file does.
 l

Canonically label outputs

D# Specify an upper bound on the maximum degree of the output
 b

 Output has no new cycles of odd length
 t

Output has no new 3cycle if input doesn't
 f

Output has no new 4cycle if input doesn't
 F

Output has no new 5cycle if input doesn't

z# Output has no new cycles of length less than #

btfFz can be used in arbitrary combinations
 q

 Suppress auxiliary information