GAP Manual: 58.3. EdgeOrbitsGraph

EdgeOrbitsGraph( G, E )
EdgeOrbitsGraph( G, E, n )

This is a common way of constructing a graph in GRAPE.

This function returns the (directed) graph with vertex set {1,...,n}, edge set cup_(einE), e^G, and associated (permutation) group G, which must act naturally on {1,...,n}. The parameter E should be a list of edges (lists of length 2 of vertices), although a singleton edge will be understood as an edge list of length 1. The parameter n may be omitted, in which case the number of vertices is the largest point moved by a generator of G.

Note that G may be the trivial permutation group (Group( () ) in GAP notation), in which case the (directed) edges of gamma are simply those in the list E.

    gap> EdgeOrbitsGraph( Group((1,3),(1,2)(3,4)), [[1,2],[4,5]], 5 );
    rec(
      isGraph := true,
      order := 5,
      group := Group( (1,3), (1,2)(3,4) ),
      schreierVector := [ -1, 2, 1, 2, -2 ],
      adjacencies := [ [ 2, 4, 5 ], [  ] ],
      representatives := [ 1, 5 ],
      isSimple := false )