Two problems have arisen regarding directed graphs in the GRAPE share
In general GRAPE deals with finite directed graphs which may have loops
but have no multiple edges. However, many GRAPE functions only work for
*simple* graphs (i.e. no loops, and whenever [x,y] is an edge then so
is [y,x]), but these functions will check if an input graph is simple.
The user should consult the documentation to see what the other
functions (such as VertexDegree, IsConnectedGraph, ...) return for
Unfortunately, there is an error in the documentation for
"CollapsedIndependentOrbitsGraph" as the output may not be as described
for a non-simple graph input. For more precise information please
email me (L.H.Soicher@qmw.ac.uk). In the next release of GRAPE,
"CollapsedIndependentOrbitsGraph" will accept only simple graphs as
Next, with the default parameters that GRAPE gives to nauty,
AutGroupGraph(gamma) (or AutomorphismGroup(gamma))
may perform very badly when gamma is a sparse non-simple graph.
If gamma is such a graph then you should instead compute
to obtain the automorphism group of gamma.
Regards, Leonard Soicher.