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Dear GAP-Forum,

Two problems have arisen regarding directed graphs in the GRAPE share

package.

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

non-simple graphs.

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

input.

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

AutGroupGraph(ComplementGraph(gamma))

to obtain the automorphism group of gamma.

Regards, Leonard Soicher.

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