A student in my discrete structures course found what he thinks is a bug in
Sage's treatment of directed graphs. Consider the relation given by the
Python dictionary:
{0: [1], 1: [0], 2: [3], 3: [2]}
So 0 is related to 1 and vice versa, and 2 is related to 3 and vice versa.
This is NOT a transitive relation, because if it were, then 0 would have to
be related to itself. (I.e. there would be a loop on the directed graph at
0.)
However, when you enter the following code:
*r = {0: [1], 1: [0], 2: [3], 3: [2]} *
*g = DiGraph(r)*
*g.is_transitive()*
...you get "True". Is this because is_transitive has a bug; because Sage
doesn't like its directed graphs to have loops; because the is_transitive
method is using a different definition of "transitive" than we are*, or
what?
Thanks in advance!
Robert
* For example it could be using a definition of transitive that says "For
all DISTINCT a,b,c in A, if (a,b) and (b,c) then (a,c)." I don't know.
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