Sorry, I'm half sleeping: this indeed doesn't specify anything about whether the pairs have to be distinct.
2014-02-07 19:45 GMT+01:00 Nico Van Cleemput <[email protected]>: > Dear Robert > > If you look at the help message for is_transitive() then you see that the > definition is this: A digraph is transitive if for any pair of vertices u,v > in G linked by a uv-path the edge uv belongs to G. > > Cheers > Nico > > > 2014-02-07 19:35 GMT+01:00 Robert <[email protected]>: > > 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. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sage-edu" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sage-edu. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-edu. For more options, visit https://groups.google.com/groups/opt_out.
