#13503: Enhancement of `is_triangle_free' addition of `triangles_count' and a
minor
change in `spanning_trees_count'
----------------------------------------------------------+-----------------
Reporter: azi | Owner:
jason, ncohen, rlm
Type: enhancement | Status:
needs_work
Priority: minor | Milestone:
sage-5.4
Component: graph theory | Resolution:
Keywords: triangles, graphs, number of triangles | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Jernej Azarija, David Coudert | Merged in:
Dependencies: | Stopgaps:
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Changes (by ncohen):
* status: needs_review => needs_work
Comment:
Hellooooooooo David !!
First, you do not know how glad I am to hear things like "the difficulty
with graph algorithms is that the efficiency depends on the data
structure" from the mouth of researchers. "Adjacency test ? O(1) !" is
their usual answer. `:-D`
I have been thinking of reimplementing another version using FastGraph,
but that would be more trouble than necessary for the moment. And I could
actually use the same technique to reimplement SubgraphSearch a bit better
anyway, so I guess I will go there directly.
About the patch :
* Where did you find that this "abs" was not needed ? I thought it was
`O_o`
* I'm not a big fan of having triangle_count in generic_graph, as I
don't really see it used with DiGraphs... And the code reflects that
indeed, but if you think they can, then why not ? Could you at least say
that not all algorithms are available for Digraphs, and that the method
looks for "directed C3" in this case, or something similar ? And in
particular not C3 in the underlying graph.
* "tests if the trace of the adjacency matrix is positive" would be
counting the number of loops `:-D` Btw I guess it would be better to have
"``return (A * * 3 ).trace() == 0``" instead of "``return (A*A*A).trace()
== 0``", just in case they might implement some smart thing for powers of
binary matrices eventually... The logarithmic power method changes nothing
for `k=3` `:-)`
Thanks for that patch !!
nathann
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13503#comment:25>
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