#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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Comment (by dcoudert):
> * Where did you find that this "abs" was not needed ? I thought it
was `O_o`
It was in the original patch from Jernej Azarija
([trac_17334_triangle_free_speedup.patch]). I don't know if its true or
not, and since the gain is very limited, we could put it back to be on the
safe side.
> * 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.
Jernej should answer that remark.
> * "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` `:-)`
OK.
I have implemented some of the modifications.
> Thanks for that patch !!
I was also thinking of some nice and fast methods from Alon et al., or
from Latapy (see the code in c and the survey at [http://www-
rp.lip6.fr/~latapy/Triangles/]). We could add them (in particular the
compact-forward method) at the cost of adding an interface and a method
for converting the graph into the tricky data structure used by Latapy.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13503#comment:26>
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