Added function transitivereduction

[simonschoelly]

As mentioned in #874 I have implemented a function to calculate the transitive reduction of a graph and added some tests. I've also added a kwargs option selflooped in order to mimic the function transitveclosure.

For some reason, the docstring I wrote for this function does not appear in my Julia v.07 repl, when entering ?transitivereduction. Anyone has a clue why this happens?

Some remarks:

1. As mentioned in Transitive reduction #874 this function could later be improved to also calculate the minimum equivalent graph or an approximation of it.
2. The outer loop of this algorithm should not be too difficult to parallelize
3. Handling each strongly connected component seems to be a good decision as the algorithm runs fast when there are just a few edges and many strongly connected components (i.e paths)and also when there are many edges and few strongly connected components (i.e. complete graphs)
   A case where the algorithm has to do a lot of work is when there are many edges and many strongly connected components (try running it on g = transitiveclosure!(PathDiGraph(5000)) ).
   The Boost graph library does something similar to calculate the transitive closure, so if someone wants to speed up the transitiveclosure function of LightGraphs, they could try something like that.

[codecov]

Codecov Report

Merging #877 into master will not change coverage.
The diff coverage is 100%.

@@          Coverage Diff          @@
##           master   #877   +/-   ##
=====================================
  Coverage     100%   100%           
=====================================
  Files          59     59           
  Lines        2989   3027   +38     
=====================================
+ Hits         2989   3027   +38

[sbromberger]

These should be tested on graphs of varying eltypes: that is, see the testgraphs / testdigraphs functions:

for g in testgraphs(barbell_graph)
   ... do tests
end

[simonschoelly]

Is the idea that we use testdigraphs for all testcases or should I just do this for this barbell_graph? I might have to replace that test anyway as I have to come up with another example that covers all lines.

[sbromberger]

In general, we prefer testgraphs / testdigraphs for all test cases, inside the loop.

[simonschoelly]

I changed the test now and fixed some errors. It should cover all code lines now, the reason if did not before was that I created an a graph with no edges instead of a path in my tests.
I'm still figuring out how GitHub works, so I'm not completely sure that I attached my changes correctly to this pull request.

[sbromberger]

This looks good. The only nitpicky comment I have is that your indents don't line up consistently, but that can be fixed after the fact (and with a good linter - try vscode w/ the Julia plugin if you have a chance!)

cc @jpfairbanks for a sanity check.

Thanks, @simonschoelly!

[sbromberger]

pinging @jpfairbanks for a quick review, please?

[sbromberger]

Thanks!!