Added clique_number, independence_number

[dstahlke]

These simple implementations use maximal_cliques as the computational engine. Perhaps there is a more efficient way, but it would be great to at least have these implemented.

[gdalle]

Thanks for the PR, sorry for the late review

[dstahlke]

I've pushed an update that hopefully addresses these concerns. (I rebased to master - hopefully that doesn't make the diffs too messy.)

After making a proper unit test for independent sets, I found I had to convert AbstractGraph to SimpleGraph in order to call complement. Performance shouldn't be an issue since this data copy is negligible in comparison to the cost of the maximal_cliques call. But I don't know if there is some other reason this would be problematic.

@traitfn function maximum_independent_set(
    g::AG::(!IsDirected)
) where {T,AG<:AbstractGraph{T}}
    # Convert to SimpleGraph first because `complement` doesn't accept AbstractGraph.
    return maximum_clique(complement(SimpleGraph(g)))

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.22%. Comparing base (5eaa071) to head (29c01d3).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #155   +/-   ##
=======================================
  Coverage   97.22%   97.22%           
=======================================
  Files         122      122           
  Lines        7240     7250   +10     
=======================================
+ Hits         7039     7049   +10     
  Misses        201      201           

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[gdalle]

I would add a warning to the docstring pointing to the conversion, but otherwise I'd say it's okay

[Krastanov]

This looks good, and thankfully it has not bitrotten in the last two years. Thank you for the contribution!