Fix modularity when self loops exist

[ryandewolfe33]

Fix the modularity function when self loops exist in the graph and some minor formatting to make the modularity computation clearer.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.19%. Comparing base (acb2c4d) to head (9c9fdf7).
⚠️ Report is 3 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #487   +/-   ##
=======================================
  Coverage   97.19%   97.19%           
=======================================
  Files         121      121           
  Lines        7105     7107    +2     
=======================================
+ Hits         6906     6908    +2     
  Misses        199      199           

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[Krastanov]

Thank you for the submission! You are introducing a very minor slowdown, but on the other hand the code is more legible. I think I am happy to merge it as is. See inline comment for more details.

[Krastanov]

I imagine whoever wrote the previous inbounds loop wanted to avoid the allocation. The new format creates a temporary array to store kin .* kout before performing the sum. I guess I personally do not care about this type of micro-optimization and prefer your new code, but mentioning this here for documentation purposes.

julia> f(a,b) = sum(a .* b)
f (generic function with 1 method)

julia> g(a,b) = begin s = 0.0; for i in eachindex(a); s += a[i]*b[i]; end; s end

g (generic function with 1 method)

julia> a = rand(100);

julia> b = rand(100);

julia> @time f(a, b);
  0.027304 seconds (13.31 k allocations: 711.914 KiB, 99.97% compilation time)

julia> @time f(a, b);
  0.000004 seconds (3 allocations: 944 bytes)

julia> @time g(a, b);
  0.007733 seconds (5.17 k allocations: 261.992 KiB, 99.91% compilation time)

julia> @time g(a, b);
  0.000003 seconds (1 allocation: 16 bytes)

and here are a few more options to consider for simpler syntax

julia> h(a,b) = sum(zip(a,b)) do (x,y); x*y; end
h (generic function with 1 method)

julia> k(a,b) = sum(splat(*), (a,b))
k (generic function with 1 method)

julia> @time h(a, b);
  0.018568 seconds (131.63 k allocations: 6.261 MiB, 15.16% gc time, 99.96% compilation time)

julia> @time h(a, b);
  0.000002 seconds (1 allocation: 16 bytes)

julia> @time k(a, b);
  0.028699 seconds (146.38 k allocations: 7.347 MiB, 99.72% compilation time)

julia> @time k(a, b);
  0.000016 seconds (403 allocations: 7.891 KiB)