Improve graph structure a little bit

[gdalle]

• Store size information in the Graph structure
• Define nb_vertices and nb_edges in lieu of length and nnz to avoid confusion
• Redefine transpose_graph(::AbstractMatrix) from Manual graph transposition #107 as Base.transpose(::Graph)
• Use a simpler implementation which does just one allocation too many (a new vector of nzval), instead of a custom handwritten loop (at least I think so)
• Add better transposition tests

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (1abd62e) to head (19eb0e4).
Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #114   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           10         9    -1     
  Lines          764       770    +6     
=========================================
+ Hits           764       770    +6     

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[gdalle]

@amontoison my initial idea was to use ftranspose! as follows:

new_colptr = Vector{T}(undef, g.m + 1)
new_rowval = similar(g.rowval) 
Sᵀ = SparseMatrixCSC{T,T}(g.n, g.m, new_colptr, new_rowval, g.rowval)
ftranspose!(Sᵀ, S, identity)

This would avoid any non-necessary allocation, but unfortunately it causes segfaults. Presumably because Sᵀ and S share their vector of nzval, which I thought wouldn't be a problem but it is.

[github-actions]

Benchmark Results

	main	19eb0e4...	main/19eb0e45483c5d...
coloring/nonsymmetric/column/direct/n=1000/p=0.002	0.0877 ± 0.0041 ms	0.0925 ± 0.0045 ms	0.948
coloring/nonsymmetric/column/direct/n=1000/p=0.005	0.192 ± 0.0081 ms	0.199 ± 0.0085 ms	0.966
coloring/nonsymmetric/column/direct/n=1000/p=0.01	0.404 ± 0.014 ms	0.408 ± 0.014 ms	0.989
coloring/nonsymmetric/column/direct/n=100000/p=0.0001	0.0784 ± 0.0059 s	0.0764 ± 0.0049 s	1.03
coloring/nonsymmetric/column/direct/n=100000/p=2.0e-5	13.9 ± 0.26 ms	14.1 ± 0.37 ms	0.986
coloring/nonsymmetric/column/direct/n=100000/p=5.0e-5	0.0336 ± 0.0009 s	0.0333 ± 0.00076 s	1.01
coloring/nonsymmetric/row/direct/n=1000/p=0.002	0.102 ± 0.0048 ms	0.108 ± 0.0052 ms	0.945
coloring/nonsymmetric/row/direct/n=1000/p=0.005	0.217 ± 0.0087 ms	0.225 ± 0.0096 ms	0.966
coloring/nonsymmetric/row/direct/n=1000/p=0.01	0.449 ± 0.015 ms	0.457 ± 0.015 ms	0.984
coloring/nonsymmetric/row/direct/n=100000/p=0.0001	0.0861 ± 0.0042 s	0.0886 ± 0.0033 s	0.972
coloring/nonsymmetric/row/direct/n=100000/p=2.0e-5	16.2 ± 0.25 ms	16.5 ± 0.46 ms	0.98
coloring/nonsymmetric/row/direct/n=100000/p=5.0e-5	0.0372 ± 0.00076 s	0.0373 ± 0.00081 s	0.997
coloring/symmetric/column/direct/n=1000/p=0.002	0.268 ± 0.014 ms	0.277 ± 0.015 ms	0.969
coloring/symmetric/column/direct/n=1000/p=0.005	0.727 ± 0.028 ms	0.745 ± 0.028 ms	0.975
coloring/symmetric/column/direct/n=1000/p=0.01	1.76 ± 0.054 ms	1.81 ± 0.053 ms	0.973
coloring/symmetric/column/direct/n=100000/p=0.0001	0.422 ± 0.029 s	0.441 ± 0.036 s	0.959
coloring/symmetric/column/direct/n=100000/p=2.0e-5	0.0381 ± 0.0012 s	0.0381 ± 0.0015 s	1
coloring/symmetric/column/direct/n=100000/p=5.0e-5	0.134 ± 0.0063 s	0.128 ± 0.0067 s	1.05
coloring/symmetric/column/substitution/n=1000/p=0.002	0.616 ± 0.032 ms	0.623 ± 0.031 ms	0.989
coloring/symmetric/column/substitution/n=1000/p=0.005	1.6 ± 0.057 ms	1.62 ± 0.06 ms	0.991
coloring/symmetric/column/substitution/n=1000/p=0.01	3.45 ± 0.099 ms	3.49 ± 0.098 ms	0.989
coloring/symmetric/column/substitution/n=100000/p=0.0001	0.835 ± 0.065 s	0.968 ± 0.081 s	0.863
coloring/symmetric/column/substitution/n=100000/p=2.0e-5	0.103 ± 0.013 s	0.108 ± 0.012 s	0.953
coloring/symmetric/column/substitution/n=100000/p=5.0e-5	0.329 ± 0.024 s	0.354 ± 0.045 s	0.93
decompress/nonsymmetric/column/direct/n=1000/p=0.002	4.05 ± 0.36 μs	4.15 ± 0.36 μs	0.976
decompress/nonsymmetric/column/direct/n=1000/p=0.005	8.25 ± 0.66 μs	8.92 ± 0.85 μs	0.924
decompress/nonsymmetric/column/direct/n=1000/p=0.01	19.8 ± 3 μs	19.4 ± 4.6 μs	1.02
decompress/nonsymmetric/column/direct/n=100000/p=0.0001	4.67 ± 0.36 ms	4.81 ± 0.51 ms	0.971
decompress/nonsymmetric/column/direct/n=100000/p=2.0e-5	0.986 ± 0.11 ms	0.963 ± 0.15 ms	1.02
decompress/nonsymmetric/column/direct/n=100000/p=5.0e-5	2.51 ± 0.43 ms	2.32 ± 0.25 ms	1.08
decompress/nonsymmetric/row/direct/n=1000/p=0.002	4.19 ± 0.42 μs	4.24 ± 0.36 μs	0.989
decompress/nonsymmetric/row/direct/n=1000/p=0.005	7.84 ± 0.62 μs	8 ± 0.61 μs	0.981
decompress/nonsymmetric/row/direct/n=1000/p=0.01	17.1 ± 2.4 μs	16 ± 2.2 μs	1.07
decompress/nonsymmetric/row/direct/n=100000/p=0.0001	2.19 ± 1.1 ms	2.21 ± 0.65 ms	0.991
decompress/nonsymmetric/row/direct/n=100000/p=2.0e-5	0.494 ± 0.17 ms	0.496 ± 0.12 ms	0.997
decompress/nonsymmetric/row/direct/n=100000/p=5.0e-5	1.1 ± 0.1 ms	1.05 ± 0.15 ms	1.04
decompress/symmetric/column/direct/n=1000/p=0.002	4.21 ± 0.36 μs	4.44 ± 0.39 μs	0.947
decompress/symmetric/column/direct/n=1000/p=0.005	8.12 ± 0.57 μs	8.82 ± 0.53 μs	0.92
decompress/symmetric/column/direct/n=1000/p=0.01	16.8 ± 2 μs	17.7 ± 1.2 μs	0.946
decompress/symmetric/column/direct/n=100000/p=0.0001	5.11 ± 0.39 ms	4.83 ± 0.36 ms	1.06
decompress/symmetric/column/direct/n=100000/p=2.0e-5	0.966 ± 0.12 ms	0.94 ± 0.067 ms	1.03
decompress/symmetric/column/direct/n=100000/p=5.0e-5	2.47 ± 0.19 ms	2.41 ± 0.71 ms	1.02
decompress/symmetric/column/substitution/n=1000/p=0.002	0.0641 ± 0.0034 ms	0.0635 ± 0.0038 ms	1.01
decompress/symmetric/column/substitution/n=1000/p=0.005	0.16 ± 0.0078 ms	0.16 ± 0.0071 ms	1.01
decompress/symmetric/column/substitution/n=1000/p=0.01	0.342 ± 0.014 ms	0.341 ± 0.013 ms	1
decompress/symmetric/column/substitution/n=100000/p=0.0001	0.0974 ± 0.0047 s	0.084 ± 0.0036 s	1.16
decompress/symmetric/column/substitution/n=100000/p=2.0e-5	14.1 ± 0.8 ms	12.8 ± 0.72 ms	1.11
decompress/symmetric/column/substitution/n=100000/p=5.0e-5	0.037 ± 0.0052 s	30.5 ± 1.9 ms	1.21
time_to_load	0.225 ± 0.0027 s	0.219 ± 0.0023 s	1.03

[amontoison]

@gdalle Please wait that I have a have a look before merging...