Clearly separate graphs from the sparsity pattern

[gdalle]

Idea

Create two clearly distinct graph structures (AdjacencyGraph and BipartiteGraph) and distinguish them from the container for the sparsity pattern.

Benefits

Now:

• Get rid of the weird Graph{true} / Graph{false} which wasn't even a graph in the rectangular case.
• Allow storing more stuff in the graph structure if we want (typically the number of edges as you suggested).

In the future:

• Gain flexibility to implement graphs based on different pattern types (for other structured matrices like banded), just by making the pattern fields parametric.

Changes

• Rename Graph into SparsePatternCSC, which is exactly a SparseMatrixCSC without nzval. Remove definitions of neighbors and friends, keep only linear algebra stuff there.
• Create a proper AdjacencyGraph based on one SparsePatternCSC, put the neighbors logic there. It is the pendant to BipartiteGraph.
• Count edges properly in the AdjacencyGraph (divide by two to account for symmetry).
• Remove the constructors adjacency_graph and bipartite_graph.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (b274008) to head (92546d0).
Report is 4 commits behind head on main.

Additional details and impacted files

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[amontoison]

@gdalle
Excellent PR! I really like this new structure.
I was not a big fan of the Graph with the attribute loops.
Aside from a small comment about the number of edges for AdjacencyGraph, the code looks good to me.
Could I request the name SparsityPatternCSC instead of SparsePatternCSC?
It’s even more explicit from my point of view.

Excellent job!!!

[amontoison]

It should be easily to remove the allocation of S' here now.

[gdalle]

Indeed that was the next step of the plan, I have opened #126 to keep track