[FEATURE] Spectral clustering methods

[Becheler]

The Structural BIoinformatics Library uses Boost Graph extensively to represent covalent structure in biomolecules. A few notes:

• The SBL is quite template-heavy and so they appreciate the BGL genericity.
• The tend to use undirected graphs more than directed graphs
• They don't suffer from scalability because proteins never have much more than 10K amino-acids.

A wish-list has been kindly communicated by Frederic Cazals :

1. Integrate classical spectral clustering algorithms (see Ulrike von Luxburg, 2008 )
2. Integrate algorithms for spectral decomposition of a graph's Laplacian, ideally with an interative version like Lanczos (see e.g. SLEPc)
3. some modernization around union find and disjoint sets. From what I understand, the current API is not practical and not competitive against:

• NetworkX (python) UnionFind() auto-initialization
• igraph igraph_union_find_init() internal management.
• So maybe a commodity wrapper is lacking?

Concerning points 1 and 2: if there is interest for spectral clustering, a challenge could be to properly disentangle linear algebra from graphs to keep BGL focused.

[jeremy-murphy]

I'm happy to take the union-find issue, so I'll split it off as a separate task.

[jeremy-murphy]

Boost has an old linear algebra library and a new one, but then there's the industry standard, Eigen. I don't think we want to touch the old one anymore but I'm not sure if the new one covers everything. Ultimately, I think we'll want to give users a choice through compile-time options, however I guess that means we'll want to write a thin wrapper layer just to keep those compile-time shenanigans out of the main logic.