[FEA]: Implement spectral_ordering

[adsharma]

Is this a new feature, an improvement, or a change to existing functionality?

New Feature

How would you describe the priority of this feature request

Critical (currently preventing usage)

Please provide a clear description of problem this feature solves

networkx implements a spectral_ordering algorithm that's useful for some applications. I couldn't find a GPU accelerated variant in cugraph.

I see two spectral clustering algorithms, which are not the same.

Describe your ideal solution

Implement a cugraph equivalent of nx.spectral_ordering()

Describe any alternatives you have considered

Used the CPU variant. It was slow.

Additional context

No response

Code of Conduct

• I agree to follow cuGraph's Code of Conduct
• I have searched the open feature requests and have found no duplicates for this feature request

[adsharma]

Some research on why existing spectral clustering algorithms in cugraph are insufficient:

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023006

[adsharma]

Extracted networkx code for easier testing:

https://github.com/adsharma/nx-spectral-ordering

Here's my attempt to speed it up:
adsharma/nx-spectral-ordering@6bb1373

Runs an algorithm copied from cupy.dev (link in the commit), but fails functional testing. Needs more debug.

Also I heard that cuSparse has a PCG solver. Not sure how to invoke it from python.

[adsharma]

Modified the networkx PCG solver to use cupy. It works, but is not faster.

https://github.com/adsharma/nx-spectral-ordering/compare/f2073213a8984e2db4816f1cfa21d61fd0402531..7104b1d74139875bab500652b316d1e6ad06995b

Still interested in exploring if cuSparse PCG solver is a better solution.