[FEA]: Multiplex leiden clustering

[niklasmueboe]

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

The (most used) Leiden implementation in leidenalg supports multiplex clustering, where you can cluster multiple graphs with the same vertices jointly. In the field of single-cell transcriptomics and spatially resolved transcriptomics this can be used to cluster multi-modality data (as done in muon) or to jointly cluster cells based on their features and spatial neighborhoods (as done in SpatialLeiden).
With the increasing datasets (hundred thousands to millions of cells/vertices), runtime for Leiden clustering on the CPU becomes a limiting factor for exploring various parameter combinations.

Describe your ideal solution

The leiden function should support a list (or similar) of graphs as input. Therefore, also the resolution parameter would need to be extended to support a resolution for each graph (layer). Furthermore, a new parameter that gives a weight to each layer corresponding to its "importance" would be needed.

Describe any alternatives you have considered

No response

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

[abs51295]

I would also consider adding support for directed weighted graphs since scanpy.tl.leiden uses a directed weighted graph with leidenalg package.(Nevermind since they are moving to igraph). Also, support for fixing the membership labels for a part of the graph is useful when dealing with merging of two different datasets: https://www.nature.com/articles/s41598-020-71805-1.