Questions on partitioning graph under specific constraints.

[Hanchen Jin]

Hi everyone, 

In the NetworkX repo, I only find the implementation for bipartition: https://networkx.org/documentation/stable/reference/algorithms/community.html#module-networkx.algorithms.community.kernighan_lin

However, I'm trying to find an algorithm&&implementation that can partition graphs with customized constraints. Specifically, I want to partition graph under the following two types of constraints:

(C1) I would like to partition graph into a specific number of partitions (k-way partitioning: https://en.wikipedia.org/wiki/Multiway_number_partitioning) with a specified score/weights of each partition. (Supported in METIS: https://github.com/KarypisLab/METIS)

(C2) I would like to cluster several specific nodes into one specific partition. (For this requirement, maybe I must refer to ILP as an exact solver or manually add edges to infer this)

Do we have implementation in the NetworkX library that supports both customized constraints (C1 and C2)? If no, what are the references should I refer to? Any responds and suggestions are greatly appreciated.

Thanks,

Hanchen Jin