Find least connected sub-graphs
You could define what "least connected" means (precisely) in a variety of ways, where the precise definition chosen may affect the output of the algorithm (and there is no unique correct definition for this). But you may wish to look into Community Detection algorithms. The general intuition of Community Detection is to find a set of sub-graphs that maximises the ratio of edges within the sub-graphs versus edges between sub-graphs. Depending on the precise definition, this may be a difficult (NP-complete) problem, and so various algorithms rather use approximate (heuristic or greedy) approaches.

Five popular Community Detection algorithms are described here and should be a good starting point for your work.