Simplify completely connected directed networkx graph

Question

Is there an algorithm in networkx for dealing with completely (or very highly) connected directed graphs (DiGraphs)?

I have a network of flows which are all non-zero but vary hugely in magnitude. I want to visualise the network, but I need a sensible way of finding an underlying structure where, ideally, each node would have a maximum of one in- and one out-flow.

N.B. This is the concept of 'nodal flows', as described by Nystuen and Dacy (1961) but I don't know what the modern equivalent is called!