For whoever might undertake this, there’s some cool research on using graph modular decomposition to visualize the structure of graphs:
The main issue is the complexity and difficulty of implementing graph modular decomposition. However, I implemented that already (thought it would be useful for something I was working on but it turned out not to be), and the code is here:
https://github.com/StefanKarpinski/GraphModularDecomposition.jl
It even supports decomposition of directed graphs, which is fairly fancy (took me forever to get right). The main issue with this code is that it works on a matrix representation of a graph rather than any of the LightGraphs data structures. I’m sure it would be straightforward to port it to use the LightGraphs API instead.