This is another idea for the Diplomacy Web and the hopefully upcoming character relationship web upgrade.  

What functionality is missing? What is unsatisfying with the current situation?

Right now, the diplomacy web puts everything in alphabetical order around a circle when using a tag. The more organizations you have, the smaller the group icons are. Furthermore, not all organizations are linked to each other or have the same number of links; thus, there are gaps in the web. This can be visually unappealing on top of the giant circle.  

How does this feature request address the current situation?

I've been playing around with Graphviz for a bit, and I think it's a good system to look into or draw inspiration from.   Graphviz uses an algorithm that weighs different nodes to determine position. This means clusters will form around closely connected groups, making it look more complex and dynamic while removing the giant circle.   Graphviz is also open source. I don't know how the dev team feels about adding open source projects into their software. But this means they can at least look at how it's done and see if they can improve their software by getting ideas from it.  

What are other uses for this feature request?

Graphviz is used for graphs, so any of the graph systems can benefit from a look.