Large graphs (just about anything larger than a karate club social network [1]) can't usually be visualized in a useful manner. There are exceptions, but in real world applications they are more useful as pretty art than helping with understanding.
Statistical summary plots are more useful.
Maybe one day someone will figure something out, but much like scatter plots fall over when you plot vast amounts of raw data, so do plotting graphs.
My answer to it is that graphs need to be manually curated. For example, a UML diagram for all the database tables on the system I am working on now would have to be printed out on a wall to make any sense, but if I picked out the tables involved in a new user registration that would be useful.
and saw a series of drafts he'd made where he had drawn many different versions of a conspiracy social network and gradually went from a hairball to something that looked meaningful.
In terms of turning this into a tool there's the interesting problem that there is a graph that comes in from the outside world (and could be regenerated) and also data that represents the curation of the graph (Do I show this? What color is this line? What position does this node get displayed at?) You've got to be able to edit one independently of the other and deal with things sometimes getting out of sync to have a tool that advances over the state of the art.
https://github.com/paulhoule/gastrodon
Overall I think of graph visualization as a problem, in particularly there are some people who just don't see that hairballs are incomprehensible
https://cambridge-intelligence.com/how-to-fix-hairballs/