The question is how much of the network (and its cells / hubs) do you have to neutralize or destroy in order to make the whole thing null?
The former seems like one of assessment through understanding
I agree, I think we're at a point now where the only way we can know if the network has become null is if it becomes null. I would say that good old fashion HUMINT is the most important key. Identify who the important nodes are (high impact, hard to replace) and go after them. If you know who they are, and you can get them, then you can be confident that you're having an impact. But this takes lots of ground work amongst the people, slowly mapping it out.

After that I think the question is how to establish conditions so it does not come back (as much as possible).
I like the idea of the alternate narrative. I just have no idea what it would look like, or who's gonna come up with it.

These sorts of networks seem to be vulnerable to infiltration, a la Donnie Brasco (FBI agent Joe Pistone who infiltrated and brought down the Bonanno mafia family). I dont know what sort of vetting procedures they have. I also dont know who would have the balls of titanium (or a convincing alibi) to even attempt that sort of work. I think if both HUMINT and SIGINT could be leveraged to sound like the intel came from an informer/infiltrator/snitch, the distrust it could sow would be highly contagious and corrosive. The distrust within the Bonanno family and between them and the other families was more damaging than the testimony Joe Pistone provided in court. This would force networks to shrink and become more and more exclusive, which would make them harder to take out, but also less effective as they approach the "lone-wolf" stage.