That's true **within** a community.
The questions come when you want to use the Communitues someone is active on as data to derive a notion of **his network** from.
As in:
When he browse to the page of a product / a new community / a podcast show / ....
Do you show the profiles on his network that are part of his network that use that product, are active in that community and are listening to that podcast?
If yes, then you need a way to define that network.
Or for the main Vertex use case too:
For knowing if you are the real Pip, you are now looking at the Web of Follows.
What changes mathematically when we start looking at a Web of Communities?
A web that works with:
- Badges: awarded by Communities, (optionally also accepted by profiles)
- payments (pay to poast, pay for badge, zap the communikey, ....)
- atomic events for reporting and black "listing"
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It really depends on the usecase, there is no silver bullet.
For example, if you are looking at a product, you could fetch all reviews for that product, and drop reviews from npubs whose pagerank is lower than a threshold. Or you could weight that review using the pagerank (influencers have higher influence, not necessarily a good idea).
Or maybe you can show the average vote of the members of the community, which is more contained. All tradeoffs.
Pagerank can be run on any graph, so one could built it by looking at who replied/zapped/liked to whom, in a given setting.
Also, not all signal should be condensed into a single rank, multiple trust signals should be provided imo. Number of followers, ranks, nip05, badges, all give some clues that your brain can interpret.