This actually makes a lot of sense. I have one question though. Why is having 2 microservices depend on a single service a problem?
I like that the author provides both solutions: join (my preferred) or split the share.
And then N4 is a shared utility service that's responsible for e.g. performance tracing or logging or something similar. To make the dependency "harder", we could consider that it's a shared service responsible for authentication and authorization. So it's clear why many root services are dependent on it—they need to make individual authorization decisions.
How would you refactor this to remove an undirected dependency loop?
The only way I can see to avoid this is to have all those cross-cutting concerns handled in the N1 root service before they go into N2/N3, but it requires having N1 handle some things by itself (eg: you can do authorization early), or it requires a lot of additional context to be passed down (eg: passing flags/configuration downstream), or it massively overcomplicates others (eg: having logging be part of N1 forces N2/N3 to respond synchronously).
So yeah, I'm not a fan of the constraint from TFA. It being a DAG is enough.
The problem is that I don't sit in the microservice or enterprise backend spaces, so I an struggling to formulate explanations in those terms.
The only alternative I can think of is to have a zillion separate public-facing API servers on different subdomains, but that sounds like a headache.
But what if we add 2 extra nodes: n5 dependent on n2 alone, and n6 dependent on n3 alone? Should we keep n2 and n3 separate and split n4, or should we merge n2 and n3 and keep n4, or should we keep the topology as it is?
The same sort of problem arises in a class inheritance graph: it would make sense to merge classes n2 and n3 if n4 is the only class inheriting from it, but if you add more nodes, then the simplification might not be possible anymore.
You'll probably also have lines pointing to your storage service or database even if the data is isolated between them. You could have them all be separate but that's a waste when you can leverage say a big ceph cluster.