Is your example really a "triangle" though? If you have a broker/queue, and your services just push messages into the ether, there's no actual dependency going on between these services.

Nothing should really depend on your logging service. They should push messages onto a bus and forget about them... ie. aren't even aware of the logging service's existence.

That example is still an undirected cycle so not a polytree and so, by the reasoning of the author of tfa not kosher for reasons they don’t really explain.

Honestly I think the author learned a bit of graph theory, thought polytrees are interesting and then here we are debating the resulting shower thought that has been turned into a blog post.