I ran into a few problems using the new API, but the Product Hunt team has been very helpful and responsive to fixing issues I found.
I was able to build pretty much what I wanted.
You start with your (or anyone else's) profile, and see all the people you've made a product featured on Product Hunt with. From there you can explore the network of each of those makers, and their network and their network, and so on.
I also added a network graph, a visualization of a makers network 3 levels deep, which produced some very interesting graphics, especially for active makers. For example:
https://makernetwork.app/users/rrhoover/graph
Overall very happy with how everything turned out.