This isn’t a proof at all, it’s an argument. Just jump to the end and assumptions abound, without even a coherent proof structure tying them together. I’m not going to spend a lot of time digging into them, but many of them look quite suspect (like their “typical” spending model).
It doesn’t really matter that much what topology lightning ends up with since it’s trustless anyway. I would have a mild preference on a highly “random” graph, but I don’t think it really matters in the effective absence of counterparty risk.
For a more compelling argument regarding LN, which takes on the linked post, see
For what it’s worth, I gave a talk with conclusions very similar to this post at Papers we Love on the Interledger protocol (which also includes a mention of Lightning):
There is a very important distinction between what Paul Baran called “decentralized” and what he called “distributed”: the former are hub-and-spoke systems, which fundamentally scale with the capacity of the hubs. “Distributed” systems, which Baran suggests optimally have at least 3 links to other nodes, can scale unboundedly as they become both faster and more resilient as more nodes join the network.
My talk steps through Paul Baran’s graphs comparing Lightning to a “decentralized” hub-and-spoke network, and concluding with Interledger as a truly distributed alternative. That’s not even to say Lightning and Interledger are competing on the same playing field: Interledger could be potentially used to interconnect different implementations of Lightning operating on different blockchains.