How does one even measure decentralization? What I love about nostr is the fact that anyone with a source of entropy can have an identity and the fact that one doesn't need a static IP address to be discoverable on the internet (NWS). That said, I strongly hope we manage to fund open source development through zaps in future: nostr:nevent1qqspcwwe3awz8s087jh8v76l9q82h2w43g6e88k2aqssvqp5cvvu5tgprpmhxue69uhkummnw3ezucmgv95k6cfwd9hxvme0qgsxyllxr558rfkrn7df69cshgd3qy0rwev0a4l5sfuq754vpu5spjsrqsqqqqqp9s5k5u https://youtu.be/JWZPN-SAO3U?feature=shared&t=10m56s
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There actually are pretty good measures of decentralization. You can look at it as graph and see what failure means (is it scale free?), and many others. Choosing the right metric is difficult though. People usually pick the one that says what they want to say. It's been the case with lightning for example.
Another problem with measures of decentralization is taking into account the dynamics. That can also be done (in this case fragility analysis). Yes, most posts are on one relay. The question is what would people do if it fails for some reason. Would they point to Peter's paper and say "haha, he told you so" or would they move on and use things differently, use other relays, mirror content, etc. Because that's what matters. With Facebook, you can't do that. I use public relays, but all my notes are backed up and frequently synced to other relays. When people lose their notes, will they perhaps demand a backup/replication service and use more relays? Very probably. And that is what really matters.
Not sure if I understand the graph approach. Do you mean somethingike a "Markov Chain" where redundancy leads to a lower probably of failure? Yes the metrics are an issue. If someone claims that nostr is a decentralized identity layer, I would strongly agree because it gives anyone with entropy an identity. However, I might disagree with claims that it's a decentralized transport layer because we rely heavily on ICANN and IANA to exchange notes.
long answer: Complexity: A Guided Tour - Book by Melanie Mitchell short answer - look up scale free networks micro answer - yes, one of the properties of decentralization is how it reacts to failure. Nostr is not a transport layer, for example I'm working on using Nostr over Reticulum/ LoRA which is a different transport layer yet using the same Nostr protocol. I believe a good question about Nostr decentralization is not about decentralization of TCP/IP, even though it inherits its properties if you use it through this protocol. The good question is how resilient the network is against attacks on relays, but you always need to have a dynamic look at things - what will the network do after the attack is as good of a question as what happens immediately after a successful attack.
Glad to hear that your working on LoRa for nostr. After struggling to add value to nutband I shifted my attention to OpenWRT and WiFi captive portals that accept Bitcoin. I think nostr relays are the perfect glue for various transport solutoons interfaces like LoRa, TCP/IP or ham radio.
RFC 1925, 6(a): It is always possible to add another level of indirection. https://www.rfc-editor.org/rfc/rfc1925