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Is the number of independently owned and operated full Bitcoin nodes more important than the total number of full Bitcoin nodes with regards to Decentralization?

Assuming the answer to the above question is yes:

  1. How can the number of independently owned and operated nodes be counted and verified?
  2. Is there an answer to question 1 above that would not violate the privacy of the nodes owner/operator?
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Yes, independently operated nodes help decentralization more than the same number of nodes operated by a single entity. That's basically the definition of "decentralization" in this context. That is not to say that a single organization running multiple full nodes does not add to overall network health, since those nodes still participate in relaying transactions and providing historical blocks.

As for your other questions:

  1. It is very difficult, if not impossible, to identify which nodes are run by which organization. Nodes are often run using proxies/TOR to obscure their true IP addresses, which is often the only way to determine ownership. If we don't know which nodes are run by whom, we cannot correlate which nodes are run by the same entities.
  2. Without a solid answer to question 1, I don't think there is a good answer to question 2 either.

You could assume that organizations running multiple nodes will broadcast or relay transactions from all their nodes simultaneously. If so, then you could figure out which nodes are a part of which group by having many nodes on the network, yourself. Then you could correlate which nodes first relayed which transactions. However, the initial assumption is bad, and adequate tracking would require you to have a large number of nodes on the network. I don't think your results could be trusted enough to be worth the effort.

In a permissionless system such as Bitcoin, it is intentionally hard for anyone to know that much about the other participants.

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