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How many full nodes are there currently in the network? Are there any sites that track the currently connected nodes in real-time?
Leading on from this - which should perhaps be a separate question - is there a minimum number of nodes which is required to keep the network secure?
(Because of that, there are also no sites that track them)
Why?
Every square is a full node. Connected nodes are neighbours.
That's why you can't and never will be able to count the full nodes in the system.
Theoretically IOTA could run on a single full node with all light clients connected to it. This wouldn't make a lot of sense though, because it wouldn't be decentralized and therefore not secure. 2 nodes would be more secure, 3 nodes even more secure and so on. The more full nodes, the more secure.
IOTA can theoretically run perfectly fine with just a single node.
However, in current stress tests, it seems like nodes can handle about 1000 TPS. So for more than that, there would need to be more nodes.
Keep in mind that currently, the coordinator limits the throughput of IOTA, so the number may vary from the above until it is changed.
To answer the question of security, a single node isn't secure. Security increases with the amount of nodes -- an attacker needs to be able to control 34% of the network in order to make a malicious attack, so the more nodes, the less possible this becomes. Security is therefore bound by how powerful any given attacker may be, divided by .34.
