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I made a mistake, though... A really silly one.
It shouldn't be 2^(n*(n-1)), but 2^(n*(n-1)/2)
The full network of n nodes had n*(n-1)/2 connections. Every node (n total) connects to (n-1) others. However, we counted everything twice, so we divide by 2 (looked over that step... how easy is it to get lost of little details
). Now each of these connections can be "there" or "not there", offering a total of 2^(n*(n-1)/2) possible networks.
The recursive way is more fun to prove, altough much longer (but you still get 2^(n*(n-1)/2) as answer). I could show the recursive way, but that would just bore everyone away.
Since Phoenix' data of 2.3 years for 8 nodes and 39 billion years for 10 nodes fit with the incorrect formula (assuming 1 billion networks per second, 365 days per year), I didn't bother to double-check my derivation for errors. A square root of these results, which the /2 does, wouldn't fit his data. No, "you forgot leap year" is no explanation of an error this size.
It shouldn't be 2^(n*(n-1)), but 2^(n*(n-1)/2)
The full network of n nodes had n*(n-1)/2 connections. Every node (n total) connects to (n-1) others. However, we counted everything twice, so we divide by 2 (looked over that step... how easy is it to get lost of little details
). Now each of these connections can be "there" or "not there", offering a total of 2^(n*(n-1)/2) possible networks.The recursive way is more fun to prove, altough much longer (but you still get 2^(n*(n-1)/2) as answer). I could show the recursive way, but that would just bore everyone away.
Since Phoenix' data of 2.3 years for 8 nodes and 39 billion years for 10 nodes fit with the incorrect formula (assuming 1 billion networks per second, 365 days per year), I didn't bother to double-check my derivation for errors. A square root of these results, which the /2 does, wouldn't fit his data. No, "you forgot leap year" is no explanation of an error this size.
