@boud All but certainly a markup failure, as what's printed is "n2" rather than the more conventional "2n" when referencing multiplication.
Then there's the issue that Metcalfe's law overstates the value of network size. Odlyzko & Tilly suggest n * log(n) as a better approximation.
http://www.dtc.umn.edu/~odlyzko/doc/metcalfe.pdf
My own view is that value 1) increases at a decreasing rate as nodes grow (Odlyzko-Tilly) and 2) that there's a constant cost function per node, 'k':
V = n * (log(n) - k*n
This also gives us an upper bound on value-increasing network scale: where k >= log(n), the network can no longer grow effectively.
Corollaries:
- By reducing k, viable network size can be increased. This is effectively the same as improving network hygiene such that cost factors are reduced.
- Increasing k will reduce the total viable size of a network.
- A periodically variable k (whether regular or irregular) will result in a network with a variable maximum viable size.
But the key is If you want to make large networks less viable, increase their constant cost function.
Ping @pluralistic
@rysiek @eff
#MetcalfesLaw #NetworkValue #NetworkEffects #AndrewOdlyzko #OdlyzkoTilly #HygieneFactors #NetworkCostFunction #Scale