@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