There is too much chatter once again about laws governing networks after the recent IEEE article critiquing Metcalfe’s law with even Metcalfe himself pitching in to defend his position/law. In all this chatter I find all these smart folks missing out two basic ( really basic) points.
- All these laws posit a boundary value calculation (maximum) and not the actual value for a specific instance of a network. Any CS grad would be easily point out that the above arguments are Big Oh evaluation (worst case) and not Theta evaluation (average case).
- Telephone kind of networks (with direct externalities) can attain a maximum of n^2 (= n*(n-1)/2 ) and no more. (Metcalfe’s)
- A network with nodes who are ‘humans’ and have value realized in the overall if sub-grouped can attain a maximum of 2^n ( = Summation[ nC1 + nC2 …. nCn] ) and no more. ( Reed’s)
- The other far more important & subtle point being that “ALL models are wrong but some models are useful“