Summary of that article: Metcalfe's law assumes that when you add a new person to a network, he will communicate equally with everybody, so that he contributes

Summary of that article: Metcalfe's law assumes that when you add a new person to a network, he will communicate equally with everybody, so that he contributes 1 unit of value per existing node, leading to O(n^2) growth. But that is wrong. Instead his communication is more likely to follow a Zipf distribution such that he contributes 1 unit of value to the existing node he communicates the most with, 1/2 unit of value to the one he communicates the second-most with, 1/3 to the third-most and so on. This means each new member contributes O(log n) additional value, leading to O(n log n) growth.