It's often said the value of social networking is O(n^2), which is basically impossible to overcome, versus n lg n, which makes the difference between 2 million and 20 million users a lot smaller (too tired for the math, sorry, maybe 20x?) instead of 100x.

If the total value of the network is O(n log(n)) then the value per user is only O(log(n)). So comparing a 2 million user network with a 1 million user network, if the second one is on a product that is 10% better, users should find switching an improvement.

Thanks for explaining! I'd always heard that O(n^2) value for social networks but never really thought about who that value is for. Now that you mention it, the value of a network to an individual user really is only O(n) or even O(log(n)). So while the company still has a massive cash advantage, it's much harder to deepen that moat and secure your customers with it than it seemed.