Metcalfe’s law was made famous by the Internet bubble as a justification for investing in growth & disregarding losses: if the value of a ‘network’ increased nonlinearly, then at some future point, the profits would materialize past an ‘inflection point’. This “law” has been blamed for inflating the bubble, and has been supposedly debunked by 2005.
However, 2005’s arguments are quite poor, and turn out to be both theoretically flawed and contradicted by available empirical data directly testing Metcalfe’s law: it turns out that networks do scale in value much like Metcalfe guessed, and companies like Facebook or Tencent get much more valuable as they scale. (Tilly continues to maintain it has been debunked.)
But on the gripping hand, the constants involved are not that large so networks may have to scale enormously to show economically-important effects, and there are hints of diseconomies of scale. So it may be that in practice, Metcalfe’s law is true but too dangerous to hold as an overriding strategic principle.