Metcalfe's Law broken
Way back when, Bob Metcalfe, one of the creators of ethernet, coined a formula that says that the value of a network grows on the order of n2. During the internet boom, that so-called "law" was used in bazillions of pitches to (attempt to) justify all sorts of aggressive growth strategies.
Andrew Odlyzko and Benjamin Tilly have recently written a paper, A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections which dissects Metcalfe's law (and Sarnoff's law). They also present arguments for a better rule of thumb: the value of a network grows on the order of n log (n). This new guideline seems to fit our intuition as well as actual practice much better.