IEEE Spectrum suggests that the Law may be wrong:
Of all the popular ideas of the Internet boom, one of the most dangerously influential was Metcalfe’s Law. Simply put, it says that the value of a communications network is proportional to the square of the number of its users.
The law is said to be true for any type of communications network, whether it involves telephones, computers, or users of the World Wide Web. While the notion of “value” is inevitably somewhat vague, the idea is that a network is more valuable the more people you can call or write to or the more Web pages you can link to.
Metcalfe’s Law attempts to quantify this increase in value. It is named for no less a luminary than Robert M. Metcalfe, the inventor of Ethernet. During the Internet boom, the law was an article of faith with entrepreneurs, venture capitalists, and engineers, because it seemed to offer a quantitative explanation for the boom’s various now-quaint mantras, like “network effects,” “first-mover advantage,” “Internet time,” and, most poignant of all, “build it and they will come.”