Earlier quoted context omitted.
So, the wikipedia first line is wrong, you're saying? "Metcalfe's law states that the financial value or influence of a telecommunications network is proportional to the square of the number of connected users of the system" Later in the article it seems like the original stating is more consistent with what you said, but everything I've ever learned in network theory and practice shows that it scales as a power of n…
The number of connected users is different from the number of user connections :) The first is the number of nodes, the second edges.
It could explain my misunderstanding, and also seems consistent with the explanation later in the article, but it's also completely the opposite of what we observe on the internet; for example, the value of the web is definitely not in its in number of pages, but in the value and quality of the connections between the pages.