Metcalfe’s law characterizes many of the network effects of communication technologies and networks such as the Internet, social networking and the World Wide Web. Former Chairman of the U.S. Federal Communications Commission Reed Hundt said that this law gives the most understanding to the workings of the Internet. Metcalfe’s Law is related to the fact that the number of unique connections in a network of a number of nodes (n) can be expressed mathematically as the triangular number n(n − 1)/2, which is proportional to n2 asymptotically (that is, an element of Θ(n2)).
The law has often been illustrated using the example of fax machines: a single fax machine is useless, but the value of every fax machine increases with the total number of fax machines in the network, because the total number of people with whom each user may send and receive documents increases. Likewise, in social networks, the greater number of users with the service, the more valuable the service becomes to the community.
The value of a network V is given by the formula shown here.Related formulas
|V||value of a network (dimensionless)|
|a||Metcalfe’s coefficient (dimensionless)|
|n||network nodes (dimensionless)|