Metcalfe's telephone network model assumed one-to-one communication. With the Internet, not only one-to-one, but also one-to-many, many-to-one, and many-to-many communication(s) occur among many sets of people. Necessarily, moving from one-to-one communication to many-to-many communications increases the number of potential interactions. Thus, it must expand the exponent beyond the square. Not only that, Internet communication extends beyond human communication: many devices with embedded systems talk to one another or to many others. Therefore, the exponent of growth in network effects is not limited to a fixed exponent of 2, but may have larger exponents.
Actually, Metcalfe's rule is based on the number of possible connections which has nothing to do with whether on communicates one at a time or many at a time. In reality, of course, it is rare that any one individual would reasonably communicate with all of the other nodes (evidence of the circulation of some jokes on the Internet to the contrary). I don't think this is crucial, however, since the value is still likely to increase exponentially. |
