A network’s tendency to explode in value mathematically

was first noticed by Bob Metcalfe, the inventor of a localized networking technology called Ethernet. During the late 1970s Metcalfe was selling a combination of Ethernet, Unix, and TCP/IP (the internet protocol), as a way to make large networks out of many small ones. Metcalfe says, “The idea that the value of a network equals n squared came to me after I failed to get networks to work on a small scale, despite many repeated experiments.” He noticed that networks needed to achieve critical mass to make them worthwhile. But he also noticed that as he linked together small local networks here and there, the value of the combined large network would multiply abruptly. In 1980 he began formulating his law: value = n x n.

In fact, n2 underestimates the total value of network growth. As economic journalist John Browning notes, the power of a network multiplies even faster than this. Metcalfe’s observation was based on the idea of a phone network. Each telephone call had one person at each end; therefore the total number of potential calls was the grand sum of all possible pairings of people with phones. But online networks, like personal networks in real life, provide opportunities for complicated three-way, four-way, or many-way connections. You can not only interact with your friend Charlie, but with Alice and Bob and Charlie at the same time. The experience of communicating simultaneously with Charlie’s group in an online world is a distinct experience, separate in its essential qualities, from communicating with Charlie alone. Therefore, when we tally up the number of possible connections in a network we have to add up not only all the combinations in which members can be paired, but also all the possible groups as well. These additional combos send the total value of the network skyrocketing. The precise arithmetic is not important. It is enough to know that the worth of a network races ahead of its input.

This tendency of networks to drastically amplify small inputs leads to the second key axiom of network logic: the law of increasing returns. In one way or another this law undergirds much of the strange behavior in the network economy. The simplest version goes like this: The value of a network explodes as its membership increases, and then the value explosion sucks in yet more members, compounding the result.