Growth Curves: How much more valuable does a network become as it grows? That depends on what kind of network it is. Let's say you have n users. The value of a television or some other broadcast network grows linearly, as shown by Sarnoff's Law [green] here. At the other extreme, according to Reed's Law [purple], growth in value of certain networks—those that can form groups, such as e-mail lists—is exponential (2n). In between are ordinary, member-based networks such as AOL, or all of AT&T's phone customers. Metcalfe's Law [red] says they grow in value quadratically (n ²). We argue, instead, that such growth increases logarithmically as n log(n) [blue], a much slower rate.