Reed's law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.
See the entry on Group Forming Networks for explanations of Reed's Law.
It is also explained in the Wikipedia article at http://en.wikipedia.org/wiki/Reed's_law
Difference between groups based on Metcalfe's Law and those base on Reed's Law
"Reed identifies three types of networks that create value.
First, there are one-way broadcast networks. Also known as the Sarnoff “push” network, the value of one-way broadcast networks is equal to the number of receivers that a single transmitter can reach. An example of a one-way broadcast network is the wire service.
Second, there are Metcalfe networks. In a Metcalfe network, the center acts as an intermediary, linking nodes. Classified advertising is an example of the Metcalfe network.
Third, there are Group Forming Networks, also known as Reed Communities. In this network, collateral communications can take place. The nodes can communicate with one another simultaneously. Chat groups are the classic example of this type of network.
The key difference between the Metcalfe network and the Group Forming Network is multi-way communications. Group Forming Networks use group tools and technologies such as chat rooms and buddy-lists that “allow small or large groups of network users to coalesce and to organize their communications around a common interest, issue, or goal.” The exponentiation increases value very quickly and may cause the number of connections/communications to exceed the ability of individuals to maintain them. Thus, it is a theoretical upper limit. On the other hand, as Reed points out, the formation of even a small subset of the theoretically possible groups would dramatically increase the value of the network - N3 in Exhibit 3. Even if not all groups form, the potential value in the option to form groups is higher. The critical point is that to capture the value of group forming networks, the members of the network must have the freedom to self-organize groups. With that freedom, they create the groups of greatest value to the users." (http://cyberlaw.stanford.edu/system/files/From+Wifi+to+Wikis+and+Open+Source.pdf)
"Other analysts of network value functions, including Andrew Odlyzko and Eric S. Raymond, have argued that both Reed's Law and Metcalfe's Law overstate network value because they fail to account for the restrictive impact of human cognitive limits on network formation. According to this argument, the research around Dunbar's Number implies a limit on the number of inbound and outbound connections a human in a group-forming network can manage, so that the actual maximum-value structure is much sparser than the set-of-subsets measured by Reed's law or the complete graph measured by Metcalfe's Law." (http://en.wikipedia.org/wiki/Reed%27s_law#Criticism)
"There are common-sense arguments that suggest Metcalfe's and Reed's laws are incorrect. For example, Reed's Law says that every new person on a network doubles its value. Adding 10 people, by this reasoning, increases its value a thousandfold (210). But that does not even remotely fit our general expectations of network values—a network with 50 010 people can't possibly be worth a thousand times as much as a network with 50 000 people.
At some point, adding one person would theoretically increase the network value by an amount equal to the whole world economy, and adding a few more people would make us all immeasurably rich. Clearly, this hasn't happened and is not likely to happen. So Reed's Law cannot be correct, even though its core insight—that there is value in group formation—is true. And, to be fair, just as Metcalfe was aware of the limitations of his law, so was Reed of his law's." (http://www.spectrum.ieee.org/jul06/4109/3)