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. David P. Reed is an American computer scientist, educated at the Massachusetts Institute of Technology, known for a number of significant contributions to computer networking. ... In economics, utility is a measure of the relative happiness or satisfaction (gratification) gained. ... A social network is a social structure made of nodes (which are generally individuals or organizations) that are tied by one or more specific types of relations, such as values, visions, idea, financial exchange, friends, kinship, dislike, trade, web links, sexual relations, disease transmission (epidemiology), or airline routes. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ...

The reason for this is that the number of possible sub-groups of network participants is , where N is the number of participants. This grows much more rapidly than either

• the number of participants, N, or
• the number of possible pair connections, (which follows Metcalfe's law)

so that even if the utility of groups available to be joined is very small on a per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system. Metcalfes law states that the value of a telecommunications network is proportional to the square of the number of users of the system (n2). ... A network effect is a characteristic that causes a good or service to have a value to a potential customer which depends on the number of other customers who own the good or are users of the service. ...

Derivation

Given a set A of N people, it has 2^N possible subsets. This is not difficult to see, since we can form each possible subset by simply choosing for each element of A one of two possibilities: whether to include that element, or not. In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ...

However, this includes the (one) empty set, and N singletons, which are not properly subgroups. So 2^N − N − 1 subsets remain, which is exponential, like 2^N. Generally, a singleton is something which exists alone in some way. ...

Quote

From David P. Reed's, "The Law of the Pack" (Harvard Business Review, February 2001, pp 23-4):

"[E]ven Metcalfe's Law understates the value created by a group-forming network as it grows. Let's say you have a GFN with n members. If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2ⁿ. So the value of a GFN increases exponentially, in proportion to 2ⁿ. I call that Reed's Law. And its implications are profound."

See also

• Coase's penguin
• Social capital
• Metcalfe's law
• Andrew Odlyzko's "Content is Not King"
• List of adages named after people

Coases Penguin, or Linux and the Nature of the Firm, is an essay written in 2002 by Yochai Benkler, Professor of Law at the Yale University School of Law. ... Social capital is a core concept in business, economics, organizational behaviour, political science, and sociology, defined as the advantage created by a persons location in a structure of relationships. ... Metcalfes law states that the value of a telecommunications network is proportional to the square of the number of users of the system (n2). ... Andrew Odlyzko is a mathematician who is the head of the University of Minnesotas Digital Technology Center. ... List of adages named after people is an annotated list of eponymous adages; some serious, some humorous. ...

External links

• That Sneaky Exponential—Beyond Metcalfe's Law to the Power of Community Building
• Weapon of Math Destruction: A simple formula explains why the Internet is wreaking havoc on business models.
• KK-law for Group Forming Services, XVth International Symposium on Services and Local Access, Edinburgh, March 2004, presents an alternative way to model the effect of social networks.