The value of a network is proportional to the square of the number of people using it. The idea is that each person acts a valuable resource to all the other people, so each person sees value N, and there are N people. 

Coined by BobMetcalfe, the inventor of Ethernet.
* http://en.wikipedia.org/wiki/Metcalfe's_law
*http://en.wikipedia.org/wiki/Robert_Metcalfe

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See also ReedsLaw which says that the utility of the network is O(2^N) if it is a group forming network that allows subgroups to form arbitrarily. This is the difference between unicast and multicast. -- EdwardVielmetti 

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Is there any empirical evidence for this? My guess would be that as the web gets bigger, you run into the law of diminishing returns, meaning that as the network gets bigger, the rate at which the value of the network increases diminishes compared to the increase in size. 

Another problem: How do you measure the value of the network? 

-- BarneyFinucane 

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MetcalfesLaw is be differentiated from ReedsLaw in its recognition of Value is a reflection of Utility.

NetworkEffect, is a similar concept from Business studies which describes the value of a product or service to a consumer is directly proportional to a number of other customers using the product or service.  Mobile Phones and Fax are common examples, but this effect also extends well beyond Networks as WikiWikians understand them into standard sizes and shapes of everything from batteries to shoes. JosephWhitworth, Engineer and Inventor was one of the first people to recognise and exploit this, with the WhitworthStandard.

The evidence to all these concepts is mathematical, not empirical; it can also be shown from the following table.

  Nodes Channels   Flows
    1       0         0
    2       1         2
    3       3         6
    4       6        12

-- MartinSpamer