Value of networks
In telecommunications networks, several informal "Laws" have been defined to state the value of networks, as they become capable of more and more complex connectivity and online collaboration. Three competing models of the value of communications also reflect the differing assumptions of radio broadcasting, the Public Switched Telephone Network (PSTN) and the Internet. This article does not deal with the finances of payments for use of the network; see telecommunications provider economics.
At the initial level of valuation, there is an assumption that all participants are trustworthy, which, in reality, becomes more and more of a problem with increasing network size. Even with unidirectional broadcast networks, a source of information may or may not be reliable. An untrustworthy source may be a deliberate miscreant, or simply have incorrect information.
There are communications facilities, such as those interconnnecting System Control And Data Acquisition (SCADA) computers that control electrical power to millions of people, which must not have connectivity beyond the minimum essential elements needed for the mission. Every new participant, as opposed to backup communication links, could be a source of critical error.
Value from Increasing Connectivity
These general models assume the value of all communications links are equal. From a pure financial standpoint, the communications link between a major nation's Minister of the Treasury and the head of its central bank has a different value than the text-messaging link between the respective financial leaders' pubescent children, on which they compare notes about the irrationality of a shared teacher. The financial communication may convey incorrect assumptions, and the teacher may be one step from involuntary hospitalization, but the links cannot be assumed to be of the same value.
The value of a one-way radio or television broadcast grows linearily with the number of viewers. In such a network, the only sessions exist between the single transmitter and the <math>N</math> users.
This does not consider the additional value of a technical monopoly, or oligopoly, of broadcast channels in a specific market. In reality, the value of a television broadcast spectrum assignment is a function of the buying power reached by that broadcast.
Metcalfe’s Law states that the value of a connection-oriented network is based on the number of users that can form connections. For <math>N</math> users, <math>(N</math>2 –1) value derives from the network being the agent that knows all participants and arranges all interactions. The PSTN, of course, manages telephone numbers and the calling plan.
Briscoe and others argue that a better valuation is <math>n</math> <math>log</math> <math>n</math>.  They emphasize that not all connections are of equal value, and, that if the value of interconnection was pure, every communications provider would be incentivized to merge.
Norton does show that there are strong special cases of increasing value by interconnection, involving telecommunications service providers rather than end users. In telecommunications provider economics, value is much less related to the desire of individual customers of Internet Service Providers will want to talk to one another, and more that each ISP, of roughly the same size, will have enough customers that want to connect to each comparable ISP.
David Reed looked beyond Metcalfe’s pairwise model to consider the formation of groups. For <math>N</math> people, there can be groups of size <math>2</math> to <math>N</math>, making the value <math>(N</math>-1)!/(<math>N</math>-1)!. 
Taken literally, the model suggests that each member added doubles the value; adding 10 members increases the value by a factor of 1000. It is probably fair to say that the increase in value can hold true as long as the participants are cooperative and share interest. Even then, beyond a certain size, supplemental tools become necessary to find others with the same interest, as evidenced by the proliferation of social networking models.
While Reed's model is intended for networking, it is highly related to models of connectionism. The connectionist idea that networks become more powerful as they create new interconnections is certainly demonstrated by increasing power of the interconnected World Wide Web. Its power is not limited to the real-time connectivity of the interactive services described above.
Trust and the value of networks
In the first incarnation of what became the modern Internet, the ARPANET, which was restricted to researchers, the participants trusted one another. That did not mean that all information would be free from errors, but the open model encouraged fact-checking and dissemination of corrections.
When the modern Internet was opened, under no centralized control, both the communications paths and the information on them were not necessarily trustworthy.
As a first stage of trust, one must recognize the expertise of a specific communications partner, be able to verify the recognition of that authority by a mutually trusted intermediary (e.g., certification authority), or verify that individual through "reputation" mechanisms (e.g., Pretty Good Privacy and distributed trust. Systems that allow anonymous or pseudonymous participation, such as Wikipedia, use a different model, which assumes that any given source may be untrustworthy, but the overall system will correct errors or untruths.
In a more formal second stage, there is not only verification of identity, but of knowledge. In the traditional and manual model of academic research, there was a lengthy publication process, in which a journal editor made certain that qualified peer reviewers had validated the results. Citizendium does not assume that the knowledge model is self-correcting; it assumes that before approval of content, not only non-anonymous individuals, but non-anonymous individuals whose expertise is verified, advises creators and validates the work. The idea of in-process feedback, from general readers and specialists, differs from classic academic review, in which feedback only goes back to authors when the content is not acceptable.
- Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly (July 2006), "Metcalfe's Law is Wrong", IEEE Spectrum Online
- Gilder, George (September 13, 1993), "Metcalfe's Law and Legacy", Forbes ASAP
- Norton, William B. (November 2003), "The Evolution of the U.S. Internet Peering Ecosystem", North American Network Operators Group
- Reed, David P., Group Forming Networks Resource Page
- Reed, David P., That Sneaky Exponential—Beyond Metcalfe's Law to the Power of Community Building