Metcalfe's law

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Metcalfe's Law states that the influence of telecommunication networks is proportional to the square of the number of connected users of the system ( n ² ). First formulated in this form by George Gilder in 1993, and attributed to Robert Metcalfe in terms of Ethernet, the law of Metcalfe was originally presented, c. 1980, not in terms of users, but "compatible communication devices" (eg, fax machines, phones, etc.). Only later with Internet globalization, this law brings to users and networks because its original intention was to describe Ethernet purchases and connections. Laws are also strongly linked to economics and business management, especially with competitive companies who want to join each other.

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Metcalfe's law describes many of the networking effects of communication and networking technologies such as the Internet, social networking, and the World Wide Web. Former US Federal Communications Commission Chairman Reed Hundt said the law provides the best understanding of how the Internet works. The Law of Metcalfe is related to the fact that the number of connections may be unique within the network ${\ displaystyle n}$ node can be expressed mathematically as a triangle number ${\ displaystyle n (n-1)/2}$ , which is asymptotically comparable to ${\ displaystyle n ^ {2}}$ .

The law is often illustrated using the fax machine example: a single fax machine is useless, but the value of each fax machine increases with the number of fax machines on the network, since the total number of people with whom each user can send and receive documents increases. Likewise, in social networks, more users with services, the more valuable the service for the community.

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Limitations

In addition to the difficulty of measuring the "value" of a network, the mathematical justification for the Metcalfe law only measures the amount of potential contacts, that is, the technological side of a network. But the social utility of a network depends on the number of nodes in contact . If there are language barriers or other reasons why large parts of a network are not in contact with other parts then the effect may be less.

The law of Metcalfe assumes that the value of each node n has the same benefits. If this does not happen, for example because one fax machine serves 50 workers in a company, the second fax machine serves half of it, a third third, and so on, the relative value of additional connections decreases. Similarly, in social networks, if the users who join later use less network than the original user, the benefits of each additional user may be reduced, making the whole network less efficient if the cost per user is set.

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Modified model

In the context of social networks, many, including Metcalfe itself, have proposed a modified model in which the value of the network grows as n ÃÆ'â € "log n rather than n ² . Reed and Odlyzko have sought a possible relationship with Metcalfe's Law in terms of describing network relationships and one can read about how it is related. Tongia and Wilson also examine the question related fees for those who are excluded.

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Validate with actual data

Despite many arguments about the Metcalfe law, no concrete data-based evidence is available for more than 30 years. Only in July 2013, Dutch researchers managed to analyze the pattern of European Internet usage in a long time and found proportionality n ² for small values ​​ n and ( n ÃÆ'â € "log n ) proportionality for big values ​​ n . A few months later, Metcalfe himself provided further evidence, as he used Facebook data over the past 10 years to show fit for Metcalfe's law (the model is n ² ).

Source of the article : Wikipedia