Metcalfe's law

A heuristic that estimates a communications network’s value as proportional to the square of its user count, based on possible connections among users.

Complete graph: A graph in which every pair of distinct vertices is joined by an edge. A fully connected network with n users has n(n−1)/2 possible pairwise links.
Internet: A global system of interconnected computer networks that communicate using shared protocols. Its users and services form a large, evolving communications network.
Odlyzko–Tilly model: A model estimating network value from the number of valuable connections, which may be far fewer than all possible pairs. It challenges the assumption that every possible pair contributes equally.
Gordon–Breach valuation debate: A public dispute over claims that network valuation based on Metcalfe's law overstated value. The debate made the gap between theoretical connections and measured value explicit.
Combinatorics: The branch of mathematics concerned with counting, arrangement, and finite structures. Counting user pairs gives the quadratic relationship behind the law.
Social network: A structure of people or organizations connected by social relationships. Its value can depend on how many other members each user can reach.
Linear growth: A pattern in which a quantity increases in direct proportion to another quantity. It represents broadcast-style value that rises with users rather than user pairs.
Network density: The proportion of possible links in a network that are actually present. Sparse networks may realize only a fraction of the law's possible connections.
Network effect: A phenomenon in which a product or service becomes more valuable as more people use it. The law models how additional users can increase value for existing users.
Telephone network: A communications system that connects telephones for voice calls. Pairwise calling possibilities offer a concrete setting for the law's estimate.

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