a borrowed note in part explanation for the power and illusion of social network power

Borrowing from Metcalfe’s law, we might conclude that the power of a network grows at an *increasing* rate with its size. But the reason that network value will increase at this increasing rate in computing is that each addition of a new computer to a network results in a greater-than-proportionate increase in possible connections within the network. It may increase at an increasing rate, but we cannot make this claim universally, as new additions to a social network may not uniformly increase network activity. In some cases, the power of a standard may grow exponentially in proportion to network size. But the rationale for this exponential relation is that each new node added to a computer network increases exponentially the number of possible connections with it. With computers or technically compatible systems, the claim is more plausible than in social systems, where the addition of another English speaker, say, no doubt adds value to English as a standard that outsiders want to adopt, but does not necessarily do so exponentially, particularly as all network members are not connected to one another except potentially. Furthermore, the social position of the new entrants must be considered in social network analysis, unlike in the analysis of networks in which the nodes are all uniform, as with machines.

– David Singh Grewal, Network Power: The Social Dynamics of Globalization, Yale University Press, New Haven, 2008, p. 305, n. 17