Size and network value: a utility perspective on Reed’s law

Reed’s law is commonly treated as an extension of Metcalfe’s law, as if both measure the same notion of ‘network value’. I show that this is not the case. Specifically, Reed’s law asserts that the “value” of ‘group-forming’ networks, such as social networks, grows in proportion to 2n, where n is the number of members. This formulation is correct if one takes a ‘system’ perspective and is interested in how the number of potential subgroups scales with size. However, if one is concerned with total utility, Reed’s law should be formulated as V ∝ n2n-1, rather than as V ∝ 2n. Only then can it be meaningfully compared to Metcalfe’s law, for which the system and user perspectives do coincide. I also examine the implications of the amendment to Reed’s law, for both practice and academic research.