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<p>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 2<sup><i>n</i></sup>, where <i>n</i> 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 <i>V</i> ∝ <i>n</i>2<sup><i>n</i> −1</sup>, rather than as <i>V</i> ∝ 2<sup><i>n</i></sup>. 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Leo Van Hove

摘要

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.