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<p>Metcalfe’s law captures the relationship between the value of a network and its scale, asserting that the value of a network is directly proportional to the square of its size. Over the past four decades, researchers have proposed different scaling laws for network values. Remarkably, these seemingly conflicting conclusions have been substantiated by robust data validation, raising the question of which laws hold greater representativeness. Consequently, underlying mechanisms that underpin these laws are needed. This study aims to bridge this gap by offering a theoretical interpretation of Metcalfe’s law and its variants. Based on a certain degree of consensus that <i>traffic is value</i>, network effects are gauged using network traffic load. A general analytical boundary for network traffic load is deduced by balancing practicality and analytical feasibility through the establishment of a comprehensive network model. From this foundation, the mechanism behind Metcalfe’s law and its variants is elucidated, aligning the theoretical derivations with previously validated empirical evidence for Metcalfe’s law.</p>

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Emergence of Metcalfe’s law: mechanism and model

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Cheng Wang,
  • Yi Wang,
  • Changjun Jiang

摘要

Metcalfe’s law captures the relationship between the value of a network and its scale, asserting that the value of a network is directly proportional to the square of its size. Over the past four decades, researchers have proposed different scaling laws for network values. Remarkably, these seemingly conflicting conclusions have been substantiated by robust data validation, raising the question of which laws hold greater representativeness. Consequently, underlying mechanisms that underpin these laws are needed. This study aims to bridge this gap by offering a theoretical interpretation of Metcalfe’s law and its variants. Based on a certain degree of consensus that traffic is value, network effects are gauged using network traffic load. A general analytical boundary for network traffic load is deduced by balancing practicality and analytical feasibility through the establishment of a comprehensive network model. From this foundation, the mechanism behind Metcalfe’s law and its variants is elucidated, aligning the theoretical derivations with previously validated empirical evidence for Metcalfe’s law.