Tencent and Facebook Data Validate Metcalfe's Law

In 1980s, Robert Metcalfe, the inventor of Ethernet, proposed a formulation of network value in terms of the network size (the number of nodes of the network), which was later named as Metcalfe's law. The law states that the value V of a network is proportional to the square of the size n of the network, i.e., V∝n². Metcalfe's law has been influential and an embodiment of the network effect concept. It also generated many controversies. Some scholars went so far as to state "Metcalfe's law is wrong" and "dangerous". Some other laws have been proposed, including Sarnoff's law (V∝n), Odlyzko's law (V∝n log(n)), and Reed's law (V∝n²). Despite these arguments, for 30 years, no evidence based on real data was available for or against Metcalfe's law. The situation was changed in late 2013, when Metcalfe himself used Facebook's data over the past 10 years to show a good fit for Metcalfe's law. In this paper, we expand Metcalfe's results by utilizing the actual data of Tencent (China's largest social network company) and Facebook (the world's largest social network company). Our results show that: 1) of the four laws of network effect, Metcalfe's law by far fits the actual data the best; 2) both Tencent and Facebook data fit Metcalfe's law quite well; 3) the costs of Tencent and Facebook are proportional to the squares of their network sizes, not linear; and 4) the growth trends of Tencent and Facebook monthly active users fit the netoid function well.