Facebook and Tencent Data Fit a Cube Law Better than Metcalfe’s Law

Metcalfe’s law states that the value of a network grows as the square of the number of its users ($V\propto n^2$), which was validated by actual data of Facebook and Tencent in 2013–2015. Since then, the users and the values of Facebook and Tencent have increased significantly. Is Metcalfe’s law still valid? This paper leverages the latest data of Facebook and Tencent to fit the network effect laws and makes the following observations: 1) actual data of network values fit a cube law ($V\propto n^3$) better than Metcalfe’s law; 2) actual data of network costs fit a cube law; 3) actual data of network sizes show a growth trend matching the netoid function well. We also discuss the underlying factors affecting such observations and the generality of the network effect laws.