Tencent and Facebook Data Validate Metcalfe's Law - Zhang XZ Liu JJ Xu ZW Tencent and Facebook data validate Metcalfes law JOURNAL OF COMPUTER SCIENCE

Tencent and Facebook Data Validate Metcalfe's Law - Zhang...

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Zhang XZ, Liu JJ, Xu ZW. Tencent and Facebook data validate Metcalfe’s law. JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY 30(2): 246–251 Mar. 2015. DOI 10.1007/s11390-015-1518-1 Tencent and Facebook Data Validate Metcalfe’s Law Xing-Zhou Zhang 1 , 2 ( 张星洲 ), Jing-Jie Liu 1 , 2 ( 刘晶杰 ), and Zhi-Wei Xu 1 , 2 ( 徐志伟 ), Fellow, CCF, Member, ACM, IEEE 1 Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China 2 University of Chinese Academy of Sciences, Beijing 100049, China E-mail: { zhangxingzhou, liujingjie, zxu } @ict.ac.cn Received November 25, 2014; revised January 17, 2015. Abstract 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 n 2 . 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 2 n ). 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. Keywords network effect, Metcalfe’s law, cost, netoid function 1 Introduction Network effect has become an influential concept not only in the technology field, but also in economy and business, social sciences, and even global public events [1 - 2] . A network effect is the effect that a net- work’s value V is dependent on its size n (the number of its nodes) [3] . Four laws have been proposed to pro- vide more precise definitions and characterizations of network effect. They are Sarnoff’s law [3] : V n , Odlyzko’s law [4] : V n log( n ), Metcalfe’s law [5] : V n 2 , and Reed’s law [6] : V 2 n . Many papers are published [3 - 9] arguing for or against these laws. However, no actual evidence was available in the literature to validate these laws with real data until December 2013, when Robert Metcalfe himself utilized Facebook’s actual data over the past decade to show a good fit to Metcalfe’s law [8] .

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