Classroom Companion: Business

 
Chapter 9 · Network Effects

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9
The value of Wikipedia for the reader is the volume and correctness of the con-
tent. The value is independent of who else is reading this content and the 
number of writers and benefactors. Wikipedia is a special case where the net-
work laws do not apply—even Sarnoff’s law—since the value is independent of 
the number of users.
9.6.3 
 Metcalfe’s Law and Odlyzko-Tilly’s Law
Fax machines, telephones, and email accounts are more valuable when more equip-
ment of the same type is connected to the network. Robert Metcalfe, one of the 
inventors of Ethernet, suggested in 1980 that the value of an Ethernet network 
would be proportional to the number of possible transactions between compatible 
devices connected to the network, that is:
V
n
n
Metcalfe
 
~
,
2
in which n is the number of devices. The law assumes that all possible interactions 
are equally valuable and probable. For small networks, such as Ethernet, this is a 
reasonable assumption. This is illustrated in 
.
Fig. 
9.12
, in which all nodes are 
connected to each other in a network consisting of six nodes. The number of links 
in the network in 
.
Fig. 
9.12
is 15 which, according to Metcalf’s law, is a measure 
for the value of the network. Note that the number of links in a network with n 
nodes, where all nodes are connected to each other, is n(n − 1)/2 ~ n
2
, from which 
Metcalf’s law follows directly.
Later, it was argued that Metcalfe’s law is also valid for social media network, 
such as Facebook, Twitter, and other digital services in which the most important 
feature is interactions between individuals. A recent paper (Zhang et al., 
2015
) indi-
cates that Facebook follows Metcalfe’s law quite accurately and that the value can 
Digital service
Users
. Fig. 9.12 A network 
where all nodes connect 
to each other. (Authors’ 
own figure)