Classroom Companion: Business

9.6 
 Estimating the Value of Networks
9.6.1 
 Size of Networks
This section provides simple mathematical arguments concerning the impact that 
network effects may have on the value of various types of digital goods or services 
depending on the way in which users interact. First, observe that in a population or 
network of n individuals, there are:
5
n singletons.
5
n
2
pairs (assuming n >> 1 and counting all one-way interactions between indi-
viduals)
5
2
n
groups (also assuming n >> 1)
Based on this observation, different laws estimating the value of digital services are 
presented next. In the following text, V(n) is a measure for the total value of a 
digital service or network, and n is the total number of users. Value in this context 
is an abstract concept that can be a measure of, for example, revenues, market 
capitalization, volume of transactions between users, or time spent using a service.
Common representations of value are the number of links between users in the 
network and the number of groups a user can be member of. These are the basis for 
the calculation of the various network laws. Note that, in the presented models, 
V(n) depends only on the number of users, n. As a general note, the value of a 
company or a service depends also on other tangible and intangible assets such as 
cash, securities, property, equipment, design value, brand recognition, and organi-
zational value. However, these variables are not considered in the following calcula-
tions; the focus here is solely on the value that arises because of the number of 
users.
 
Chapter 9 · Network Effects

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9
The value each new user adds to the network, or the network effect generated 
by a single user, is given as:
F n
V
n
dV n
dn
 

 

 

.
When a new user joins a network, they link to other users that are already a part of 
the network. This is illustrated in 
.
Fig. 
9.10
.
The tilde notation “~” is used to indicate the growth rate of the value of a net-
work. For example, V(n)~n indicates that the value of the network grows (at most) 
as fast as cn, where c is a constant. This is equivalent of the “big O notation,” 
O(n) = cn, commonly used to assess the growth rate of algorithms in mathematics 
and computer science.