Classroom Companion: Business

9.2 · Positive and Negative Network Effects

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9
Another concept that has to do with the size of human groups is the Dunbar num-
ber; see 
7
Box 
9.2
. The concept is used later in this chapter to evaluate the strength 
of certain networks.
different fields of mathematics. One of 
the authors (Audestad) has a collabora-
tion distance 4 to Erdös and 5 to 
Einstein!
Facebook has analyzed the average 
degree of separation between any two 
users of the network and found that this 
distance has decreased from 5.28 in 2008 
to 4.74 in 2011 and 4.57 in February 
2016. In the Watts-Strogatz model, 
which produces random graphs with 
small-world properties, the average path 
length between two nodes is calculated 
using the formula lnN/ ln K, in which N 
is total number of nodes and K is the 
average number of links per node. For 
Facebook, with 2.2 billion users (nodes) 
in 2018 and 150 number of friends 
(links) per user as suggested by Dunbar’s 
number (see 
7
Box 
9.2
), the average 
path length is calculated as:
ln N/ ln K = ln 2.2 × 10
9
/ ln 150 ≈ 4.29
in good agreement with the observed 
numbers presented above.
. Fig. 9.2 Social network. (Authors’ own figure)
Box 9.2 Dunbar’s Number
Robin Dunbar is a British anthropolo-
gist that studied the volume of the neo-
cortex of various animals and their 
corresponding social group sizes. Based 
on his findings, he predicted the num-
ber of people with whom a human can 
maintain a stable relationship. His ini-
tial studies suggested a number between 
100 and 250, but he later argued for 150 
as a mean group size for communities 
with high incentives to stay together. 
The latter was based on studies on 
human societies, both existing and his-
torical. Dunbar’s number is, then, 150. 
It is argued that this is the number of 
people an individual can call a “friend,”