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Table of Contents

1. Introduction .......................................................................................................... 3

2. Network Economics ............................................................................................. 3

2.1 Principles ....................................................................................................... 3

2.2 Value of a Network ........................................................................................ 4

2.2.1 Metcalfes Law ........................................................................................ 4

2.2.2 Zipfs Law ................................................................................................ 5

3. Social Network Services ...................................................................................... 7

3.1 SNS today ..................................................................................................... 7

3.2 Value of SNS ................................................................................................. 9

4. Conclusion ......................................................................................................... 10


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1. Introduction

Whereas the old economy was driven by economies of scale, the new one is driven

by the economies of networks. (Shapiro,1999)

Since the late 1980s, when computers became constantly more present in our daily

lives, people became more and more part of an network where country borders and

location dont matter. Personal computers, smartphones and the internet give us the

opportunity to connect with anyone around the world at any time. This circumstance

also changed the dynamics of doing business and economics. Networks became a

big and important factor in the economies of our time.

This paper will focus on the principles of network economics and how they can affect

businesses. Furthermore a real world example will be given to better understand the

functioning of network economics. This real world example will be based on a small

comparison of Social Network Services, as they perfectly demonstrate some of the

principles of network economics.

2. Network EconomicsThis chapter will focus on the basics of network economics and explain the ways of

evaluating a networks value.

2.1 Principles

Basically speaking, a network is a system of objects connected with each other. The

amount of connected objects can be infinite, but the minimum number of network

participants is 2. It can be also distinguished between two types of networks: real

networks and virtual networks.

Real networks exist in the real world and are physical. Those networks can be

telecommunication networks, physical computer networks or railroad/highway

networks. The connection between those networks is physical.

In contrast to that, virtual networks have no physical existence. Those networks can

be for example users of a certain internet platform or social network services like

Facebook or cyworld.


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According to the basic theory of economics, the value of a good or product

decreases with the rising number of consumers, or the value of a product increases

as the amount of available products decreases. But the system of internet economics

works differently, as the value of the network or service rises with the rising number

of consumers. The more people are part of a network, the higher is the value of the

network.

These days most people in our modern society are part of one or more physical or

virtual network. Therefore it is very important and a big challenge for companies to

attract customers to their own networks in order to increase their value.

The following part will now explain how the value of a network can be defined.

2.2 Value of a Network

As mentioned before, the increasing number of consumers of a network or service,

the value for all other consumers of the same network or service increases. In this

context there are two different ways of evaluating the value of a network. The

Metcalfes law and the Zipfs law. Both will be described in this chapter.

2.2.1 Metcalfes Law

Metcalfes law is often being used to measure the value of a network based on thenumber of connected objects in the given network. This law states the following:

V = n

V = Value of the network

n = Number of participants of the network

This means that the value of a network is n if n is the number of participants in the

network. This situation can easily be illustrated with the following picture,

demonstrating the value of a telephone network based on the number of participants:


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As the above picture shows, the number of connections in the network increases with

the rising number of participants. Two phones have one connection, five phones

have ten connections and 12 phones have 66 connections. The value of those

networks would be 2 for the network with two phones, 25 for 5 phones and 144 for

the network with 12 phones (n).

In a real world context Metcalfes law can be shown as in the following illustration:

The picture above shows that the value of a network increases exponentially, but the

costs of operating the system show a linear growth depending on the number of

participants (N). This results in the conclusion, that the network becomes profitable

after the network value becomes higher than the costs of operating the network. This

point is also called critical mass crossover.

2.2.2 Zipfs Law

The IT bubble burst of 2001 demonstrated that Metcalfes law cant be always

applied to evaluate the value of communication networks, especially when it comes

to internet based networks. Before 2001 the value of networks was evaluated by

Metcalfes law, which led to a big overestimation of the actual value of networks. This


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situation will be explained in more detail in the third chapter. The principle of Zipfs

law is the following:

V = n log(n)

V = Value of the network

n = Number of participants of the network

These days Zipfs law is taken to evaluate the value of social media networks,

because experts share the opinion that the value of a network grows much slower.

This idea is also based on the research result of Robin Dunbar, an anthropologist

who did research on the extent of connectivity in effective social organization. Hisresearch indicates that the human brain is able to maintain meaningful relationships

to a maximum 150 people. This means that if a single person has more than 150

connections in a network, the benefit doesnt increase.

The difference between Metcalfes and Zipfs law can be illustrated with the following

graph:

As Metcalfes law grows in a very high speed, it is easy to see that according to Zipf

the value is much lower. The actual value of the network lies between Zipfs andMetcalfes law. The calculation process of this value includes many complex factors


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and is not relevant in this paper at this point. A more detailed overview about the

differences between Metcalfes law and Zipfs law can be seen in the following table:

As shown in the table above the difference between the two laws becomes bigger

and bigger with the increasing number of connection nodes in the network. The

calculated value represents the most accurate value of a social network.

3. Social Network ServicesIn recent years social network systems experienced a huge rise on users, and people

spend daily many hours of their time on those networks for communication, business

or entertainment. Many companies already recognized the importance of social

network systems (SNS) and realized that they can be a very effective distribution and

marketing channel.

3.1 SNS today

Today Facebook is the biggest social network service with now more than 1 billion

users (since October 2012). Automatically it is the most valuable social network

service. Other important SNS are Twitter (> 500 million users), the business and

professional networking platform LikedIn with more than 160 million users and the

Chinese platform Weibo with over 300 million users in China. Google tried to break

the success of Facebook with introducing its own SNS called Google+, but with only

400 million users it is not as nearly as successful as Facebook.


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One of the reasons of Facebooks success can be explained with the fact, that

Facebook was the first truly international social network service that also fitted all

tastes and needs of the average person. Before the introduction of Facebook most

SNS were limited to countries like the Korean cyworld or the German studiVZ. The

limitation to only one country and language automatically limits the number of

network participants and therefore the value of the network. In contrast to that,

Facebook became a platform where everyone can connect with everyone, no matter

which country the participants are from or which language they are speaking.

Similar as with other products and services, the success is depending on the number

of early adopters who become convinced of the product and recommend it to others.

This is also applicable with social media and internet services, as the followingillustration shows, using the Rogers bell curve:

In the upper image the first 15%, called the Innovators and early adaptors are more

likely to take risks and try new things. They are willing to spend extra money to do so.

People in the early majority are also open for new ideas and technologies, but

balance positive and negative aspects of it. Laggards will only adapt to a certain

technology or standard if it is mainstream and a standard.

The illustration above shows that for example after Facebook was made popular by

early adopters it became a standard for the mass market. Google tried to introduce


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its new SNS platform Google+ when Facebook was already a standard in the mass

market. Currently Google+ only reached the early adopters and a little bit of the early

majority, but it didnt really reach the tipping point where the SNS becomes a

standard in the mass market.

Facebook has already such a high number of network participants, so that most

users are not ready to switch from Facebook to Google+ because the value for each

individual is higher while using Facebook.

3.2 Value of SNS

As mentioned before there are two ways of evaluating the value of a network. When

it comes to social network services the Zipfs law is generally seen as more accurate

and realistic. The earlier mentioned Dunbars number sets the size of a meaningful

social group for humans at about 150. Beyond that size, additional members add

diminishing value. But even within that 150 there is considerable range in affinity and

sentiment. An example of the difference in valuation between Metcalfes law (n) and

Zipfs law (n log (n)) is illustrated in the following 2006 IEEE article:

Imagine a network of 100,000 members that we know brings in $1 million. We haveto know this starting point in advancenone of the laws can help here, as they tell us

only about growth. So if the network doubles its membership to 200,000, Metcalfes

Law says its value grows by (200,000/100,002) times, quadrupling to $4 million,

whereas the n log( n ) law says its value grows by 200,000 log(200,000)/100,000

log(100 ,000) times to only $2.1 million.

Although the example is being calculated with only 100,000 users, the difference of

evaluation between Metcalfes law and Zipfs law is very significant (4 million vs. 2.1

million). If more realistic numbers would be taken (Facebook has 1 billion users) the

difference of evaluation will be extremely high. Thats why usually a value between

Zipfs law and Metcalfes law is taken to evaluate the actual value of a social

network.

This big difference demonstrates that the evaluation of networks should be done

carefully and that Metcalfes law can lead to a severe overestimation of a networks

value. This is especially important for companies that use social network services for


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reaching customers or promoting their products, trying to evaluate the actual value

of a given network.

4. ConclusionThe fact that these days almost everyone is member of networks changed the

principles of doing business and made it essential to understand the dynamics and

functioning of network economics. Especially in internet-based businesses or social

network services the knowledge about the functioning of network economics is

important. As mentioned before, it also shows for example how and why Google+

failed to gain a similar popularity as Facebook.

The wrong evaluation led to the big internet bubble in 2001 which severely damaged

the internet services industry and decreased peoples trust in it. Thats why the way

of evaluating this kind of networks was adapted and improved to be more accurate

and realistic. Still today the evaluation of social services may be too high, as the

recent stock market launch of Facebook showed, as its stock market value is

decreasing.

Documents

Forces of network economics.pdf