Network Value.

Last time I have been writing about the size of social networks, hence the quantitative characteristics. Today I want to continue with a brief article about a related subject: the value of networks. 

Since the advent of telecommunication and broadcast media, scholars from around the world studied the economies of mediated networks. To identify the value of a certain network was an important issue and part of monetization strategies. Network laws can be used as guidelines to determine the value of certain networks. Although an important aspect has always been the direct economic value of the network, other values such as diffusion, dynamic, or potency of the network are becoming increasingly important recently as they may lead to possible indirect monetization strategies. Although most of these laws have been invented with the concept of electronic networks in mind, it is also absolutely necessary to understand them for the study of non-mediated social networks.

An early law of the economics of computer-mediated networks is called Sarnoff’s law. This law was drafted in the early twentieth century by David Sarnoff, a pioneer of commercial US-American radio and television. During the advent of mass-media Sarnoff described, that the value of a broadcast network is proportional to the amount of its consumers. The more consumers, the higher the vale. The proportion between consumer and value grows linearly as with every new consumer the value of the network increases by 1.

Another law that has become important especially in the field of modern networks is known as Metcalfe’s law. It was first described by Robert M. Metcalfe, the inventor of the Ethernet, in 1980 in relation to “compatible communication devices” (Simeonov, 2006), such as fax machines or telephones, and later revised with regard to “people” or user (Hendler, Golbeck, 2008). The law depicts that the value of a telecommunications network is proportionate to the square of the number of connected users of the system. The value of networks can be calculated from the amount of nodes (e. g., users, computers, or fax machines). Nodes in a network are interconnected, that means that every node has a direct connection to every other node. The total number of connections of a single node is n-1, because it cannot connect to itself. The value of such a network grows to the square of the number of nodes (n²). A network that consists of 10 nodes has the value 10² (=100). If two networks each consisting of 10 nodes with the value 100 are joined the result is not 200, but 20² or 400.

The simplified conclusion of Metcalfe’s law is that while the cost of a networks grow linearly, bigger networks have a proportionately greater value than smaller ones or “connecting two networks creates far more value than the sum of their values as independent networks” (Rheingold, 2002:59). This is a good reason why the Internet is most effective when widely used and even in business management this law can be applied when two companies merge to one. This law is most famously applied to the page rank algorithm by Brin and Page (1998), where pages are ranked based on the amount of links that point to them. This algorithm is the basis of the well-known search engine Google.

A third law that was developed to calculate the value of networks is Reed’s law. Reed argues that when users are given the opportunity to create social groups within a network the value grows even faster than what we originally described with Metcalfe’s law (Reed, 2001). These Group Forming Networks, as Reed coins them, grow by the value of two to the power of the number of nodes (2ⁿ). When the value of a network of 10 nodes according to Metcalfe’s law is 100, it would be 2¹º or 1024 according to Reed’s law. What this means is that when the nodes of a network are human beings (instead of documents or servers) and they can form sub-groups inside the network, the value of this network is significantly greater.

It is important to say that these laws have not been overall accepted. Especially Reed’s law seem to be quite controversial, considering that the social network service Facebook would have a value of about 1⁹⁵⁵ ⁰⁰⁰ ⁰⁰⁰ (as of June 2012). What does that mean? Briscoe et. al (2006) suggest that not all connections are of equal value and propose a proper formula O(n log n) to calculate network value.

In 2009 Beckstrom developed the New Network Valuation Model, which defines that “the value of a network equals the net value added to each user’s transactions conducted through that network, valued from the perspective of each user, and summed for all”. Beckstrom believes that the earlier approaches by Reed and Metcalfe wrongly focused on the architecture or structure of a network, but that instead we have to calculate a net value which evolves from using the network. According to Beckstrom this model applies to any network: “social networks, electronic networks, support groups, and even the Internet as a whole”. In this model the net value differs for every single user. Beckstrom provides the example of an individual buying a book. If the book costs € 26,- in a real world book store, but only € 16,- on the Internet than the net value of this single transaction is € 10,-. Other factors that are important to calculate the final value are the benefit of using either the network or the bookstore over the other and the time elapsed to complete the buying and delivery process. The total net value of all transactions of a single user define the networks value for this single user and the sum of all users transactions net value define the total value of the network. Similar to the other laws the value of the network increases as more users join, as they bring more possible transactions to the network.

Although the underlying formula of these laws and models differ quite significantly, the result is often the similar: In a theoretic approach, where resources are not limited the value of networks grows with the quantity of its users. This effect is also known as Network Effect. On the other hand, this process of rapid increase of network value can turn back. This is then called the Inverse Network Effect.

BECKSTROM, Rob (2009). “A New Model Of Network Evaluation”, from http://www.beckstrom.com/The_Economics_of_Networks, last modified: March 26th, 2009.

BRIN, Sergey & PAGE, Lawrence (1998). “The anatomy of a large-scale hypertextual Web search engine”. Computer Networks and ISDN Systems, vol. 30, issues 1-7, 107-17.

BRISCOE, Rob & ODLYZKO Andrew & TILLY Benjamin (2006). “Metcalfe’s Law is Wrong”, IEEE Spectrum, from http://spectrum.ieee.org/computing/networks/metcalfes-law-is-wrong/1, last modified: July 2006.

HENDLER, James & GOLBECK, Jennifer (2008). “Metcalfe’s law, Web 2.0, and the Semantic Web”. Journal of Web Semantics, in press, from http://www.cs.umd.edu/~golbeck/downloads/Web20-SW-JWS-webVersion.pdf

REED, David P. (2001) “The Law of the Pack”. Harvard Business Review, February 2001.

RHEINGOLD, Howard (2002). Smart Mobs. The Next Social Revolution. Transforming Cultures and Communities in the Age of Instant Access. Cambridge, Perseus Books Group.

SIMEONOV, Simeon (2006). “Metcalves’s Law: more misunderstood than wrong”, from http://blog.simeonov.com/2006/07/26/metcalfes-law-more-misunderstood-than-wrong/, last modified: July 26, 2006.

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