# What is Metcalfe's Law?

Why do Google and eBay open their source code?

Quick to "why" answer: so what is the logical evolution of a Save the Metcalfe a Red Group. If you are interested in topics ... read on.

Lets start by the beginning:

## What is a Network Metcalfe?

A Save the Metcalfe is a business with a particular structure thus generating value from Metcalfe's Law.

(... yeah okay, thank you)

## What is Metcalfe's Law?

Metcalfe's Law postulates that the value of a network increases as the square of the number of system users. This is not true 100% (after I explain why), but the truth is that this law is of great application to determine the expected growth for a business and creating value that is linked to this growth.

Consider this ...

(Whether they are online as if you are offline)

In a traditional business, a provider offers a service or sell a product to a number "n" of customers. And the number of potential transactions to be performed in a given repeat customers without time, exactly equals the number of customers you have. (See Figure 1)

The value of this business depends on the number of customers who have (of course, there are more factors that influence business value, but in a hypothetical formula for calculating the value, our "n" is one of the variables ... and it is in this article we will analyze).

In a traditional business, the number of possible transactions grows linearly. That is: +1 customer equals +1 possible transaction.

### The structure of business networking

Hay ciertos negocios, como el de una red telefónica, que no funcionan como un negocio tradicional. Todos los usuarios son oferta y demanda a la vez (emiten llamadas y reciben llamadas), así que el número de posibles transacciones es prácticamente n^2 (“n” al cuadrado) … y digo “prácticamente” porqué en realidad es n*(n-1) ya que la oferta son todos los usuarios, pero la demanda, son todos menos tú mismo… no se realizan llamadas sobre uno mismo. (En el resto del artículo, consideraremos que es n^2 para no complicar las fórmulas, pero por favor, téngase en consideración).

The first person to apply a law on this kind of behavior in a business was Robert Metcalfe (or so the legend goes), inventor of the Ethernet when Xerox invented the first laser printer in 1974 and did not know how to connect more than one computer while this printer. Metcalfe's Law It postulates that the value of a networked system grows at approximately the square of the number of users of the network itself. (See Figure 2)

Image 2: Business Network structure Metcalfe

Hence, businesses with circular structures where all users can be supply and demand at the same time, are called Metcalfe networks.

The most beautiful example of Save the Metcalfe we have it on eBay. It tends to perfection, specifically, in its C2C (consumer to consumer) aspect. Any user is a potential seller and any user is a potential buyer. Its growth is the closest to n ^ 2 that we can find on the Internet.

The webs of contacts that are proliferating so much in recent years, are also clear examples of beautiful redes de Metcalfe perfectly round. And I say round, because there are networks whose structure is not round like the one in image 2. They are networks where there is clearly one side with supply and another with demand. In that case, the number of potential transactions is still supply * demand, but it does not tend to the square since they are different numbers. Of course, they are raised to a coefficient that is greater than 1, which would be that of the traditional business; but it is less than 2, which would be a perfect Metcalfe Network.

An example of this type of network would be SoloStocks.com not perfect, where companies sell their stocks, are not all potential buyers of stocks (except if all brokers ... then yes, you see the difference?). (See Figure 3)

Figure 3: Business with varying network structure Metcalfe

If the number of potential transactions in a perfect network Metcalfe 8 users would be 8 * (8-1) = 56, the number of possible transactions in a network noncircular 8 users (4 suppose that offer and 4 demanding) it would be 4 * 4 = 16 ie the coefficient network externality that market would be 1.33 instead of 2, and therefore value generation grow at lower speeds than those of a Save the Metcalfe perfect since it offers more value to its users, but higher than those of a traditional business that offers much less.

In a market like SoloStocks it is interesting to note that the greater the imbalance between the number of bidders users and demanding users, the lower the growth of the business and therefore always have to struggle to balance the number of bidders and plaintiffs .

Veamos un ejemplo de esto: supongamos una red de 8 usuarios donde 5 son oferta y 3 son demanda, el número de potenciales transacciones sería 3*5=15 y, por lo tanto, el coeficiente de externalidad de red 1,29. Si la desequilibramos más y tenemos 6 ofertantes y 2 demandantes el número máximo de transacciones es de 12. Y así…, hasta llegar al máximo desequilibrio posible, que sería el negocio tradicional (o cualquier comercio electrónico), donde hay 1 vendedor y 7 compradores (…para seguir con una red de 8 como teníamos antes); el número de potenciales transacciones sería 1*7=7 y por lo tanto el coeficiente de externalidad de red, sería 1, que es justamente lo que comentábamos cuando hemos explicado al principio la estructura de un negocio tradicional: el número de transacciones potenciales equivale al número de clientes.

Well ... if you have not giddy with both numbers and letters, and you read on, we will pass to the next level of evolution of a network and discover finally :-) why eBay and maybe Google (judging by the rumors by the network) open source code:

### Las Redes Grupales o Group Forming Networks

When a Save the Metcalfe technology allows users to organize around common interests or goals, begin to appear small Metcalfe networks gravitating around a large network to which the feed. (See Figure 4)

4: Business structure Red Group or Group Forming Network

For some time, eBay has been creating or participating in the creation of small sites specializing in certain types of auction and, therefore, has evolved into this model of network structure reminiscent of a daisy. Opening its code, leads to an infinite number of programmers begin to develop applications that revolve around the great network and eventually forming daisy petals.

With closed source, only they can create the petals. With open source have a chilling potential of possible petals to be created.

Growth Networks group tends to this formula: a ^ n, where "a" depends on the number of possible channels that can be opened, and where "n" is the number of users.

The theoretically perfect business would be one that consiguiese that for each user of the main network, possible to create a subnet. Its structure would be something like: n ^ n (I know of none and I'm sure it's just a theoretical model ... but the less, it is interesting to keep in mind).

## Summarizing:

Traditional businessesGrow linearly as the number of clients (plaintiffs service) having: supply * 1 * suit or buyers

Businesses with network structure MetcalfeGrow almost square of the number of users who have: n * (n-1) or simplifying: n ^ 2

Businesses with Red Group structureGrow exponentially: a ^ n
Opening codes applications accelerate this growth, growing "a".

### What happens when you join several networks Metcalfe?

Business 1: m number of users

Business 2: n number of users

Sum of users 2 networks Metcalfe:
(m+n)^2=m^2+n^2+2mn –> synergy appears !!! 2mn

(... and yes ... this is the Binomial of Newton studied at school! ;-)

Growth Metcalfe two networks together is greater than the sum of both growth separately.

Is not it beautiful to see the word "synergy" represented mathematically?

3 replies

1. […] En la época del 2.0 había negocios que con solo formar parte de ellos ya se generaba valor, lo que se denominaba “las externalidades de red” (network externalities, en inglés). Eran el tipo de negocio de floreció desde 1998 hasta más o menos 2010 y que se regían por la llamada “Ley de Metcalfe” que postula que el valor de pertenecer a una comunidad incrementa al cuadrado del número de usuarios que forman parte de ella. Este es el caso de Facebook, de eBay, de todos los portales de citas, de Wallapop, y un sinfín más de negocios online. En 2004 escribí un artículo donde explicaba qué es la Ley de Metcalfe y qué es una Red de Metcalfe, si quieres leerlo lo encontrarás aquí: Qué es la Ley de Metcalfe. […]

2. […] En la época del 2.0 había negocios que con solo formar parte de ellos ya se generaba valor, lo que se denominaba “las externalidades de red” (network externalities, en inglés). Eran el tipo de negocio de floreció desde 1998 hasta más o menos 2010 y que se regían por la llamada “Ley de Metcalfe” que postula que el valor de pertenecer a una comunidad incrementa al cuadrado del número de usuarios que forman parte de ella. Este es el caso de Facebook, de eBay, de todos los portales de citas, de Wallapop, y un sinfín más de negocios online. En 2004 escribí un artículo donde explicaba qué es la Ley de Metcalfe y qué es una Red de Metcalfe, si quieres leerlo lo encontrarás aquí: Qué es la Ley de Metcalfe. […]

3. [...] By the way, if you want to know why companies open their source code, and create the APIs that third parties connecten seek their services, you are interested in this article What is a Network Metcalfe? [...]

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