Bob Metcalfe, the father of Ethernet, proposed that; “the value of a network is proportional to the square of the number of nodes.” He had an axe to grind at the time. He was trying to accelerate the take-up of networking and his “law” is really a value proposition. Like Moore’s Law in its original statement it’s not exactly accurate, but it’s not exactly wrong either.

Metcalfe’s Law is a derivative of a simple result in Graph Theory (a branch of Mathematics), which states that the number of lines that can be drawn between n points is n(n-1)/2 (in other words, it’s proportional to n squared). So, for example, this is the number of different 2-way conversations that can take place in a telephone network. With 10 telephones, 45 different conversations are possible. With 100 telephones, 4950 different conversations are possible. See how the value escallates.

Metcalfe’s Law can be viewed as the driver for many of the social networks that have emerged recently and also for many successful Internet businesses. A prime example is eBay. Before the Internet, auctions were constrained to the number of people you could get into a room. The Internet virtualized the room, and suddenly thousands or even tens of thousands of people could attend the same auction. And that meant that many items that could not previously have been auctioned suddenly could be.

While the Internet made on-line auctions possible, we should not forget the fact that the low transaction cost was also a factor in this. If the cost had been high the “network magic” would still have worked, but the growth of on-line auctions would have been slower.

The problem with Metcalfe’s Law is that you do not actually communicate with every device in a network. For example, there are hundreds of millions of email addresses, if you take the Internet as a whole, but you do not and cannot send email to them all. You send email to just a few thousand at the most. Even with automation, very few companies will send out to millions of email addresses. So, Metcalfe’s “rule of thumb” can be a vast overstatement of value.

There are other “laws” that value networks:

Sarnoff’s Law

This states that “the value of the network is proportional to n, the number of devices” or in most instances, users. Sarnoff’s Law regards the network as a broadcast medium with few transmitters and many receivers (that is, only a scant few among the n members of the network are transmitters; the vast majority are receivers). Here the network represents the linear value of services targeted toward individual devices.

This is reasonably accurate for broadcast networks, like the television network or a radio network. However, it is also an absolute value. With major international or sporting events the actual number of receivers may get close to n but in most instances it is only a fraction of n. This “law” takes no account of interaction and only deals with broadcast.

Also, there is Reed’s Law:

Reed’s Law

According to Reed, “the value of the network is proportional to 2n.” Reed’s Law regards the network as a grouping medium in which as many as 2n - n - 1 nontrivial interest groups may coalesce. From this perspective, the network represents the exponential value of group affiliations.

This takes account of the fact that many interest groups may arise within a single network, each creating some value to the participants. In the Internet we have, for example, game players, auction fans, email users, researchers and so on - and some users may do all of these things. However, when you start to count significant groups, although the number gets quite large, it gets nowhere near 2n.

Stated in this way, these “laws” will probably bewilder anyone who is not mathematically inclined. However, collectively they point out something quite interesting:

Networks have values in three ways:

  • Because they create communication connections (Metcalfe’s law)
  • Because they are a broadcast medium (Sarnoff’s law)
  • Because they enable interactive interest groups (Reed’s Law)

Companies might want to examine how much of these three aspects of network value they enable.

Note: This is a key IT Trends posting that I will probably refer back to, to discuss various business events as they occur in the IT market. A list of such postings can be found here: