The Maths of Group Forming Networks

April 29th, 2006

In his article Weapon of Math Destruction David P. Reed says

Conventional wisdom is that a remarkably powerful effect known as Metcalfe’s Law is driving the growth of the Internet. The law says that the value of a network grows in proportion to the square of the number of users, which means that, once a network achieves a certain size, it becomes almost irresistibly attractive. But Metcalfe’s Law actually understates the potential value of the Internet, and by a huge margin

Reed Explains in more depth

It helps to first understand the two laws of networks that have been around for some time. First is what might be called Sarnoff’s Law , after the pioneer of the broadcast industry. This law says that the value of a network grows in proportion to the number of viewers.
Second is the law named after Metcalfe’s Law , the inventor of the Ethernet computer-networking technology. He reasoned that 1,000 people on a network can have roughly one million different conversations, so he said the value of a network grows in proportion to the square of the number of users. The n? value explains the growth behavior of networks, such as phone systems or electronic-mail systems, that are mainly used for one-on-one communication. The n? effect says that, given the choice of joining a large existing network with many users or an incompatible new one with few users, new users will almost always decide that the bigger one is far more valuable. The result is often explosive, accelerating growth once a network establishes dominance. This behavior explains why there is now one global e-mail system, while just a few years ago there were thousands.

Reed sums up the challenges for businesses who are still acting/thinking in a linear fashion in a non-linear world, super-distrubured world.

As the scale increases, what’s important also shifts. When Sarnoff’s Law dominates, content such as TV programs is king. When Metcalfe’s Law kicks in, transactions are king. When the Group-Forming Law takes hold, communities are king.

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