### Everything I Knew About Metcalfe's Law Turns Out To Be Wrong

In the recent Release 2.0, which covers the next generation of CRM, I invoke Metcalfe's Law, which I've always understood to state that "the value of a telecommunications network is proportional to the square of the number of users on the system."

Well, maybe not. Release 2.0 subscriber Simeon Simeonov, a partner at Polaris Venture Partners, sent me a kind letter about the issue, but he says I got Metcalfe's Law wrong.

I also heard, and repeated, Metcalfe’s Law this way many times until I learned that the statement of the law had nothing to do with users. It’s not even about nodes per se. The original formulation was more subtle and had to do with the nature of the exchange between devices. Bob Metcalfe is one of my partners at Polaris so I got the straight scoop a few years ago, including seeing the copy of the original transparency that Bob used when he talked about what George Gilder later on called Metcalfe’s Law. Another thing that very few people know is that Bob was talking about very small network sizes--nothing like the size of the Net. I blogged about this in 2006. It would be really cool if you can use the platform you have to help set the record straight.

Consider it done.

tags: news from the past, release 2.0
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fwiw, Metcalfe's law only works mathematically for point-to-point networks -- eg, telephones, and pre-conference-calling at that -- not many-to-many networks like the Internet. So I've kind of never got why it's used so much when talking about the Net.

Briefly, here's why...

For a network where any single node can talk to any other single node, it's pretty clear that the number of possible connections for a network of n nodes is n times n or n squared. Metcalfe's law, as commonly used.

But the Internet and its ilk allow communication between all possible subsets of nodes. Without going through the derivation -- it's pretty easy, and you can find it on the Net -- the number of subsets of a set with n members (or a network with n nodes) is 2 raised to the power of n. Note that this is larger than n squared for n greater than 4.

Time for a new law?

Metcalfe's Law always seemed like a wannabe; Moore's Law Envy. What after all does it mean to say the power of the network? It's a metaphor, or maybe an analogy, and therefore provably wrong if you try to make it a law. What I think Metcalfe is trying to say is that one dimensional network is trivial. Once you get to two dimensions, small or large, all of a sudden you have (the possibility of) something that coheres, that is, a network. A physicist might say, simply, you can't have a phase dimension in one dimension.

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Rachel Happe [03.02.08 03:24 PM]

I'm so glad to see this commentary. I've started to think a lot about selection, context, and relevancy and how they impact the value of a social network. I believe that at a certain point there is decreasing value of adding additional nodes to social networks - depending on their goals. For example, when I am a teenager and my mother can find me on Facebook it is no longer quite as cool as it once was. If LinkedIn was full of school children that would also not be useful. Interesting line of thinking - thanks for exposing.