Friday, July 31, 2009

The value of a network

Breathless reports of a speech by the new ICANN chief in which he has challenged the validity of Metcalfe's Law.

It is stupid to report it as if it is a eevelation since the "Law" has always been based on the simple calculation that the number of links between nodes on a network of n nodes is n*(n-1). From this Metcalfe opined that the value of the network grew in proportion to n squared.

Andrew Odlyzko* has pointed out back in 2006 that this is based on an assumption that each link is equally valuable. Odlyzko proposed an alternative that the network's value increases as n*logn which effectively assumes an exponentially decaying value in each extra link.

I haven't seen the actual paper referred to in the above, but it sounds like it is referring to yet another feature that is the feature of "congestion" effects. In the case of the article Bill Gates found he had so many friends on Facebook none of it was of any value. An alternative version of this was offered by Eli Noam in the introduction to Telecommunications in Europe. In that Eli explained that large corporations had benefitted greatly from network effects in telecommunications but it got to a point where congestion and other factors resulted in them having a higher utility in private not public networks.

That is, just as positive network effects could explain the growth of telecommunications networks and a justification for effectively mandated monopoly (I'd have to digress on a history of ATT), the negative effect also had a role in seeing the pressures build for deregulation and the relaxation of rules prohibitting interconnection of private and public networks.

I think there are two important lessons here. The first is that Metcalfe's Law certainly isn't a law at all and should not be referred to as such - at best it is Metcalfe's Conecture or Hypothesis. The second is that networks do not behave uniformly and are deserving of far more analysis than they receive.

* I see that Joshua Gans has even blogged about Odlyzko. I concur with him on how amazing his output has been. The paper I find most interesting was the one when he pointed out that the capacity of the Internet wasn't doubling every hundred days - just when everyone believed it did!


Anonymous said...


Regarding the revision of Metcalf's Law (or postulate, hypothesis, or guess): It's interesting to note who is working on the revision:


"Who cares how many nodes there are?" Beckstrom said. "If you look at a value of the network, focus on the transactions. The value of the network equals the net value added to each user's transactions, summed for all users."

This model, which Beckstrom developed with Google chief internet evangelist Vint Cerf, changes the way many companies should view their value, as well as helping to quantify the value of the work done by network administrators and security officers. "

Vint Cerf, of course, was the WorldCom executive credited with the sales memo about "Internet traffic doubling every 100 days", which later became an article of faith!

Richard Chirgwin said...

Oops. I didn't mean my comment to be anonymous ... I fat-thumbed the "submit" key.