Saturday, 19 January 2008


Metcalfe's Law was originally used to describe how the value of a telecommunications network increased in value exponentially with the number of connections to that network, by n squared. On Wikipedia, they illustrate the idea by talking about the fax: "a single fax machine is useless, but the value of every fax machine increases with the total number of fax machines in the network, because the total number of people with whom each user may send and receive documents increases." Below you'll find Metcalfe's original graph from 1980 used to convince early Ethernet adopters to try networks large enough to exhibit network effects – networks larger than some “critical mass.” This is Hollywood Economics, where the most successful are disproportionally rewarded compared to their competitors.

In addition to being able to calculate the value of the network we can also calculate the possible number of connections mathematically as n * (n − 1) / 2. Readers of previous postings on the Clustering Coefficient will know that this mathematical expression forms part of the formula for calculating the Clustering Coefficient, which is a measure for describing how interconnected a network is. The more interconnected, the higher the coefficient.

Is it fair, therefore, to use Metcalfe's Law to value social networks? I think Facebook would like this, which explains its reluctance to open up to data portability, and hold us in its walled garden. But who owns your Facebook social graph or your social graph on any other site? There is a raging debate on right now about the data now contained in Facebook, and other social media. Facebook believe they own your social graph, but other social networks are starting to allow portability and integration with initiatives such as Open Social. But the stakes are high if Facebook is to monetize it's huge user base, and its sky high valuation.

Compare, an invitation only social network for the rich and fabulous, which is small but very interconnected to Facebook which is large and dispersed. What if you could value and sell access to your own social graph on either of these sites? How would you value it? One option is per user and thus Metcalfe's Law would be a good model for valuation. But many don't agree with its application to human networks.

The Washington Post recently reported ASmallWorld, "has 300,000 select members who have become a magnet for companies that make luxury goods and are trying to reach people who can afford them. The site’s biggest advertisers include Burberry, Cartier and Land Rover. Cognac maker Remy Martin last month threw a tasting party for the site’s elite members, at which its top-shelf, $1,800-a-bottle liquor flowed freely."

In addition to their individual wealth, the invitation only basis, and its wealthy homogeneity make ASmallWorld more interconnected and thus easier for messages to travel freely. It would consequently have a higher Clustering Coefficient than Facebook, and might argue its niche, focused, and interconnected audience, as measured by Clustering Coefficient was more valuable. So as an advertiser there is a greater likelihood your message could go viral, or at least benefit from advocacy, as like minded people recommend your brand to their like minded social graph. Which is the best measure? Perhaps neither, the jury is still out!