“The value of a social network is defined not only by who’s on it, but by who’s excluded.”

This quote is from futurist Paul Saffo in an Economist article that makes a contrarian case for Facebook, in part by arguing that as social networks grow, they will eventually encounter the inverse of Metcalfe’s law, becoming LESS valuable with each new user rather than more valuable.

This analogy to address books points to an important limitation for social networks, such as Facebook, compared with older sorts of network, such as the postal or telephone systems. These benefit from Metcalfe’s Law, which says that the value of a network is proportional to the square of the number of its users. In other words, the more people have phones, the more useful they become. This “network effect” leads to rapid adoption and puts up barriers for new entrants.

But unlike other networks, social networks lose value once they go beyond a certain size. “The value of a social network is defined not only by who’s on it, but by who’s excluded,” says Paul Saffo, a Silicon Valley forecaster. Despite their name, therefore, they do not benefit from the network effect. Already, social networks such as “aSmallWorld”, an exclusive site for the rich and famous, are proliferating. Such networks recognise that people want to hobnob with a chosen few, not to be spammed by random friend-requests.

This suggests that the future of social networking will not be one big social graph but instead myriad small communities on the internet to replicate the millions that exist offline. No single company, therefore, can capture the social graph.

On the one hand, you could argue that once all of your friends — or all of your professional colleagues — are on Facebook, it achieves a kind of perfect value, and that it doesn’t matter whether the network is overrun by hoards of irrelevant people. You don’t have to be “friends” with them.

But even if only your friends can see your full profile, anyone can see your “listing” on Facebook and request to be your friend. So what, you might say, just ignore or decline people you don’t want to be friends with.

Well, sure, just like you could hang up on all those telemarketers who used to call during dinner time, before the Do Not Call list, when we discovered that everyone having a telephone actually reaches a point of diminishing returns, i.e. an inverse of Metcalfe’s law.

I still find a great deal of cognitive dissonance around the idea the one social network can serve the needs of EVERY group — shouldn’t the web as platform lead to MORE customization and more verticalization, simply because it’s cheap and easy to tailor applications to individual users’ needs?

Let’s not forget why Facebook is called “Facebook” — because it was designed to serve the needs of a defined group of users, i.e. college students. Facebook has only been successful in opening up beyond that original defined user base because it had a much better design than MySpace (i.e. didn’t suck) and because so many people over 30 wish they were back in college again.

The web has until now been about the pendulum swing from a world of monopoly distribution, local applications, hierarchy, and static information at one extreme, to a world of completely open, dynamic networks at the other extreme. There’s no question that this is the Age of the Network — the open question (pun intended) is whether the greatest value is derived from fully open networks or whether the pendulum swings back towards the center, with the greatest value derived from DEFINED networks, i.e. both delimited and dynamic (two qualities which are not in fact at odds).

Looking at the most successful web companies suggests that defined networks are the key. What is Google PageRank but a way to put boundaries around the network, to define some nodes as more powerful, more influential than others? Facebook, as already cited, was driven by the .edu limitation. YouTube didn’t become huge as a mass medium for online video, where everyone watched the same thing — it grew because it was a platform for easily sharing video content among defined groups, i.e. email it to friends, share it with friends on MySpace.

Perhaps what’s most counterintuitive about the web is that the network is liberating only to a point — the value of the network needs to be harnessed. A purely open, unbounded free-for-all is chaos.

Right now, Facebook feels like a free-for-all — there’s huge value in so many people I know professionally and personally being on Facebook, but the value is diminished because when I logged in everything is all mashed together. Doc Searls posted about the diminishing returns of Facebook, as he’s been overrun by non-value-creating requests from the network.

Facebook is introducing a feature that will enable users to segment that chaos into more clearly defined, higher value segments, e.g. my personal friends, my professional colleagues.

Facebook may yet succeed in being the one network for all interactions among people on the web — but that ambition might also bump up against the inverse of Metcafe’s law, and against what we may discover is the natural grain of the web.