What If Metcalfe’s Law Is Wrong?

Networks — be they telecom, social, transportation or otherwise — are the fabric of modern society. They provide immense value to consumers and businesses alike, enhancing mutual relationships and enabling the distribution of goods, services and information. But does this value grow as the size of the networks grow? And if so, how much?

Metcalfe’s Law” has long been accepted as characterizing the value — and value growth — of fully connected networks. It states that the value of a network is proportional to the square of the number of its nodes, which may take the form of devices — such as computers — or users, in which case a network connection is represented by a “friend” or “follower.” But there are times when the “law,” which has been used to explain network effects and justify mergers and acquisitions, appears to overstate a network’s value. And if that’s the case, what can service providers do about it?

While the number of possible connections in a network is indeed proportional to the square of the number of nodes, value is not necessarily equivalent to number. After all, I may have 10 bills in my wallet, but it matters a lot whether they are $1 or $10,000 denominations.

As I’ve previously observed (at Telecosm and via some math (PDF)), there are several reasons that Metcalfe’s Law can overestimate the value of a network. First, typically only a fraction of the possible connections have value. Second, there are natural limits to consumption of that value. And third, the value of the entire network may decline over time.

Convergent Value Distributions

The number of links in a fully connected network is certainly proportional to the square of the number of nodes. If each connection had the same value as any other, then Metcalfe’s Law would be correct. What would that mean in practice? It would mean that you would spend equal time on the phone with each of the nearly 7 billion people in the world, that they would all friend you or follow you, and you would reciprocate. But humans don’t behave that way.

In 1992, anthropologist Robin Dunbar posited that primates have neurobiologically-based limits to the size of their social networks. For humans, “Dunbar’s Number” is 150. This is exemplified by the fact that the most popular social networking site on the planet now has more than 400 million users, yet the average number of “friends” a person has is only 130 and only a small percentage of those “friends” actually communicate with one another. And although there are a variety of ways to slice the data, the largest microblogging site has close to 100 million users but the average number of followers is roughly 126. Even if we were to assume that tweets have the same “value” as intimate face-to-face interactions and that electronic media might expand Dunbar’s number in some way, there is still an upper bound to the number of relationships, or even weak ties, that can be maintained. If the total value of such social media is related to engagement, and engagement is related to the number of friends, such value would in these cases be linearly proportional to the size of the network, rather than the square of its size.

Intrinsic Limits of Consumption

Suppose you did have equal social interest in the nearly 7 billion people on the planet, or the more than 100 million shared video clips or even the more than 100,000 touchscreen phone apps out there. You then would run into intrinsic limits to your ability to benefit from all those relationships or consume all that content. Perhaps in the early days of TV it would have been possible for a single individual to consume all the content produced. Currently, however, nearly a day’s worth of content is uploaded to YouTube every minute. Assuming that all those clips did have equal value, even a multitasking insomniac couldn’t keep up. All networks have intrinsic upper limits of consumption, be they bandwidth or dollars or time or attention span.

Holistic Network Value Declines

Even if all nodes were of equal value, and there were no limits to consumption, well, people get jaded. Emotional rewards from novel stimuli are processed by dopamine receptors in the striatum, but the brain is designed to habituate, that is, not get so excited by repeated stimuli. What this means is that an entire social or content network may “grab” you at first, or even for a couple of years, but this infatuation may eventually wear off, and you’ll depart in search of the next new thing. Technological progress can also cause the value of the entire network to decay — consider what the web and email have done to the value of fax networks.

Strategies

There are ways to manage these three effects, however.

If the network node values follow a convergent distribution, ensure that whatever value is present can be extracted by reducing or eliminating core bottlenecks and enhancing the process of discovery. Specific approaches such as scalable non-blocking network infrastructure, content delivery networks, tagging, recommendation and search engines can help.

To extract maximum value when there are intrinsic limits of consumption, not only is removing access bottlenecks effective, but so are personalization, richness, context sensitivity and multitasking facilitation.

And to keep a given network exciting and the dopamine system revved up, new features, content or applications can help. Even if the core “network”— whether social site or app store — remains the same, using a platform for new content or apps can continue to trigger the pleasure receptors associated with novelty, maximizing value and engagement.

Overall, the behavior of real-world networks isn’t always as simple as what’s represented by Metcalfe’s Law. However, understanding their underlying characteristics can help users and service providers maximize their value as well as create new business opportunities.