Category Archives: Metcalfe

The inevitable disutility of networks (or why Facebook will fade)

It’s hard to believe, but the day will come when you stop using Facebook. Here’s why.

So imagine you’re on the phone with your boss and beeep a new call comes in from your spicy Argentinian lover who’s in town and then beeeeep yet another call arrives from your Aunt Mildred who used to nag you about flossing your teeth and you have to decide — quick! — whether to keep talking to your boss, or find an excuse to pick up your lover’s voice, or get reacquainted with Auntie.

And you get it. Like those calls, not all network connections are created equal. The inequality of network links is the basic flaw in Metcalfe’s law, a hypothesis by the founder of 3Com and inventor of the ethernet that as networks grow, they rise exponentially in value. Metcalfe’s math, you see, showed that the connections inside networks grow more rapidly than the number of users do — two phones make one connection, but five phones make 10 links, and 12 phones make 66. Because every additional node, or user, links to all the users before her, each addition creates waves of new linkages — and if value comes from links, then networks must scale in value. Metcalfe’s law was famously behind much of the hyperbole of Internet Bubble 1.0 in the 1990s, pushing sky-high valuations for any networked business regardless of whether it was profitable.

Humpty Dumpty sits on the wall
Of course, March 13, 2000 was not kind to pet food companies heavy in e-commerce. After the Nasdaq crash, economists pointed out that Metcalfe’s law has several gaping flaws; for instance, if larger networks are always exponentially more valuable, any firm in the world with a network of users should immediately merge with a similar business. Why would Facebook and Twitter compete, if by joining their numbers 2x they make 200x more value? In 2006 Bob Briscoe, Andrew Odlyzko and Benjamin Tilly pointed out the most famous flaw of all … if we follow Metcalfe’s law to its logical exponential-value conclusion, eventually the addition of one final user would equal all the wealth on the planet, an impossible outcome.

Briscoe and team, pondering why networks may have less value than supposed, pointed to linguist George Kingsley Zipf, who created, yes, Zipf’s law. Zipf noticed that words in the English language are used in descending order of magnitude, with “the,” the most popular expression, making up about 7% of all word uses, followed by “of” with 3.5%, “and” at 2.8%, with all other words trailing in a slow fall-off. Zipf’s law resembles the Pareto Principle that states in any collection a few resources hold the most value, and Chris Anderson spun off of Zipf’s concept with his “long tail” discussion of Internet commerce’s ability to meet diminishing niche consumer needs. Zipf’s finding means that not all network connections have the same value; your boss, lover, and aunt all are connected to you, but like the English words you use daily, you value each connection in different ways.

Humpty Dumpty took a great fall

So if networks have less value than supposed when they grow — when, conversely, does network value fade? Every network, as old as the roads of the Roman Empire, eventually falls into disrepair, replaced by something else. This disutility happens before users bail; at some point, there is a sense that the thing which made a network hot has faded, building an impetus to flee. See: AOL, Friendster, Myspace, Second Life.

Intuitively this makes sense: you can feel the itch today with your land-line telephone and the postal service, the desire to give up on these once-useful services. Other networks you still use are growing painful, too; email is cresting, a slow slog every morning over coffee, and one might suggest Twitter with its elegant 140-character tweets is a new email with less commitment. Facebook and Twitter are growing cumbersome too, one filled with silly games and the other adding complexity to its once elegant system; hipsters are moving past both to Instagram, an app that requires sharing only photographs. (Don’t think the brains behind Facebook and Twitter aren’t worried about such risks; this explains the near-constant innovation and entanglement strategies, such as Like buttons, being spread by both to stave off your boredom.)

Networks have more than a utility based on connections; they also have a shelf life. Our fundamental insight is all those connections can grow or diminish in value at once — based on the context of the network vs. its competitors. Yes, networks rise in value and build gravity to draw masses to their center. But like a planet teeming with life that begins to pollute its own atmosphere, eventually all users long for a fresh start.

Ben Kunz is vice president of strategic planning at Mediassociates, an advertising media planning and buying agency, and co-founder of its digital trading desk eEffective.

Image: Neal Fowler

Metcalfe gets a haircut

Brian Morrissey threw out a line in a podcast last night that everyone today is getting a haircut. We were debating union pay issues with him, but it occurred to us later that even Robert Metcalfe is getting a trim.

You see, Metcalfe was wrong. Metcalfe’s law — the idea that networks grow exponentially in value as more users join them — drew the curve too high. The reason, at least for humans, is that people don’t act the same as fax machines; not every link has the same value, we have a limit to the number of relationships we can maintain, and so our networks tend to fragment into subpopulations.

Networks don’t grow wildly in value if the links inside break and fall apart.

Which is why the recent trend of social media tools like Facebook and Twitter being sliced up is so interesting. Tweetdeck is a free software/mobile app that now accounts for nearly 10% of Twitter traffic, and it allows users to create groups of people they want to watch closely within Twitter. Web sites such as ExecTweets or’s new feed into Twitter are creating silos within the human networks, easier to access, depending on your interest or mode or point of entry.

All of which points out social media is fragmenting even as it connects us, limited the total utility of the network. Step back and count the sheer number of systems you now use to communicate. Email. Gmail. Hotmail. Facebook. Twitter. Desk phone. Home phone. Cell phone. Fax. Physical mail. Voicemail. LinkedIn. Blogs and their comment threads. Do you really plug in seamlessly to each, reaching all possible connections? (Ha. If you do, please come help us with our In box!) Each system is a network with potentially unlimited contacts and ways to tweak it, but to function we filter out insanity by limiting access in each.

Advertisers who still believe social networks equal wild potential, where a message can scale to the masses, aren’t paying attention and perhaps should wise up. Networks are largely illusions. We all aren’t connected, because if we want to listen to a few, we have to find new ways to shut some others out.

This isn’t to suggest your marketing message can’t scale. Just beware of the limits within new networks — humans tend to cluster, and each subgroup is a disconnect that can turn your message off.

Evan Williams slices up the Twitter network

Twitter CEO Evan Williams hints at coming changes in the microblogging service. Foremost is helping users segment the hundreds (or thousands) of people they follow. It’s difficult, Williams notes, to share thoughts with the world when your spouse and family and workmates and drinking pals all read the same thing.

So Twitter plans to help you slice up your online social network into bits.

Williams calls this the “collapsing domain” problem affecting many social networks, meaning that on face value the link structure may appear huge — but in reality it consists of little microbubbles of communications. We wrote in BusinessWeek this year that Twitter is not a vast communications network of 2.3 million users squared. Rather, it consists of small pools of people with gaps and limits on how they interact. This is important to marketers and investors, because it puts big brakes on how internal communications could propagate inside any social media network.

Metcalfe’s Law might work for telephones and fax machines, but in human networks, the value of links is not exponential. Or as marketers often complain in ad planning meetings, if making a message go viral were easy, everyone would be doing it.

Metcalfe, say it ain’t so

This just in. BT researcher Bob Briscoe, math prof Andrew Odlyzko and programmer guy Benjamin Tilly say Metcalfe’s law is wrong. You know: the basic idea that the more people use something, the more exponentially valuable it becomes. One plane going to one place isn’t worth much; but knowing that plane can connect you to almost anywhere in the world is worth a lot. Robert Metcalfe, inventor of the Ethernet, dreamed it up and social media hyperbolists now tout it as gospel.

The value of a network is proportional to the square of the number of its users.

But Briscoe, Odlyzko and Tilly suggest that different types of networks have differing increases in value. Networks that can form groups — email lists, or Twitter, or MySpace — can explode in value as more join. Others, such as a network of users signing up for a cable system, grow more linearly.

To put this in plain English, if networks really did jump in value at an accelerated rate for every person or node you add, eventually adding one additional person to, say, Facebook would add value equal to the entire global economy. Briscoe and team note common sense tells you that can’t possible be true. Or, in a business sense, if adding to a network increased value exponentially, then every communication group in the world should merge with another one — since the combined larger network would be valued infinitely more than the two standing alone.

Look, if this gives you a headache, we’re sorry. Just assume the following: Not all social media bubbles rise forever, and not all 2n joined systems are worth (2n)2 or 4n2. Microsoft and Yahoo, are you listening?

(Illustration by Serge Bloch. Inspiration via Fake Steve.)