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Metcalfe’s Plateau

At this point most of us in the geek contingent have heard of Metcalfe’s Law. For those that haven’t, Metcalfe describes the law named after him like this: “The network effect says that the value of that Ethernet card to the person on whose desk it sits is proportional to the number, N, of other computer users he can connect to. Now multiply this value by the number of users, and you have a value for the whole operation that is roughly proportional to N2.” Or as I explained just over a year ago, “If one person has a fax machine it’s got no value, if two people have it, it’s still got very little value. From there, however, the value really starts to grow for everyone involved and eventually it hits a ‘tipping point’ where you can’t not have one.”

It looks like this (taken from Forbes):

metcalfeslaw.gif

The reason most geeks have heard/talked about Metcalfe’s Law is because it’s become the de facto religion of Web 2.0: A technological revolution that relies on the network effects described by Metcalfe over 25 years ago. Facebook is the simplest illustration of this, after all a social network without any of your friends is hardly worth joining. Even if Joe Corporate could have gotten on the site when it was just filled with students from 11 universities it would have been pretty boring, after all in a closed system like Facebook, just browsing isn’t really an option. Looking at Facebook today, however, you find a site where it’s harder to find someone you know who’s not on it than who is (especially as someone who had heard of Facebook while they were still in college).

Putting it in context of Metcalfe’s Law, it all seems logical. The more people on the network, the greater value the network has, which only attracts more people to the network. I’ve said it before, and I’ll say it again: The number one feature of Facebook is the Facebook network. It’s not apps or news feed, it’s that every single person you know is on Facebook.

But that can be a bit of a gift and a curse. After all we’ve all spent a bit of time Facebook gardening: Pulling out the weeds, deleting random friend requests and desperately trying to avoid those stupid vampire bites. At some point, probably around the time Facebook apps launched, I realized that I was actually spending more time gardening than I was doing things I found useful/enjoyable on the site. For the occasional acquaintance I reconnected with, I was approving five friends I either didn’t care about talking to or already had other, preferred, modes of communication. Facebook became a bit of a drag.

That’s when it occurred to me that I was witnessing Metcalfe’s Plateau, a place where the value of the network no longer increases with each additional node. In fact, thanks to spam (as deemed by me), the value of the network had started to decline, I was looking for other places to spend my time online.

I’ve been noodling on this idea for a while and been trying to figure out just what to say. I don’t think it’s a particularly new problem. Anyone who’s “discovered” a new bar can attest to the initial rise, as you tell all your friends and they tell their friends, which inevitably ends with a place that’s so full of random folks that everything you loved about it is gone. In the world of email we see Metcalfe’s Plateau even more clearly: Spam. When the network hit a point large enough that you couldn’t afford not to have an email, it also hit a point where you could afford to reach massive amounts of individuals for little to no money. Thanks to spam filters, we’re able to hold back the flood waters. However, I think it’s pretty safe to say for me that new additions to the network are unlikely to provide any additional value to me, since everyone I know or likely will ever know (minus those not born yet or too young to have an email) already has an email. Therefore each new email address (node) holds a certain likelihood to be spam or at least some unrequested contact. (I am not entirely sure about what I’m saying there, it’s just a theory now. Feel free to tear it apart.)

As Jeffrey Stibel wrote in a piece called Networks Don’t Grow Forever (which inspired me to finally get these thoughts down), “Networks do not always grow more powerful with size and scale. To be sure, Metcalfe’s Law applies to networks up to a point, call it a growth phase. But let us stake our claim to a new Law: all networks eventually hit a point of diminishing returns.”

Thinking about it further, I think the distinction probably lies in who reaps the benefits of the network. In other words, the value of the Facebook network to Facebook likely does increase exponentially with each new user, as it allows them to attract even more people to the site. However, for the individual users like us, that value isn’t necessarily passed. As Clay Shirky wrote in A Group Is Its Own Worst Enemy,

You have to find a way to spare the group from scale. Scale alone kills conversations, because conversations require dense two-way conversations. In conversational contexts, Metcalfe’s law is a drag. The fact that the amount of two-way connections you have to support goes up with the square of the users means that the density of conversation falls off very fast as the system scales even a little bit. You have to have some way to let users hang onto the less is more pattern, in order to keep associated with one another.

Or, as Paul Saffo was quoted as saying in the Economist, “The value of a social network is defined not only by who’s on it, but by who’s excluded.”

As should be obvious at this point, I don’t know the answers here. Would love to hear everyone’s thoughts. I’m also exploring some of this stuff with a mathematician friend of mine because I’m curious to see whether this idea can be worked out with numbers (and goodness knows I can’t figure it out myself).

July 6, 2008

Comments

  • Greg Yardley says:

    Metcalfe’s Law is for computer networks. It doesn’t take into account that some connections have more value than others and that some connections have asymmetrical value – one party gets more out of it than the other.

    If you’ve already got your high-value connections (aka close friends) into a social network, and you’re a high-value connection to others (due to the status of a connection, or the benefits of access to you), an increase in the number of strangers is jut going to lead to the irritation you face and degrade the value of the social network.

    Personally, I’d love to see a social network that limited your number of friends to an arbitrary low number – say, ‘seventeen’. Interaction patterns would be totally different.

  • Willem-Jan says:

    Interesting post, Noah. I noticed a similar FB usage pattern myself. Also, I’ve been tempted to remove people from my LinkedIn network who tend to link to anyone and everyone, thereby effectively making the service less useful to me, as it makes my network less ‘cohesive’. This got me thinking that while the value of the network to the owner may grow exponentially with each user (assuming all users are similar/equal), the value to an individual user should probably also take the ‘importance’ of his/her connections into account: as the network grows, you’re likely to connect to people who aren’t as close to you, so the average value of your connections (and of their connections to you) drops. I’m not a mathematician either, but some back-of-the-envelope calculations seem to indicate that if the value of a network to a user is a function like (connections)squared*(average value) and this ‘average value’ decreases with an increasing number of connections, the value of your network will start dropping at some point indeed.

  • andy says:

    For me, another factor is the ratio of each additional person to the existing network. If I have 2 contacts and gain another 2 then I’ve doubled my network, which is exciting and I can immediately feel the difference. If I have 50 contacts and I gain 2, I see no change.

    Add to this the presumption that I connected with my closest friends first and you can see how the excitement fades quite quickly.

    Isn’t it ’50’ people that we (supposedly) have room in our brains to have a meaningful connection with? Perhaps your plateau occurs at a similar time to that social soup swallowing up 50 people..

  • Doc Searls says:

    Metcalfe is right about networks, while Clay and Paul are right about groups.

    I submit that groups are also different than “social networks,” a term that used to be synonymous with groups but now means two things: personally collected associations, also called “social graphs,” and online habitats such as Linkedin and Facebook. Both of the latter prove Clay’s point.

    For what it’s worth, Linkedin has no conversation density for me because I do no conversation there. It’s just a CV viewer, and it’s good enough at that. Facebook also has no conversation density for me because keeping up with it takes too much work. This might be my fault, for somehow allowing myself to have 396 “friends,” when the number of my actual friends is far lower than that — and most of them aren’t on Facebook. Add “2 friend suggestions, 187 friend requests, 2 event invitations, 1 u-netted nations invitation, 1 blog ownership request, 180 other requests” and “23 new notifications” … plus more “pokes” than I’ll bother to count, and Facebook compounds what it already is: a gridlock of obligations in an environment architected, blatantly, to drag my eyeballs across advertising, most of which is irrelevant beyond the verge of absurdity. (On my entry page is an ad for dresses by American Apparel. It replaces one for singles. I’m male and married. You’d think Facebook could at least get *that* much right.)

    The only way we can immunize ourselves from overly “scaled” services — or improve them in ways that are useful for us and not just their clueproof “business models” — is by equipping ourselves as individuals with tools by which each of us controls our ends of relationships. That means we assert rules of engagement, terms of service, preferences, additional service requests and the rest of it. This is what we are working on with ProjectVRM.

    While it’s hard to imagine a world where a free market is not “your choice of silo” or “your choice of walled garden”, imagining one is necessary if we wish to fulfill the original promise of the Net and the Web.

  • Faris says:

    Too much of any kind of signal – social or otherwise – and eventually the signal becomes noise:

    http://farisyakob.typepad.com/blog/2008/04/pvr-pressure-or.html

    FX

  • Anjali says:

    In a sense, networks can grow forever, but the value of each new added friend will diminish considerably after you reach Dunbar’s number (or a figure around that), and as you personally face social networking fatigue. The question is, after the Plateau, what? I’ve faced what you describe – too much time spent on Facebook gardening, too many not-really-relevant ‘friends’ added (your limited profile list tends to start growing at the Plateau stage, I feel), and while I do see a definite reduction in the number of friend requests, they don’t seem to stop, and as long as man is a social animal, I don’t think they will.

  • Vikram Alexei Kansara says:

    You start building your online network with your closest friends, who are of greatest value. But the added value that Facebook or other SNS bring to those relationships is small, because you already have many other ways to communicate with your closest friends. However, as you add connections, it’s likely that the people you friend are a bit more distant. Their overall value to you may be less. But the added value created by friending them online, as a percentage of their total value, increases dramatically. Where the relevance of these extended connections starts to diminish is very hard to predict and seems to be anything but uniform from individual to individual and across different social sets.

  • Giles P says:

    Interesting post. I’ve done a little work in this area and started to think about some of the same issues. Cory Doctorow talks about the inevitability of social networking going through boom and bust cycles as they are inherently unstable, especially when there is too much ‘noise’:
    “Having watched the rise and fall of SixDegrees, Friendster, and the many other proto-hominids that make up the evolutionary chain leading to Facebook, MySpace, et al, I’m inclined to think that these systems are subject to a Brook’s-law parallel: ‘Adding more users to a social network increases the probability that it will put you in an awkward social circumstance.’ … I think that’s why these services are so volatile: why we’re so willing to flee from Friendster and into MySpace’s loving arms; from MySpace to Facebook.”

  • Jim says:

    Last year I read this an IEEE article refuting/revising Metcalfe’s Law – arguing instead that the value of the network increases according to n*log(n). It doesn’t make any argument for a plateau – but it does make a seemingly compelling argument for a lower take-off angle to begin with. The article is still online if you’re interested:

    http://spectrum.ieee.org/print/4109

  • Seni Thomas says:

    I’ve always called this ‘Crossing the Gluttonous Chasm’

    Basically, to keep expanding and ‘Cross the Chasm’ seeking profits companies end up alienating the early adopter community that helped it grow and it eventually just becomes a generic space. All social apps are first adopted by a specific community then grow to try to be everything to everyone, and eventually meaning nothing to everyone.

    Similar idea, but a very significant one.

    Cheers,

    Seni

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