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Some very interesting debate recently about Metcalfe’s Law, network effects and its application to Web 2.0 communities. I picked up the trail at Silicon Beat here which led me to a post by Metcalfe himself here, and some clever comments in an earlier post by Fred Stutzman here.

Metcalfe’s Law states that the value of a network grows as the square of its number of users. This graph shows what he means.

Metcalfe was working in telecommunications, so he’s thinking about phones and computers connected together. What this means is that when you have a new network and you don’t have enough members, its worth is lower than its cost. You need to reach a certain number of users before it becomes either useful or profitable.

Think about when mobile camera phones were first introduced. If you didn’t have friends who also had camera phones, then they weren’t very useful. That wasn’t good news for the operators either. They had to subsidise the phones till such a point that lots of people had them. So to begin with, more users increased the loss for the operators, because they were paying more money on subsidies than they were gaining on messaging charges. Only when they had sold a few million did they become profitable, as people started to send picture messages to each other on a regular basis. At that point, the operators could also drop the subsidies, as users began to demand a camera phone.

The same things would be true for other new communication devices. Owning the only fax machine in the world would be utterly worthless. When they become an interconnected network of millions of such machines, then they are invaluable. Or they were, until email came along.

When the number of people on the network reaches its critical mass then the law says the value of that network increases far faster than its costs. We don’t need to take this too literally. Metcalfe himself says that, “Metcalfe’s Law is a vision thing. It is applicable mostly to smaller networks approaching ‘critical mass.’ And it is undone numerically by the difficulty in quantifying concepts like ‘connected’ and ‘value.’”

In the era of Web 2.0, a large part of which is about networks of some kind, and the power of network effects, it’s interesting to try to apply this to some of the key players.

For digg, more people in the network adds value for users. If there were only a dozen people on digg, then it wouldn’t be much of news hub. Each additional user adds a lot of value up until the point that there is more interesting news than you can read. The extra users will find and submit more stories from more far-flung corners of the internet. Plus larger numbers of people voting means that the promoted stories that get to the front page will be more representative of what the larger population finds relevant and interesting. Of course, whether that’s a good thing or not, depends on how much you, the individual user, are similar to the average digger. The average digger will change over time as people join and leave the network.

For the owners of digg, though, the value of more users comes from what they contribute via ad clicks. I see no reason why a site’s Click-Through Ratio would change at all, no matter how many users it had. The same thing goes for any other ad-supported site, unless there were a mechanism to target ads more precisely depending on the individual user’s profile. (Why do you think the search engines want to push ‘personalised search? To be able to better target their advertising.)

On flickr, the value of more users depends entirely on how you use it. If you use it to share photos with your friends, then all you really care about is that your friends are able to connect to the site. It doesn’t matter at all if there are 20 users or 20 million. On the other hand, if you’re using it to find photos on a particular topic or to look at pictures, then the more the merrier.

With MySpace and other social networks, again more is better. Ideally, you’d like to connect with all your friends. If they aren’t on MySpace, then that’s a pain, if you’re using it as your main communication tool. That’s why the bigger networks continue to get bigger and the smaller ones fade away, unless they’re for a niche audience. Once your friends are on, then the value of the network is enormous. If you’re seeking new friends with similar interests to you, then the chances of doing that are far higher if there are many users. The network effect multiplier - the extent to which extra users add value - depends on how you use it. If you only want to talk to your existing social group, then the other 99,999,990 users are an irrelevance.

Lastly, Google Calendar. Again, it depends entirely how you use it. If you go in for sharing calendars with family, friends and colleagues then, like a social network, it adds value when all those people are also users. If you use it as a personal diary, then it doesn’t matter at all.

So the law applies to Web 2.0 when each new user does have the capability of adding value for the existing users. And that is during the period prior to that site or service’s critical mass. For the individual user, the critical mass might actually be very small - their school friends, for example. For other networks and uses, then the number could be much larger - flickr had to get thousands of users before it became a good place to search for pictures, for example. Once the critical mass is achieved, then the additional value offered by more users may well not be so great as it was before that point is reached.

For site owners whose model is advertising, there’s no real difference from Web 1.0. The value of more connected users is directly proportional, rather than exponential, because the Click-Through Ratio won’t change. However, the ability to sell more lucrative, brand advertising instead of Google Ads will only come after the number of users has reached critical mass. There’s a step-change in value at that point which owners hope will lead them into profitability.