Andrew Chen had a great post up a few days ago titled “Social network death spiral: How Metcalfe’s Law can work against you.” I do recommend you read the entire pose, but if you’re short on time here’s a recap:

Metcalfe’s Law
Does everyone remember Metcalfe’s Law? It was formulated by Bob Metcalfe, the inventor of Ethernet and co-founder of 3Com, who stated:

The value of a network is proportional to the square of the number of users of the system (n²).

For those that are interested in the math behind it, basically the idea is that if every new node in the network connects with every pre-existing node, then as you gain nodes, you non-linearly increase the number of connections that everyone has with everyone else.
Andrew also notes that the formula obviously works in reverse as well. If you start loosing users, you loose them just as fast as you gained them:

Eflactem’s Law
Funny enough, everyone always talks about Metcalfe’s Law like it’s a good thing, and they say that because they assume that N is increasing! But let’s consider the opposite: If Metcalfe’s Law says that your network grows value competed by N^2, then Eflactem’s Law states the reverse. It says:

As you lose users, the value of your network is decreases exponentially (doh!)

That is:

• If you have 100 users, and then grow to 200 users, your “value” has increased from 10k to 40k.
• But if you START with 200 users, and end up with 100, then you are going from 40k in value to 10k in value.

Andrew also argues that when your current amount of users reaches the carrying capacity of the user ‘universe’ - things in theory have only downhill to go. Unless… you find a way to make your network expand, or become recursive, to continue to expand the carrying capacity.

What do I mean by that? To use an example, think Facebook or MySpace vs Ning (a build your own social network place). Facebook and MySpace are reaching their carrying capacity. Most of the people who are into that sort of thing, already checked it out. There will be a time they will need to move on - to fresher things, or to sites that handle their data flow better (entire separate discussion there).

Ning on the other hand allows an unlimited amount of mini social networks to be created within it. It allows new experiences to be created by anyone, getting more local if you will. With this strategy the carrying capacity is spread out, almost as if these were tree branches that can separate and take root on their own, vs just one main tree.

I suppose sites like Last.fm also do this to a degree, by allowing the creation of Groups - as opposed to bunching everyone together as an equal user. This spreads out the carrying capacity, takes longer for people to get bored. But eventually, even this approach will hit its limit - my prediction is people will want to create their own Last.fm, just like with Ning.

This is why our strategy with Internet radio in the past has been to continue to get more channels. It increased our carrying capacity much quicker, and we were able to grow much quicker because the channels themselves reach their own mini carrying capacity pretty quickly and grow only gradually on their own (think inflation like).

But even that is the old way, the service and portal itself still reaches a limit, and so I recommend people think about launching multiple services and multiple brands - precisely for this reason. Hope it makes sense to you.