Despite what you have heard about the new economy, networks don’t grow forever. This is true of the Internet and it is true of the brain. Your brain is nothing more than a network of neurons, and it has been shrinking for most of your life. And what about the Internet? Think bigger is better? Think all networks grow? Think again.

The Internet bubble was fueled by one thought: as networks such as the Internet grow bigger, they grow more powerful. This is what is known as Metcalfe’s Law, named after the inventor of Ethernet and founder of 3Com. In Metcalfe’s own words: “bigger networks are better.”

This simple statement not only supported the idea of the “New Economy,” but pumped air into the Internet bubble. And then, of course, the bubble burst and billions in market cap were washed away.

But now the Internet is alive again and growing, and if it isn’t Pets.com or Kozmo.com that are the Internet darlings, it is MySpace, Facebook and the other social networks. The question today is: Now that Metcalfe’s Law is on the loose again, is it valid?

The answer is yes, but only to a point. 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.

Nowhere is this more evident than in the brain. When we are conceived, the brain begins a nine-month race to produce neurons, a pace that equals about 250,000 neurons per minute. The brain continues to grow after birth, but following the first few months, something extraordinary occurs: The brain hits the edge of the envelope. It slows. Why? Perhaps nature, in balancing out all our parts, realized that if we couldn’t hold up our heads well enough to run, the additional smarts weren’t going to get us very far.

Then something even stranger happens. Just as we enter our twenties, when we would think that the brain would really kick in, it stops growing. By the age of twenty, the growth of the brain actually reverses. From then on until the end of our lives, we lose about one gram of brain weight every year. And we wind up with some 100 trillion neural connections, compared to the 10 quadrillion of a three year old.

Will the Internet behave any differently? The Internet is in the early stages of development, call it a baby brain. Websites are proliferating; users are coming online in droves. But eventually the Internet will mature, stop growing and may even shrink.

And this is true of all networks: ant colonies, highways, beehives, brains, the Internet and yes, social networks. All networks grow according to Metcalfe’s Law until they hit a point of critical mass…and then they stop growing because the value equation changes.

So what will become of the social networks? Well, we have already seen the fate of Friendster, it imploded. And the company we owned at United Online—Classmates.com—its growth has slowed. As for MySpace, I suspect that it is nearing its point of critical mass. These sites in many cases are seeing lower value because of their size: unwanted user connections (just watch To Catch a Predator on Dateline NBC), untenable navigation (try searching for John Smith on MySpace), and large numbers of inactive profiles. Facebook today is a different story. Its growth has yet to be tempered but it too is likely to hit a point of diminishing value.

But none of this is necessarily bad. Like the brain, a social network at critical mass enables higher level functioning: better communication, interaction and even consciousness. We can even see a “collective consciousness” emerging among some of the stronger social networks. So social networks should temper their growth to allow richer connections. The real power of a network does not lie in its growth, but in its stability: when the network reaches a point where higher level functioning can develop.