Jason Steinhorn sent me a link to this fairly interesting blog post on the growth dynamics of social networking sites.

The mathematics of Web 2.0: Why don’t ALL social networking sites experience phenomenal growth?

The article looks at two interesting questions:

1. Do social networking sites show N^2 growth (ala Metcalfe’s Law), or do they show 2^N growth (exponential)
2. Why do some social networking sites show far more rapid growth than others.

I need to think about this a bit more.  My initial reaction was no, these sites are showing N^2 growth (which is huge), and the author is getting confused about the fact that trees don’t grow to the sky, and not all sites are going to fulfill their algorithmic destiny.

However, on further consideration, the growth of groups is really the key.  Since groups can continue to form, and can “repeat” membership fairly aggressively, you might be seeing more of a combinatorics equation, like the one in his article.   A study of the growth of groups might be the real key here – I’m not sure these sites really support full combinatorics, which is what you’d need to see 2^N behavior.

If you are wondering why this matters, let’s try a mathematical explanation.  These equations define the “growth characteristics” of certain types of models.

N^2 (N Squared) tends to get you numbers like:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Pretty good.  1 to 100 in just 10 steps.

2^N (2 to the N) tends to get you numbers like:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024

1024 in just 10 steps.  Much more powerful growth, and the difference gets more and more staggering as the model grows.

This is why, by the way, compound interest is your friend.  Exponential growth is your savings doubling regularly, over some period of time.

Of course, this article has me thinking… Metcalfe’s Law is about computer networks.  But why wouldn’t computer networks actually show exponential growth?  After all, I can belong to multiple networks – my ISP’s network, my home LAN, my workplace LAN (VPN)… is there some element of this growth in the networking business as well?  Is that why wireless networking has been so powerful?  The overlay of these “networking groups”?

There’s something interesting here… but it’s just too late tonight for me to figure it out…