How does network value scale with network size? Is the number of members of the network the right parameter to look at? Or can we measure something else more indicative of network value?

Look at some of the value scaling ideas currently in play:

• Sarnoff’s scaling law says a network has value in proportion to the number of users, n.
• Metcalfe’ scaling law says a network has value in proportion to the number of possible connections between pairs of possible endpoints, n(n-1)/2.
• Reed’s scaling law</a> says a network has value in proportion to the number of possible non-trivial groups that can be formed by network members, 2^n-n-1.

These scaling laws are covered nicely in the wikipedia entries at Metcalf and Reed. There have been a number of criticisms (see Tom Evslin among many others) of these scaling laws. Many based on very common sense, e.g., the value of a very large network doesn’t double every time a new user joins, as Reed would predict.

Among the more recent scholarly looks at the issues, Odlyzko and Tilly provide a good overview of the question and propose another scaling law, this time network value scales faster than Sarnoff, but slower than Metcalf, at nlog(n). One of their key points is that not every connection in a network has the same value, and that dealing with this when deriving a scaling law is not so simple.

Also, this article is valuable in that it explicitly recognizes the importance and connection of a network scaling law with the economic ideas of the Long Tail and the idea of locality (see some of my previous posts).

I am not convinced that Odlyzko and Tilly have hit the right scaling law, but their hint at the synthesis of these ideas is definitely moving us in the right direction.

When I think about why I join networks and how I use and value them, I think the value of a network to an individual scales with the number of desirable groups one can afford to find and join. Maybe following this line of thinking results in a new scaling law?