Calculating the Maximum Effective Size of a Social Network?

February 2nd, 2004

Dave Douglas has asked an interesting question about my article about Some Hypothetical Laws of Social Networks, which I am excerpting here because I think it is a worthwhile thread to follow-up on:

Monday, January 26, 2004

Just read Nova Spivack’s attempt at some Laws for Social Networking. If you work through his 4 laws, I think they all boil down to 2 fundamental issues: 1. For any given person there’s a number of direct links beyond which it is difficult to manage and a pain to deal with, and 2. The nature of social interactions makes it desirable to not traverse more than 3 hops to make a connection.

Combining these two, simple math suggests there’s a natural limit to the effective range of a social network. If the number of direct links a user can deal with is L, and the max number of useful hops is H, then the max effective size (E) of a network is E=L^^H (L to the H power). This doesn’t mean the network can’t contain more people, just that the max useful network for any given person is E.

Let’s look at some numbers. If H=3 as Nova argues, then if L= 50 (a bit high?), then E = 125,000. If L is really only 20, then E drops quickly to 8,000.

Anyone have an idea of L for some of the existing networks?