Calculating the Maximum Effective Size of a Social Network?

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?

Comments

[David Douglas]

Nova, Sorry, I mixed up our variables. Yes, I meant H. To re-summarize my hypothesis:

1. If I'm in a point-to-point (H=1) network every message I receive is intended for me personally, so is presumed to have some positive value.

2. If I'm in a network with H>1, I get two new kinds of message: 1) messages directed at me but not from my "inner circle" (i.e. directly connected) contacts. It is probably safe to assume that these are, on average, of lower value than "inner circle" messages. 2) messages which are passing through me to others. These have no value and are only a cost if I have to interact with them at all.

3. My hypothesis is that in an environment with H>1, I will naturally set a lower limit for how many people I maintain a direct connection, since each one also brings associated costs, and people who might have been marginal choices before are now not worth linking directly to.

(I think there's an analogy to in-laws here somewhere, but it's probably not worth going there...)

[Nova Spivack]

David, in your example below you use the variable "N" -- just to be clear, what does N stand for? We have been using H for "average number of hops" -- I think you mean N=H but not sure. Can you clarify?

Nova

[David Douglas]

Patrick Barry (above?) says that L = 150 to 200 is probably more accurate. However, this is assuming direct interactions (N=1, as in AOL IM). Massive antecdotal evidence suggests that this number may be lower when people are asked to also participate as an active intermediary (N = 2 and up). In other words, if each person I let into my circle also raises amount of work I'm required to do in which I am not a direct beneficiary, I will probably opt for a lower limit. Succintly, I conjecture that L drops as N goes up.

[Patrick Barry]

Actually, I think 50 is far too low. There is an evolutionary argument in social psychology that relates brain mass to the number of social relationships that can be successfully maintained. After interpolating from various primates, the prediction for humans is about 150, which aligns pretty darn closely with some other experiments. I sometimes wonder if AOL knew what they were doing when the AOL IM client used to limit users to 160 buddies (now 200).