Using Facebook to assess the size of social networks

There are some people who argue that the Internet increases the size of people's social networks by lowering the transaction costs of interacting with people.

Facebook -- as a dataset -- is handy for determining whether this is true. Everyone on Facebook has friends with whom you communicate on a regular or irregular basis. Therefore, it could allow you to quantify the size of social networks on the Internet.

This is precisely what Cameron Marlow, a sociologist at Facebook, did at the prompting of the Economist.

Marlow looks at the size of social networks on Facebook in terms of friend list size and the rate of communication between those friends. The Economist relates those findings to the Dunbar number -- a number posited by anthropologist Robin Dunbar to represent the upper limit in the size of a primate's social group due cognitive costs.

From the Economist article:

Several years ago, therefore, Robin Dunbar, an anthropologist who now works at Oxford University, concluded that the cognitive power of the brain limits the size of the social network that an individual of any given species can develop. Extrapolating from the brain sizes and social networks of apes, Dr Dunbar suggested that the size of the human brain allows stable networks of about 148. Rounded to 150, this has become famous as "the Dunbar number".

Many institutions, from neolithic villages to the maniples of the Roman army, seem to be organised around the Dunbar number. Because everybody knows everybody else, such groups can run with a minimum of bureaucracy. But that does not prove Dr Dunbar's hypothesis is correct, and other anthropologists, such as Russell Bernard and Peter Killworth, have come up with estimates of almost double the Dunbar number for the upper limit of human groups. Moreover, sociologists also distinguish between a person's wider network, as described by the Dunbar number or something similar, and his social "core". Peter Marsden, of Harvard University, found that Americans, even if they socialise a lot, tend to have only a handful of individuals with whom they "can discuss important matters". A subsequent study found, to widespread concern, that this number is on a downward trend.

The rise of online social networks, with their troves of data, might shed some light on these matters. So The Economist asked Cameron Marlow, the "in-house sociologist" at Facebook, to crunch some numbers. Dr Marlow found that the average number of "friends" in a Facebook network is 120, consistent with Dr Dunbar's hypothesis, and that women tend to have somewhat more than men. But the range is large, and some people have networks numbering more than 500, so the hypothesis cannot yet be regarded as proven.

What also struck Dr Marlow, however, was that the number of people on an individual's friend list with whom he (or she) frequently interacts is remarkably small and stable. The more "active" or intimate the interaction, the smaller and more stable the group.

Thus an average man -- one with 120 friends -- generally responds to the postings of only seven of those friends by leaving comments on the posting individual's photos, status messages or "wall". An average woman is slightly more sociable, responding to ten. When it comes to two-way communication such as e-mails or chats, the average man interacts with only four people and the average woman with six. Among those Facebook users with 500 friends, these numbers are somewhat higher, but not hugely so. Men leave comments for 17 friends, women for 26. Men communicate with ten, women with 16.

The debate over the actual value of the Dunbar number is, I think, beside the point. This data is interesting to me because it seems to show that a) there is an upper limit to the number of people in a social network and b) that most people's core network is much smaller than that limit.

Anyone who has spent much time on Facebook probably understands this experience: you have a lot of "friends" on Facebook that are not really friends in the strictest sense. Setting aside your boss -- who you are obligated to friend but who you don't allow to see anything other than your name -- there are a lot of passing acquaintances on your friend list. Maybe you met them at a party once two years ago and don't feel comfortable doing wholesale purges of your online retinue.

The Internet has brought me in contact with all manner of interesting people. With some of them I have struck up more lasting friendships. But at some point you begin to realize that you only have so many hours in the day, and you have to decide whom in your life you want to keep track of. The Internet -- while wonderful in many ways -- is unlikely to change that.

But this realization is revealing. The core issue is: what are the specific transaction costs of keeping a relationship? What is all that effort going towards?

I would argue that the cost the transaction costs of keeping track of someone is not primarily the effort of actually speaking with them. Rather, it is the cost of remembering their name, what they do, what they think, and how they have related to you in the past. Just because the Internet has lowered the cost of talking with someone doesn't make it easier to remember all this information. (I guess you could make a system that does, but if it exists I don't know about it.)

Anyway, I think this study is particularly compelling because it illustrates that cognitive costs of social interactions are probably more about memory than about the actual effort of meeting.