From Nature:
quote:
Friends are stranger than strangers
If your friends were normal people they would not know you.
20 November 2001
PHILIP BALL
Friends weave a tangled web.
© A. S. Klovdahl/Australian National University
"Your friends are unusual people", says physicist Mark Newman: simply because they are someone's friend.
This is not some homespun philosophy to make us all feel better. Newman, of the Santa Fe Institute in New Mexico, USA, has proved that our friends are not a random selection of the population1. If they were, the chance that you and I share a friend of a friend would be much smaller than it is.
Newman is exploring social networks. More specifically, he wants to know what the chances are that we have a friend of a friend who supports Real Madrid or the New York Giants. Or who went to Florence last summer. Or who likes water polo.
If we asked these questions about our immediate friends, the answer is simple enough. The average probability of a US citizen having a friend who supports the Giants is equal to the number of Giants supporters in the US divided by the country's population. Of course, the probability is higher if you live in New York, but the number still applies on average.
But estimating how many friends of friends fall into a particular group is harder, because the structure of the social network is complex. For example, each of our friends doesn't just have a circle of other friends unknown to us, plus us. Rather, we share mutual friends. And two of our friends who share a mutual friend not known to us probably know each other too. It is a tangled web.
These complications become important in various areas of social science, such as the technique of 'snowball sampling'. This is a method of deducing how many social contacts people have by asking a person to identify his or her friends, and then asking the friends to do the same, and so on. The deductions made this way can be highly biased, Newman shows, unless a large number of 'generations' of friends is sampled - which rarely happens.
The problem, says Newman, arises from the assumption that we are average members of the population who know other average people. "The people we know are anything but average", he says.
"Friends are by definition friendly people, and your circle of friends will be a biased sample of the population because of it", Newman points out. We are, in other words, far more likely to know 'friendly' people than 'average' people. Newman finds that a small number of people with a large number of friends skews the network relative to one made up of uniformly 'average' people.
He has devised a mathematical approximation for coping with these biases. It makes a more accurate estimate of the number of 'friends of friends' that fall into a particular subset of the population.
Newman shows that his approach gives better estimates than conventional network-tracking methods by looking scientific collaborations. Here two scientists who write a paper together are considered 'friends'. Because scientific publication records are scrupulously documented, this is an unusually well defined network.
"The most important moral to this story", says Newman, "is that your friends just aren't normal. No one's friends are."
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