Ivars Peterson's MathTrek
In the Jan. 6 Science, Gueorgi Kossinets and sociologist Duncan Watts of Columbia University describe a study in which the researchers analyzed 14,584,423 messages exchanged by 43,553 students, faculty, and staff at a large university over the course of a year. What they discovered was a turbulent sea of constantly changing relationships among individuals yet remarkable stability in the properties of the network as a whole.
It's almost as if people were behaving randomly, with individual changes more or less canceling each other out. "In the absence of global perturbations," Kossinets and Watts concluded, "average network properties appear to approach an equilibrium state, whereas individual properties are unstable."
In their massive study, Kossinets and Watts recorded the time that each e-mail message was sent, who sent it, and to whom it went, but they collected no message content information. The researchers cross-referenced these data with such information as the gender, age, and status of the individuals, along with who attended and taught each class at the university. For privacy protection, all individual and group identifiers were encrypted.
Earlier studies had confirmed that e-mail communication is closely correlated with face-to-face and telephone interactions. So, e-mail exchanges appear to be a reasonable proxy for the underlying social ties.
It was no surprise that the researchers found that shared activities, such as taking courses together, or shared friends greatly increased the probability that two individuals would interact. Their massive database, however, allowed them to quantify the importance of such factors.
For example, sharing a single class had roughly the same effect on developing a new relationship as sharing a single mutual friend. Curiously, additional mutual friends counted for more than additional shared classes. And shared activities and friends counted for more than such attributes as age or gender.
The most striking result was the observation the network's stability in the face of rapidly shifting relationships among individuals. So, in network terms, the typical "distance" between pairs of people remained relatively constant over the course of a semester but the identities of the most highly connected individuals varied with time.
This suggests that, in studying such social networks, researchers can readily determine the network's average properties by taking a snapshot at any time. But individual characteristics, positions, and rankings will vary greatly from one snapshot to the next.
Of course, the study concerned people in a particular environment, and conclusions drawn from it may not necessarily apply in other social situations.
"Comparative studies of corporate or military networks could help illuminate which features of network evolution are generic and which are specific to the cultural, organizational, and institutional context in question," Kossinets and Watts noted.
Copyright © 2006 by Ivars Peterson
2006. Analysis of network of 14.5 million e-mail messages. Institute for Social and Economic Research and Policy, Columbia University press release. Jan. 5.
Kossinets, G., and D.J. Watts. 2006. Empirical analysis of an evolving social network. Science 311(Jan. 6):88-90. Abstract available at http://www.sciencemag.org/cgi/content/abstract/311/5757/88.
Peterson, I. 2005. Ask-a-friend marketplaces. MAA Online (Oct. 31).