From butterfly wings to single e-mail, if one action can cause a torrent

“Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” Zoologist Konrad Lorenz once asked in postulating the “butterfly effect,” the idea that the flapping of fragile wings could start a chain reaction in the atmosphere. In today’s world of the Internet the question might be rephrased: Can a single e-mail from Brazil set off a torrent of action in Texas?

Sociologists postulate that what a few influential leaders think and say can spread and grow and bring about big changes in the thinking of large numbers of people. The Internet offers a compelling new place to look for this phenomenon by studying very large groups and especially, seeing how groups change over time.

But how do you find those influential people? Computer scientists at Cornell University, Ithaca, N.Y., have some suggestions. Their ideas could be applied to such diverse goals as selling a new product, promoting new agricultural techniques in developing countries, predicting the spread of a disease or identifying leaders of terrorist organizations.

Jon Kleinberg, Cornell professor of computer science, discussed the problem, and some computer algorithms to solve it, in a talk on Feb. 15 at the annual meeting of the American Association for the Advancement of Science (AAAS) in Seattle. His talk was part of a symposium on “Community Structure of the Internet and World Wide Web: Mathematical Analyses.” His research collaborators were Eva Tardos, Cornell professor of computer science, and former post-doctoral research associate David Kempe, now at the University of Washington.

A common approach used by sociologists is to interview every member of a group and find out who associates with whom — essentially a snapshot of one moment. Collaboration with computer scientists now makes it possible to send out Web crawlers to map the communications links in a group, something that can be done repeatedly over time, and with much larger groups.

Groups on the Internet can take many forms, including Usenet and chatroom discussion groups, e-mail mailing lists and links between Web sites on related topics. Most recently, the writers of personal online journals known as Web logs, or “blogs,” have begun to link to one another and comment on each other’s work.One way to find the influential people would be to identify those who have the most links to others, or the ones who can reach the largest number of others with the fewest “hops” through other people. That, Kleinberg says, introduces redundancy: the two or three top candidates could all link to the same subset of the network. So, Kleinberg suggests, “After targeting the first few people you discount others, then you look for people who are still influential but in diverse parts of the network.”

The researchers tested their algorithm on another kind of network, the pattern of co-authorship in scientific papers. Their data pool was the online E-print Archive of physics and mathematics publications, commonly known as the arXiv, maintained by Cornell University Library. People were considered to be linked when they co-authored papers. The studies ignored any real-world information, such as whether two people might be at the same institution. In simulations Kleinberg and colleagues found that their method significantly outperformed methods that rely solely on counting links or measuring the distance between candidates and the rest of the network.

Kleinberg also has been studying the way networks grow over time, working with David Liben-Nowell, a Ph.D. student at the Massachusetts Institute of Technology. One goal is to try to predict where new links will form in a network. In the arXiv network, the researchers hypothesized that two people who haven’t been linked would be likely to form a link if they are near one another in linkage terms. What they found, however, was that the number of hops was not the best measure of nearness. The reason, Kleinberg says, is the “small world phenomenon” — the fact that everyone is on average “six degrees of separation” from everyone else — so counting the number of hops between people doesn’t help. “It’s better to look for people who have many different short paths connecting them, ” he says. “This is an interesting open question with a lot of room for further research.”